PhD; Maria-Carmen Medrano

Florence Darlot

PhD Martine Cador

PhD Stephanie Caille
email: stephanie.caille-garnier@u-bordeaux.fr

Poor inhibitory control predicts sex-specific vulnerability to nicotine rewarding properties in mice

Keywords: nicotine, conditioned place preference, fixed consecutive number task, inhibitory control, sex, mice

Rationale. The risk of becoming tobacco addict is not equal from individual to individual, raising the hypothesis of potential behavioural biomarkers for predicting vulnerability to nicotine reward, an important step to transition to nicotine addiction. Among all nicotine pharmacological properties, one is to increase cognitive performances, which depend on the balance between attentional processes and inhibitory control. However, whether the effect of nicotine as a cognitive enhancer is predictive of the reward properties of nicotine is still unknown.

Objective. We investigated in mice whether the effects of nicotine on their cognitive performances are predictive of their sensitivity to nicotine reward and, if so, whether it is sex dependent.

Methods. Naïve male and female mice were first assessed for their performances in baseline conditions and after nicotine injections (0.15 and 0.30 mg/kg) in a cued-Fixed-Consecutive-Number task (FCNcue) measuring both optimal (attention) and premature (inhibitory control) responding. Next, all mice underwent nicotine-induced conditioned place preference in order to evaluate inter-individual differences in response to nicotine reward (0.30 mg/kg).

Results. Results showed that males and females benefited from the effect of nicotine as a cognitive enhancer in the FCNcue task. However, only those males showing poor inhibitory control, namely high-impulsive, were subsequently responsive to nicotine reward. In females, sensitivity to nicotine reward was independent of FCNcue performances whether basal or after nicotine.

Conclusion. Thus, our study suggests that poor inhibitory control and its modulation by nicotine may be a behavioural index of the development of nicotine reward in males but not females.

INTRODUCTION

Tobacco addiction is one of the most widespread addictions in the world and continues to be one of the leading risk factors for premature deaths globally. Every year, 8 million people die because of tobacco use (World Health Organization 2022). Despite the dangers of smoking being highly publicized, every day tens of thousands of people smoke a first cigarette, opening themselves to the risk of becoming addicted to nicotine, the major psychoactive component in tobacco. That risk is not equal from individual to individual (Office on Smoking and Health (US) 2010); however, we lack a complete understanding of what makes one person more likely to become addicted than another.

The multifactorial aetiology of smoking behaviour largely contributes to the lack of successful understanding of tobacco use disorder as well as treatment outcomes (Garcia-Rivas and Deroche-Gamonet 2019). Indeed, there are important inter-individual differences in response to the effects of nicotine. In some humans, nicotine has a central role by activating the reward system and triggering the dependence processes. However, in others, nicotine has weak primary reinforcing properties, which are not sufficient to explain its highly addictive potential. Therefore, in these individuals, vulnerability is more likely to depend on the key role of nicotine-associated cues in the maintenance and persistence of the addictive behaviour [START_REF] Chiamulera | Cue Reactivity in Nicotine and Tobacco Dependence: A "Multiple-Action" Model of Nicotine as a Primary Reinforcement and as an Enhancer of the Effects of Smoking-Associated Stimuli[END_REF]. We and others have suggested that the inter-individual variability in the maintenance of nicotine taking and seeking behaviours is associated with several cognitive dysfunctions in flexibility, behavioural inhibition, planning or working memory in humans and in rodents [START_REF] Besson | Cognitive Dysfunction, Affective States, and Vulnerability to Nicotine Addiction: A Multifactorial Perspective[END_REF][START_REF] Diergaarde | Impulsive Choice and Impulsive Action Predict Vulnerability to Distinct Stages of Nicotine Seeking in Rats[END_REF][START_REF] Vandaele | Attentional Capacities Prior to Drug Exposure Predict Motivation to Self-Administer Nicotine[END_REF]).

Importantly, most of studies have been conducted exclusively in males, leaving open the question of vulnerability to nicotine in females as well. The study of sex differences in the vulnerability to addiction has been often overlooked whereas a large body of evidence support sexual dimorphism in the epidemiology, social considerations, psychiatric comorbidity and neurobiology of drug effects, including nicotine (10.1016/S0193-953X(05)70074-5). For instance, it has been shown that initial sensitivity to nicotine is lower in women than in men (Perkins et al. 2009), that women are less sensitive to the interoceptive stimuli of nicotine [START_REF] Perkins | Sex Differences in Nicotine versus Nonnicotine Reinforcement as Determinants of Tobacco Smoking[END_REF] and that women smoking habits depend more on visual and olfactory/taste from cigarette smoke than men [START_REF] Perkins | Sex Differences in the Subjective and Reinforcing Effects of Visual and Olfactory Cigarette Smoke Stimuli[END_REF]. On the other hand, preclinical studies have indicated that the sexual dichotomy in nicotine addiction goes from differences in the mesolimbic dopamine system [START_REF] Lee | Sex Differences in the Ventral Tegmental Area and Nucleus Accumbens Proteome at Baseline and Following Nicotine Exposure[END_REF] to differences related to the amount of self-administered nicotine [START_REF] Donny | Nicotine Self-Administration in Rats: Estrous Cycle Effects, Sex Differences and Nicotinic Receptor Binding[END_REF][START_REF] Flores | Sex Differences in Nicotine Intravenous Self-Administration: A Meta-Analytic Review[END_REF]) and to the reward deficit and somatic signs associated with precipitated nicotine withdrawal [START_REF] Tan | Sex Differences in the Reward Deficit and Somatic Signs Associated with Precipitated Nicotine Withdrawal in Rats[END_REF].

Thus, we aim to fill the gap of knowledge concerning the relationship between cognitive deficits and vulnerability to nicotine reward-related behaviours in females.

In the present study, we want to study the attentional performances in order to stablish attention and inhibitory control parameters in a naïve population of male and female mice before testing their response to nicotine reward. We have previously investigated the attentional performances in rats using our established cued-Fixed Consecutive Number task (FCNcue, [START_REF] Rivalan | Reduction of Impulsivity with Amphetamine in an Appetitive Fixed Consecutive Number Schedule with Cue for Optimal Performance in Rats[END_REF].

Interestingly, we had demonstrated that male rats who paid more attention to the food rewardpredictive cue light showed also higher sensitivity to both reinforcing and incentive properties of nicotine during intravenous self-administration sessions [START_REF] Vandaele | Attentional Capacities Prior to Drug Exposure Predict Motivation to Self-Administer Nicotine[END_REF]). However, whether the impact of nicotine as a cognitive enhancer was predictive of higher sensitivity to the drug reinforcing effects and motivation to self-administration remained unknown. Thus, the objective of the study was twofold: 1) to adapt the FCNcue complex task to mice and 2) to examine a potential sexual dimorphism in the relationship between cognition, the effects of nicotine on attention and inhibitory control and nicotine rewarding properties in both sexes. To do so, cohorts of naïve male and female mice were first assessed for attention performances and inhibitory control in the FCNcue in basal as well as in response to acute amphetamine or nicotine. Next, all mice underwent nicotine-induced conditioned place preference (CPP) to evaluate differences to the nicotine rewarding effects.

MATERIALS AND METHODS

Animals

A total of 48 C57BL/6 mice, 21 males and 27 females, all 7-8 weeks old at the beginning of the study, were used in this work. Mice were housed in collective cages of 6-9 animals each, on an inversed 12/12 light/dark cycle. Behavioural experiments were performed during the dark phase. All mice were maintained in a controlled-temperature room (22 ± 1 °C). Oestrous cycle phase was systematically checked in all females on FCNcue drug-test days following the protocol described by Byers and colleagues [START_REF] Byers | Mouse Estrous Cycle Identification Tool and Images[END_REF]. Females were tested across the different stages of the cycle.

All procedures were conducted in accordance with the local ethics committee of the University of Bordeaux and the European Committee Council Directive (approval number 2016012716035720). All efforts were made to minimize animal suffering and reduce the number of animals used.

Cued Fixed Consecutive Number task

Apparatus

The Cued-Fixed Consecutive Number (FCNcue) procedure was conducted in 12 identical sound-attenuated and ventilated operant chambers (24 x 16 x 21 cm; Imetronic, France) located in a dimly lit room with a background white noise. Each operant chamber was equipped with two nosepoke holes (NP), one on the right wall called "fixed consecutive number-NP" or "FCN-NP" and one on the left wall called "reward-NP" or "RWD-NP". A cue light was situated above each NP. The floor consisted of stainless-steel bars separated by 0.4 cm. A liquid dipper (licker) was situated on the left wall, next to the RWD-NP. 75µl of diluted condensed milk solution was delivered in the licker as a reward (See Fig 1 A). The operant chambers were interfaced with a PC computer for data acquisition and storage. The reward delivery, presentation of visual stimuli, and recording of behavioural data were controlled and recorded by POLY software (Imetronic, France).

Cued-Fixed Consecutive Number (FCNcue) procedure

The FCNcue had been previously used in our laboratory to measure attentional capacities in rats [START_REF] Rivalan | Reduction of Impulsivity with Amphetamine in an Appetitive Fixed Consecutive Number Schedule with Cue for Optimal Performance in Rats[END_REF][START_REF] Vandaele | Attentional Capacities Prior to Drug Exposure Predict Motivation to Self-Administer Nicotine[END_REF]). In the present study, we adapted the FCNcue in order to assess individual attentional and inhibitory control strategies in mice. The FCNcue measures the ability of mice to terminate a chain of actions to reach a goal (obtain a reward). The task required a fixed minimum number of responses on the FCN-NP (1 for FCN1, 2 for FCN2, and so on, to 6 for FCN6) followed by a response on the RWD-NP, resulting in one reward delivery. The completion of the required number of FCN-NP is signalled by the switching off of the cue light above the FCN-NP.

Then, the RWD-NP becomes active, which is indicated by the switching on of the cue light above it.

Once the reward is totally consumed, the cue light above FCN-NP is turned on indicating the beginning of a new chain. A successful sequence of actions is called an "optimal response" (or an "optimal chain", 1 optimal chain = 1 reward) (Fig 1 A). Responding on the RWD-NP prior to the completion of the chain of visits to the FCN-NP results in the absence of reward distribution and resets the chain counter to 0. We call "premature response" a visit in the RWD-NP right after the first visit in the FCN-NP (chain of 1).

FCNcue timeline

The full experimental timeline is shown in Figure 1 C. During the whole FCNcue procedure, mice performed the task once per day. The habituation consisted in three sessions across three consecutive days. The first day, mice were habituated to empty operant cages (no NP, cue lights or licker) for 30 minutes. The second and third day, mice were habituated to the FCN-NP, the cue light and the reward delivery. Each visit to the FCN-NP resulted in the delivery of a reward. Then, mice underwent FCNcue training during which both, FCN-NP and RWD-NP, were continuously available throughout 1-hour sessions. First, mice had to nose-poke once in the FCN-NP and then once in the RWD-NP to obtain the reward (FCN1). After 3 sessions, mice were moved to the next level, FCN2 according to the same criterion. Then to FCN3. After three consecutive stable sessions in FCN3, they moved to FCN4 and then to FCN6. Once mice performances in FCN6 were stable, pharmacological tests started. For each condition, mice were first injected with vehicle for three consecutive sessions as a control. In the following sessions, mice were tested alternatively with vehicle or drug injection.

Studies from our laboratory and others have demonstrated that an acute injection of a low dose of amphetamine improves performance on attentional tasks in healthy humans and rodents [START_REF] Macqueen | Amphetamine Modestly Improves Conners' Continuous Performance Test Performance in Healthy Adults[END_REF][START_REF] Rivalan | Reduction of Impulsivity with Amphetamine in an Appetitive Fixed Consecutive Number Schedule with Cue for Optimal Performance in Rats[END_REF]. In total, N mice (n males n females) were trained in the FCNcue task.

Among these, we injected a subgroup with amphetamine 0.30 mg/kg, i.p (males, n = 9 and females, n = 10); and another subgroup (males, n = XX and females, n = XX) was injected with mecamylamine DOSES in order to test the involvement of the nicotinic receptor in nicotine-induced increase of attentional control in the FCNcue.

Behavioural measurements

All behavioural data showed in this study are calculated as follow. The mean percentage of optimal responses [(number of chains of 6 FCN-NP/ total number of chains) × 100] is an index of attention. Therefore, high percentages of optimal responses denoted good attention, whereas low percentage of optimal responses denoted poor attention. The mean percentage of premature responses [(number of chains of 1 FCN-NP / total number of chains) × 100] is an index of inhibitory control.

High percentage of premature responding denoted poor inhibitory control, i.e. impulsivity levels in the FCNcue task. Response efficiency is an index of success in the task [(total number of rewards/ total number of RWD-NP) x100]. High percentages of optimal responses and response efficiency both denote good attentional control since they directly depend on the capacity to perceive the cue light switch off as an indicator of the next action to execute, i.e., selective attention to the reward-predictive cue. Response rate, calculated as the total number of nose pokes per minute [(FCN-NP + RWD-NP) / 60] and the total number of chains were used as an index of motivation. The total number of photocell beam breaks was used to measure general locomotor activity. The mean latency (in milliseconds, ms) to collect the reward as soon as available reflects the sensitivity to the reward.

Conditioning Place Preference (CPP)

We used two chambered conditioning place preference (CPP) boxes (70 x 80 x 35 cm). The boxes consisted of two side chambers that featured different wall and flooring patterns to make them easily distinguishable (Fig 1B). A 10 x 15 cm door provided access between the boxes. First, mice were submitted to a 15-minute, drug-free, preconditioning test (pre-test) in which mice had free access to the two chambers. In a second phase (conditioning), the door between the two chambers was closed.

Mice received subcutaneous (s.c.) injection of saline (5 ml/kg) on days 1, 3, 5, and 7 prior to being confined to their vehicle-paired chamber for 30 min. On days 2, 4, 6, and 8, mice received nicotine solution (0.30 mg/kg/5ml) immediately prior to confinement in the nicotine-paired chamber for 30 min. Lastly, on day 9, the test session was conducted exactly as in the pre-test condition, with mice having free access to the two chambers for 15 min. Animals were tested drug-free (Fig 1 C).

The time spent in each chamber during the pre-test and test sessions was counted. A preference score was calculated as the difference between the time spent in the nicotine-associated chamber during the test and the time spent in the same chamber during the pre-test. A positive preference score was considered as a preference for nicotine-paired compartment (i.e. sensitive to nicotine rewarding effects) and a negative score, as an aversion for nicotine-paired compartment. In addition, we quantified for each sex the proportion of the total population which showed CPP.

Drugs

Nicotine hydrogen tartrate (Sigma-Aldrich®, France) was dissolved in saline and pH adjusted at 7.4. NaOH (Sigma-Aldrich®, France) was used to adjust the pH. Nicotine was injected at doses of 0.15 and 0.30 mg/kg, expressed as nicotine base. Nicotine or its vehicle, saline, were injected subcutaneously (s.c.) 5 min before the behavioural task. In order to test if the effect of nicotine was due o its interaction with nicotinic receptors, we used mecamylamine (a nicotinic receptor antagonist).

Mecamylamine 1.5 mg/kg (Sigma-Aldrich®, France) was dissolved in saline and injected s.c. 15 min before nicotine in the FCNcue task. Amphetamine 0.30 mg/kg (d-amphetamine sulfate, Cooperative Pharmaceutique Française, France) was dissolved in saline and injected i.p. All solutions were injected at a volume of 5 ml/kg.

Statistics

The statistical analyses were performed using GraphPad software (Prism 9 for Windows, GraphPad Software, Inc., San Diego, CA, USA). For the analysis of data from FCNcue, Unpaired t test was used to compare males and females for each parameter. The effects of different doses of the tested drugs on attentional performances in male and female mice were compared with a two-way analysis of variance (ANOVA) with sex as between-subject factor and treatment (drug dose) as within-subject factor. When the two-way ANOVA revealed that there was a statistically significant main effect or sex x treatment interaction, post hoc comparisons in pairs with the Bonferroni's multiple comparison test were used. CPP data did not show a normal distribution (Pearson test), thus we used non-parametric statistical analyses. Male and female mice preference to nicotine-paired compartment was analysed by the Wilcoxon test. Fisher's exact test was used to compare the proportion of individuals that showed preference for nicotine-paired compartment in the groups of males vs. females. We used the principal component analysis (PCA) to distinguish variables from the FCNcue that cluster with the CPP score from orthogonal variables, in order to make this hypothesis to be further tested. Then, to explore the putative direct relationship between impulse control and sensitivity to nicotine reward, mice were screened based on their level of premature responses during the control FCNcue sessions. Mice were ranked and we extracted the lower tercile, classified as low-impulsive (n = 7 for males and n = 8 for females); and the upper tercile classified as high-impulsive (n = 7 for males and n = 9 for females).

Tercile analyses could be used because the basal percentage of premature responses followed a continuum. It allowed constituting cohorts to assess inter-individual differences. The interest of this approach is to identify and describe in detail the extreme behaviours of individuals, within a normal population. Intermediate mice were not considered in this analysis [START_REF] Vandaele | Attentional Capacities Prior to Drug Exposure Predict Motivation to Self-Administer Nicotine[END_REF].

Data are given as mean ± standard error of the mean (s.e.m.). A significance level of p < 0.05 was used for all statistical analyses.

RESULTS

Validation of the FCNcue task in mice reveals differences in attention and inhibitory control between males and females.

First, we addressed the inter-individual variability among males and females regarding their performance in the FCNcue task. Performance among individuals, males and females, was heterogeneous as illustrated by an example of all individual responses during an FCNcue session (Fig 2 A-B). Indeed, in control conditions (no injection) optimal responses ranged from 13% to 64% in males and 10% to 53% in females responses (Fig 2 A-B). When we compared the performances of females and males (Fig 2C), males showed a significantly higher percentage of optimal responses than females with 37.7 ± 3.7 % vs. 27.4 ± 2.4 %, respectively (t (46) = 2.415, p = 0.0198, Unpaired t test), suggesting that males show better attention than females in the FCNcue task. Moreover, we found that females showed a significantly higher percentage of premature responses than males with 30.7 ± 2.7 vs. 20.8 ± 2.4 %, respectively (t (46) = 2.613, p= 0.0121, Unpaired t test, Fig 2 D). These differences in attention and inhibitory control between sexes appear to be specific to FCN6 because there are no significant sex differences when comparing responses during the training phase FCN3. The percentage of optimal responses for males in FCN3 was 41.10 ± 4.39 % and for females, 40.14 ± 2.81 % (t (46) = 0.1911, p = 0.8493) and the percentage of premature responses during FCN3 for males was 35.74 ± 3.37 % and for females, 36.60 ± 2.40 % (t (46) = 0.2128, p = 0.8325; Unpaired t test; data not shown).

This indicates that the females' poor attention and inhibitory control in the FCNcue task is not related to a learning issue since at intermediate stage of acquiring the task there is no difference.

In addition, we calculated other parameters that may account for the inter-individual differences in the FCNcue task performances (Table 1). We did not find any significant difference in the response rate (t (46) = 0,5974, p = 0,5531), the total number of chains (t (46) = 1,578, p = 0,12449) and the latency to retrieve the reward (t (46) = 2,642, p = 0,1273). However, males and females showed significant differences in the response efficiency (t (46) = 2,611, p = 0,0117), males were more efficient, and females showed higher locomotor activity than males (t (46) = 3,841, p = 0,0004).

When we tested the effect of amphetamine (0.30 mg/kg) on optimal responses we found no significant interaction between sex x treatment F (1, 17) = 2.395, p = 0.1402; however, there was a main effect of treatment (F (1, 17) = 26.55, p < 0.0001) indicating that amphetamine significantly increased the proportion of optimal responses (Fig 2E). Likewise, no interaction was found between sex and treatment for premature responses (F (1, 17) = 1.669, p= 21.37) but we also found a significant main effect of treatment (F (1, 17) = 8.25, p = 0.0106) amphetamine decreasing the n% of premature response (FIG 2F). These results validated pharmacologically the FCNcue as a task to measure attention and inhibitory control in mice.

Nicotine improves both attention and impulse control in males and females.

Next, we aimed to explore if nicotine improved attention and inhibitory control and if this effect was similar between males and females. For this, we compared mice FCNcue performances after saline (s.c.) and nicotine injections (0.15 and 0.30 mg/kg, s.c.). First, we analysed if an acute injection of nicotine had an effect on attention i.e. % optimal performances. A two-way ANOVA showed no interaction between sex and treatment (F (2, 92) = 1.862; p = 0.1612, Fig 3 A). However, we found a main effect of sex (F (1, 46) = 11.88, p = 0.0012, In order to corroborate that the effects of nicotine 0.15 mg/kg in attention and inhibitory control was due to the interaction of the drug with the nicotinic acetylcholine receptors (nAChRs), we injected a group of males and females with the nAChRs antagonist mecamylamine 1.5 mg/kg s.c. [START_REF] Stolerman | Discrimination and Self-Administration of Nicotine by Inbred Strains of Mice[END_REF]) 15 minutes before nicotine injection. A two-way ANOVA showed no interaction between sex and treatment (F (2, 28) = 2.043, p = 0.1485) and no main effect of sex (F (1, 14) = 1.619, p = 0.2240, Fig 3 C). However, we found a main effect of treatment F (2, 28) = 22.46, p < 0.0001, Fig 3C). Bonferroni's post hoc test showed that nicotine significantly increased the percentage of optimal responses (saline vs nicotine, p = 0.0001) but not in the presence of mecamylamine (p = 0.4637 saline vs Nic 0.15+Meca; p<0.005 Nic 0.15 vs Nic 0.15 + Meca 1.5Fig 3C). Likewise, when we analysed the effect of mecamylamine on the percentage of premature responses, a two-way ANOVA showed no interaction between sex and treatment (F (2, 28) = 0.1214, p = 0.8861) and no main effect of sex (F (1, 14) = 0.3636, p = 0.5561, Fig 3 D). However, we found a main effect of treatment (F (2, 28) = 13.13, p < 0.0001, Fig 3 D). Bonferroni's post hoc test showed that nicotine significantly reduced the percentage of premature responses (saline vs nicotine, p = 0.0024) but not in the presence of mecamylamine (p = 0.7988, saline vs nicotine + mecamylamine, Fig 3D). These results show that nicotine improves attention and inhibitory control in mice by activating nAChR.

Next, we explored the effect of nicotine on other parameters obtained with the FCNcue (see table 2).

Overall, these results suggest that the drug did not change the motivation for the food reward. Nicotine had no effect on the response rate (sex x treatment interaction (F (2, 92) = 0.1044, p = 0.9010), main effect of sex (F = (1, 46) = 1.324, p = 0.2559) and main effect of treatment (F = (2, 92) = 1.852, p = 0.1627). On the total number of chains of actions (chains from 1 to 6 NP-FCN) there was no sex x treatment interaction (F (2, 92) = 0.0058, p = 0.9959), but there was a tendency for main effect of sex (F = (1, 46) = 3.935, p = 0.0541) with females doing more chains than males and a tendency for main effect of treatment (F = (2, 92) = 3.023, p = 0.0535; Table 2) with nicotine decreasing the total number of chains. Moreover, nicotine had no effect on latency to collect reward (sex and treatment interaction (F (2, 92) = 0.9430, p = 0.3933), sex main effect (F (1, 46) = 2.811, p = 0.1006) and treatment effect (F (2, 92) = 0.9895, p = 0.3758).

As we described previously, high response efficiency is also indicative of good performance in the task. A two-way ANOVA analysis showed no interaction between sex and treatment (F (2, 92) = 1.763, p = 0.1772), however, there were main effects of sex and treatment (Table 2). A Bonferroni's post-hoc test (Table 2) showed that nicotine enhanced dose-dependently the response efficacy in the FCNcue. Finally, nicotine reduced the general activity in males and females during the tests in a dosedependent manner (Table 2).

Attentional control profile and the effect of nicotine as a cognitive enhancer predict nicotine rewarding properties in males but not in females.

The conditioned place preference (CPP) procedure is commonly used to study drug reward in rodents, a key process in the initiation of drug addiction. All mice tested in the FCNcue behavioural task were then tested in the nicotine CPP paradigm. Mice were injected with nicotine 0.30 mg/kg since we had previously shown that this dose induces CPP in mice [START_REF] Allain | Impact of Acute and Chronic Nicotine Administration on Midbrain Dopaminergic Neuron Activity and Related Behaviours in TRPV1 Knock-out Juvenile Mice[END_REF]) whereas we (data not shown) and others (Kota et al, Jackson et al) found that lower doses such as 0.15 mg/kg did not induce CPP.

Conditioning with nicotine 0.30 mg/kg increased the time spent in the drug-paired compartment during the test in the group of males (Wilcoxon, pretest vs test, p=0.05, Fig 4 A1) but not in the group of females (Wilcoxon n.s., Fig 4 B1). Moreover, we found that the proportion of males that showed a preference for nicotine-associated compartment was significantly higher than that of females. 76% males showed preference for nicotine-paired compartment while only 41% of females did (p = 0.0199, Fisher's exact test, in figure 4 A1 and 4 B1). These results showed that male mice responded more to the rewarding effects of nicotine 0.30 mg/kg than female mice.

To relate the main cognitive features that defined attention and inhibitory control in the FCNcue test and the response to nicotine reward in the CPP paradigm, we performed a multidimensional analysis of all classical parameters sampled. To do this, we applied principal component analysis (PCA) based on a correlation matrix. Our PCA analysis was based on 3 FCN and 1 CPP behavioural parameters for the 21 males and 27 females included in the study. These parameters were the percentage of optimal (Opt) and premature (Prem) responses in saline (sal), nicotine 0.15 (Nic 0.15) and 0.30 (Nic 0.30) mg/kg, the latency to collect the reward (Lat rew), and the score of preference (CPP).

In males, the correlational analysis revealed two independent factors representing respectively 37.37 % (PC1) and 32.04 % (PC2) of the total variability. Premature responses for saline, nicotine 0.15 and 0.30 mg/kg (0.517, 0.688 and 0.538 respectively), latency to collect reward (r = 0.498) and CPP (0.741) clustered on component PC2, which seems to capture sensitivity to reward (Fig 4 A2).

Nicotine-induced conditioned place preference clustered to premature responding, i.e. chain of one correct action interrupted by reward-NP visits. Moreover, the PCA showed that premature and optimal responses were not likely to be linked.

In females, the correlational analysis revealed PC1 accounted for 40.27% of the overall variability of our observations as compared to 27.53 % in PC2 component. The multidimensional analysis showed that premature and optimal responding clustered on PC2, which seems to capture the FCN performances. In PCA analysis for female mice, nicotine-induced preference did not cluster neither to premature responses nor to any other parameter extracted from FCNcue (Fig 4 B2).

The main aim of this study was to identify potential behavioural biomarkers related to the attentional control that were linked to nicotine reward, as a signature to vulnerability to develop nicotine addiction. Therefore, our goal was to isolate individuals whom sensitivity to nicotine rewarding effects would be predicted by their performances in the FCNcue task. Selection was made by extracting subgroups of individuals with low or high scores according to the upper and the lower terciles in premature responses (Fig 5 A1 andB1). Noteworthy, high and low-impulsive male and female mice showed large differences in premature responses (p < 0.0001, Unpaired t test for both, males t (12) = 5.853 and females t (16) = 20.71; Fig 5 A2 andB2), corroborating that they are different populations Remarkably, high-impulsive males showed a significant increase in the time spent in the nicotinepaired compartment, indicative of a preference (Wilcoxon, pretest vs. test, p = 0.0078, Fig 5 A3) whereas the low-impulsive males did not show this preference (Wilcoxon, pretest vs. test, p = 0.22344, Fig 5 A3). In females, neither the high-impulsive nor the low-impulsive subgroups showed significant nicotine-induced conditioned place preference (Wilcoxon, pretest vs. test, p = 0.1484 and p = 0.1797, respectively, Fig 5 B3). These results suggest that in a population of male mice, those showing naturally poor inhibitory control, i.e. high-impulsive, are more susceptible to nicotine rewarding properties. Whereas in the case of females, it confirmed that there was no link between the poor inhibitory control and nicotine rewarding properties.

DISCUSSION

We sought to examine whether cognitive performances and the effects of nicotine as a cognitive enhancer in mice could be predictive of the vulnerability to nicotine reward and, if so, whether this characteristic was sex-dependent. To do this, first we adapted the FCNcue procedure to study attention and inhibitory control capacities in male and female mice. We validated the task by testing the effect of an acute injection of amphetamine, which enhanced performances in all mice as expected.

Moreover, we were able to observe sex differences in attentional processes in basal conditions, the male population showed better attention and inhibitory control than female mice. Then, a low dose of nicotine improved not only attention but also inhibitory control (reduced impulsivity) in all mice, corroborating its effects as a cognitive enhancer in the FCNcue task. Thereafter, a global population analysis failed to show that either males or females developed nicotine-induced CPP. However, when we performed a multidimensional analysis of different parameters obtained from the FCNcue and CPP tasks, we showed that naive males with poor inhibitory control (i.e. high impulsive individuals) were more responsive to the rewarding properties of nicotine than low impulsive individuals. On the opposite, females did not show correlation between FCNcue parameters and nicotine-induced CPP score, even when divided in sub-populations such as males. These results may open new avenues to study sex-specific physiological and neurobiological mechanisms of vulnerability to nicotine reward and addiction.

We have previously developed the "cued fixed consecutive number" task (FCNcue), which enabled the characterization of complex attentional processes in rats [START_REF] Rivalan | Reduction of Impulsivity with Amphetamine in an Appetitive Fixed Consecutive Number Schedule with Cue for Optimal Performance in Rats[END_REF][START_REF] Vandaele | Attentional Capacities Prior to Drug Exposure Predict Motivation to Self-Administer Nicotine[END_REF]. The principle of a fixed consecutive number task (FCN) is simple and efficient: it measures the ability of subjects to perform a chain of sequential actions directed to obtain a reward. The addition of a cue light (FCNcue) to the original FCN task [START_REF] Evenden | The Pharmacology of Impulsive Behaviour in Rats II: The Effects of Amphetamine, Haloperidol, Imipramine, Chlordiazepoxide and Other Drugs on Fixed Consecutive Number Schedules (FCN 8 and FCN 32)[END_REF]) is central to dissociate attention from the inhibitory control deficits that gives rise to impulsive responses [START_REF] Rivalan | Reduction of Impulsivity with Amphetamine in an Appetitive Fixed Consecutive Number Schedule with Cue for Optimal Performance in Rats[END_REF]. With this modification to the task, the animal does not rely on internal signals such as timing [START_REF] Evenden | The Pharmacology of Impulsive Behaviour in Rats II: The Effects of Amphetamine, Haloperidol, Imipramine, Chlordiazepoxide and Other Drugs on Fixed Consecutive Number Schedules (FCN 8 and FCN 32)[END_REF] for successful performance of the chain of actions, but rather on its attention to cue to start and to the switch off of this cue to go on to the next step. Here, we adapted the FCNcue test to mice and examined the effect of nicotine on male and female mice performances. The variability we observed in the parameters related to attention and inhibitory control of male and female mice in the FCNcue and the subsequent improvement following acute challenge with amphetamine are both consistent with previous studies performed with rats [START_REF] Evenden | The Pharmacology of Impulsive Behaviour in Rats II: The Effects of Amphetamine, Haloperidol, Imipramine, Chlordiazepoxide and Other Drugs on Fixed Consecutive Number Schedules (FCN 8 and FCN 32)[END_REF]McLaughlin et al. 2017, 1;[START_REF] Rivalan | Reduction of Impulsivity with Amphetamine in an Appetitive Fixed Consecutive Number Schedule with Cue for Optimal Performance in Rats[END_REF][START_REF] Haaren | Scopolamine and Methylscopolamine Differentially Affect Fixed-Consecutive-Number Performance of Male and Female Wistar Rats[END_REF]. In addition, it allowed us to test the response to nicotine on the execution of chains of actions without a possible confounding effect of its deleterious properties on timing performances [START_REF] Daniels | Revisiting the Effect of Nicotine on Interval Timing[END_REF][START_REF] Geller | Delayed Effects of Nicotine on Timing Behavior in the Rat[END_REF]. Our present results thus constitute a robust proof of concept for the adaptation of the FCNcue task to mice, which opens new possibilities to study specific neuronal circuits underlying attention and inhibitory control thanks to the wide range of transgenic mice lines available. Moreover, healthy population classification on the basis of attentional performances in the FCNcue task makes it ideal for broader application in the investigation of behavioural biomarkers for clinical conditions characterized by poor attentional control, such as ADHD, or schizophrenia [START_REF] Hayward | Low Attentive and High Impulsive Rats: A Translational Animal Model of ADHD and Disorders of Attention and Impulse Control[END_REF]. Thus, both the reliability showed in our studies of attentional performance sampling across littermates and sexes, and the effects of drugs that improve cognition support i) the utility of the FCNcue as a means by which to assess attention and inhibitory control in rodents in a comparable form to the Continuous Performance Test (CPT) used in humans [START_REF] Celeste | Continuous Performance Test in Children with Intellectual Disability and Attention Deficit Hyperactivity Disorder[END_REF][START_REF] Riccio | The Continuous Performance Test: A Window on the Neural Substrates for Attention?[END_REF] and ii) its translational validity for investigating attentional deficits in psychiatric disorders and new pharmacological therapies.

We aimed at showing that inter-individual variability in naïve animals in this task contributed to explain differential susceptibility to develop psychiatric conditions such as those involving attention and loss of impulse control, including substance use disorder [START_REF] Armario | Individual Differences and the Characterization of Animal Models of Psychopathology: A Strong Challenge and a Good Opportunity[END_REF][START_REF] Diergaarde | Impulsive Choice and Impulsive Action Predict Vulnerability to Distinct Stages of Nicotine Seeking in Rats[END_REF][START_REF] Molander | High Impulsivity Predicting Vulnerability to Cocaine Addiction in Rats: Some Relationship with Novelty Preference but Not Novelty Reactivity, Anxiety or Stress[END_REF]. Recently, we have demonstrated that rats with high attentional capacities were prone to show high motivation for nicotine intravenous self-administration [START_REF] Vandaele | Attentional Capacities Prior to Drug Exposure Predict Motivation to Self-Administer Nicotine[END_REF]. We have hypothesised that it might have been related to the "cue-magnifying" effect of nicotine on discrete cues associated with nicotine delivery [START_REF] Bueno-Junior | Repeated Nicotine Strengthens Gamma Oscillations in the Prefrontal Cortex and Improves Visual Attention[END_REF], thus making operant behaviour for nicotine taking and seeking more efficient in this sub-population of males. Here, we evaluated the predictive value of the individual variability in the FCNcue on appetitive conditioning to nicotine (i.e. the vulnerability to reward), which is crucial in the risk of developing nicotine addiction. All mice that had undergone the FCNcue task were submitted to a nicotine-induced conditioned place preference paradigm (CPP). CPP is a widely used protocol for measuring drug abuse liability in humans as well as in animals (McKendrick and Graziane 2020). Drug abusers report strong associations with environments in which they use drugs and the acquired incentive properties of drug-associated places can elicit craving and/or relapse in the abstinent addict [START_REF] Napier | Using Conditioned Place Preference to Identify Relapse Prevention Medications[END_REF]. Our results confirmed the existence of a sexual dimorphism in nicotine-induced conditioned place preference, the proportion of males showing preference for nicotine-paired compartment (i.e. nicotine reward) was almost two-fold the females one [START_REF] Lenoir | Sex Differences in Conditioned Nicotine Reward Are Age-Specific[END_REF]. It is consistent as well with clinical reports in which it has been suggested that the direct primary rewarding effects of nicotine may be more critical for the regulation of smoking behaviour in men, while for women non-pharmacological effects may be more important (K. A. [START_REF] Perkins | Sex Differences in Nicotine versus Nonnicotine Reinforcement as Determinants of Tobacco Smoking[END_REF].

In our research, we observed a discrepancy between the optimal nicotine dosage for enhancing attentional control in FCNcue and the conventional dose used to induce nicotine-induced CPP in mice, which has been previously documented [START_REF] Allain | Impact of Acute and Chronic Nicotine Administration on Midbrain Dopaminergic Neuron Activity and Related Behaviours in TRPV1 Knock-out Juvenile Mice[END_REF][START_REF] Jackson | Characterization of Pharmacological and Behavioral Differences to Nicotine in C57Bl/6 and DBA/2 Mice[END_REF][START_REF] Kota | Nicotine Dependence and Reward Differ between Adolescent and Adult Male Mice[END_REF]. Our results suggest that the effective dose of nicotine required to enhance overall attentional control is lower than the dose needed to induce rewarding effects. One plausible explanation is that nicotine 0.30 mg/kg caused a slight decrease in locomotor activity in the FCN task, as shown in Table 2, which may have hindered the enhancement of performances. This finding has been shown in earlier studies on other compounds, such as the psychostimulant amphetamine, which optimal pro-cognitive dose is 0.30 mg/kg, while the dose used to induce CPP is usually 2 mg/kg [START_REF] Macqueen | Amphetamine Modestly Improves Conners' Continuous Performance Test Performance in Healthy Adults[END_REF][START_REF] Wang | Parvalbumin Interneurons of the Mouse Nucleus Accumbens Are Required For Amphetamine-Induced Locomotor Sensitization and Conditioned Place Preference[END_REF]). Thus, our results suggest that the pro-cognitive effects of nicotine might predict the response to nicotine reward, but that there is a complex and non-linear dose-effect function of nicotine [START_REF] Picciotto | It Is Not "Either/or": Activation and Desensitization of Nicotinic Acetylcholine Receptors Both Contribute to Behaviors Related to Nicotine Addiction and Mood[END_REF].

Nicotine has been shown to improve general performances of smokers in attentional tasks and it has been suggested that the perceived benefits of the drug would have later implications both for the initiation of smoking behaviour and for maintenance of tobacco dependence (for review, see [START_REF] Heishman | Meta-Analysis of the Acute Effects of Nicotine and Smoking on Human Performance[END_REF]. Thus, the ultimate goal of this study was to investigate if behavioural parameters related to attention and/or inhibition control could be used as biomarkers to predict vulnerability to nicotine reward, the role of which is crucial in smoking onset. Moreover, we wanted to probe whether the effects of nicotine on attention and inhibitory control in the FCNcue could also be predictive of this vulnerability. A multidimensional correlation using a principal component analysis pointed out that in males, poor inhibitory control (i.e. high impulsivity), the effect of nicotine on impulsivity and sensitivity to the reward (latency to collect the reward) were positively linked to an increase in nicotine-induced preference score. Moreover, acute nicotine did not alter their motivation or sensitivity to natural reward [START_REF] Romero | Suppressive and Enhancing Effects of Nicotine on Food-Seeking Behavior[END_REF]. Importantly, the same principal component analysis of females' data reported different results. Indeed, none of the above-mentioned parameters were correlated to each other, thus none of the FCNcue parameters could be predictive of subsequent reward to nicotine in the CPP paradigm. Consistently, when we classified female mice such as male mice based on the premature responding we confirmed that there was no increase in the preference score for nicotine-paired compartment. Thus, our findings further support the importance of studying sex as a biological variable in biomedical research for a better understanding of specific risk factors in the development of addiction and effective treatments for males and females [START_REF] Carroll | How to Study Sex Differences in Addiction Using Animal Models: Sex Differences in Addiction[END_REF].

It has been previously suggested that the effect of nicotine on cognition may be linked to tobacco abuse in psychiatric disorder related to an impairment of inhibitory control such as schizophrenia and ADHD [START_REF] Freedman | Α7-Nicotinic Acetylcholine Receptor Agonists for Cognitive Enhancement in Schizophrenia[END_REF][START_REF] Nees | The Nicotinic Cholinergic System Function in the Human Brain[END_REF]. However, there is still no consensus about the origin of nicotine abuse in these patients: if they use it as a self-medication due to its properties as cognitive enhancer or if they are more sensitive to the rewarding effect of the drug, or both. To our knowledge, this is the first time that effects of nicotine on cognition are linked to nicotine rewarding properties in subjects who naturally show impulsive behaviours. This opens the possibility to use the FCNcue test as a behavioural task to measure impulsivity as a biomarker to develop other psychiatric syndromes such as ADHD or schizophrenia. Our data also show that the positive effect of nicotine on attention and inhibitory control does not seem to have any impact on the vulnerability to develop nicotine addiction in impulsive females. These results would be in the same line as others suggesting that women have a higher sensitivity to the non-pharmacologic effects of nicotine (visual, olfactory and taste cues) than males [START_REF] Perkins | Sex Differences in the Subjective and Reinforcing Effects of Visual and Olfactory Cigarette Smoke Stimuli[END_REF].

To conclude, this study highlights the importance to develop preclinical models that consider the inter-individual variability of behavioural responses and to assess both sexes. Here, we propose that in males showing poor inhibitory control the beneficial effect of nicotine on attentional performances makes them more susceptible to the rewarding effects of the drug and therefore to seek for it and develop addiction. Moreover, this suggests that the cognitive strategies involved in impulsivity may not be the same in males and females, and the neuronal bases are likely to differ. (green box, optimal responses). C-D) The whole population of males showed higher optimal performances while the population of females showed more premature ones. E-F) Acute injection of amphetamine 0.30 mg/kg s.c. (Amph 0.30) enhanced optimal and reduced premature responses in both males and females compared to saline condition (Sal). Bars and errors represent mean ± s.e.m. *p<0.05, Unpaired t test; # p < 0.05, ### p < 0.001, main effect of amphetamine, Paired t-test. showed that there was an increase of the time spent in the drug-paired compartment during the test in males but not in females. Moreover, a significantly larger percentage of males showed nicotine-induced conditioned place preference in comparison with the percentage of females that showed preference for the drug-compartment. A2 -B2) Principal Component Analysis (PCA) taking into account behavioural parameters of FCNcue and CPP performances were performed to define behavioural biomarkers that may predict vulnerability to nicotine addiction. Opt sal = % optimal responses in control conditions, Opt Nic 0.15 = % optimal responses after nicotine 0.15 mg/kg injection, Opt Nic 0.30 = % optimal responses after nicotine 0.30 mg/kg injection; Prem sal, Imp Nic 0.15 and Prem Nic 0.30 = % premature responses in control, after nicotine 0.15 and 0.30 mg/kg injection, respectively; Lat rew = latency to the reward in control conditions) and the CPP (CPP = score of preference in seconds for the nicotine-associated compartment in the CPP test). A2) In males, the PCA showed segregation of CPP, premature responses under control and nicotine conditions (red area) and latency to collect the reward, suggesting that in males, nicotine-induced CPP is associated with premature behaviour in the FCNcue test and to a larger sensitivity to the reward. B2) PCA showed no segregation of CPP and FCNcue test results, suggesting that in females, attentional performances are not related to nicotine rewarding properties. ns = no significant, * p = 0.05, Wilcoxon test; # p < 0.05, Fisher test.

FIGURES & LEGENDS

TABLES & LEGENDS

Fig 3 A

 3 Fig 3 A), males showing better performances than females. We also found a main effect of treatment

Figure 1 .

 1 Figure 1. Schematic representation of the behavioural paradigms and experimental timeline. A)

Figure 2 .

 2 Figure 2. FCNcue reveals differences in attention and inhibitory control between male and

Figure 3 .

 3 Figure 3. Nicotine improves attention and reduces impulsivity in male and female mice. A)

Figure 4 .

 4 Figure 4. Attentional control profile and effect of nicotine as a cognitive enhancer are linked to

Figure 5 .

 5 Figure 5. High impulsivity as a biomarker to predict higher sensitivity to the rewarding

Table 1 shows FCNcue variables indicative of global motivation (response rate, total number of chains), sensitivity to food reward (latency), response efficiency and total activity during the task in control conditions.

 1 For details, see section 2.3.2. Data are represented as mean ± s.e.m; Unpaired t test, * p < 0.05, *** p < 0.001.

		Males ( n = 21) Females ( n= 27)
	Response rate (NP/min)	3,12 ± 0,37	3,86 ± 0,31
	Total number of chains	26,49 ± 3,58	31,76 ± 14,77

Table 2 shows that the effect of nicotine in the FCNcue test is independent of altered motivation or sensitivity to food reward.

 2 There are significant differences in response efficiency between males and females (two-way ANOVA, main effect of sex F (1, 46) = 12.58, p = 0.0009, bold) as well as between nicotine doses (main effect of treatment, F (2, 92) = 10.35, p < 0.0001). Lastly, nicotine decreases dose-dependently global activity (two-way ANOVA, interaction F (2, 92) = 3.179, p = 0.0463, followed by Bonferroni's post hoc test saline vs nicotine, && p < 0.01, &&&& p < 0.0001).

			Males ( n = 21)			Females ( n= 27)
		Saline	Nic 0.15	Nic 0.30	Saline	Nic 0.15	Nic 0.30
	Response rate (NP/min) 2,98 ± 0,36 2,67 ± 0,30	2,67 ± 0,34	3,40 ± 0,30	3,23 ± 0,29	3,10 ± 0,30
	Total number of chains 22,81 ± 2,35 19,10 ± 2,07 21,05 ± 2,95 29,06 ±2,51 25,30 ± 2,37	27,56 ± 2,81
	Latency (ms)	2693 ± 561 3045 ± 596	2506 ± 426	2137 ± 426	1727 ± 374	1542 ± 373
	Response efficiency (%) 16,24 ± 2,22 26,93 ± 3,68 24,03 ± 3,80 10,41 ± 1,30 17,49 ± 2,22	10,85 ± 1,43
	Total Activity (counts)	1046 ± 71	942 ± 66	804 ± 73 &&	1459 ± 401 1274 ± 90 &&	946 ± 87 &&&&

ACKNOWLEDGEMENTS

The authors thank Yoan Salafranque for his technical help and Shauna Parkes for her comments on previous version of the manuscript.

This work was supported by the Institut National du Cancer (INCa_14796 to SC), CNRS, the University of Bordeaux and La Region Nouvelle-Aquitaine.

COMPLIANCE WITH ETHICAL STANDARDS

The authors have nothing to disclose.

AUTHORS' CONTRIBUTION

SC developed the concept and designed the study. MCM and FD performed the experiments. MCM, FD and SC participated in data analysis and interpretation of the findings. MCM and SC wrote the


Zineb Kerrami

Salma Lahbabi

Yannick J Dappe

Surface symmetry effect on the charge transfer at the black, blue, and green phosphorene/graphene interfaces

Surface symmetry effect on the charge transfer at the black, blue, and green phosphorene/graphene interfaces

Zineb Kerrami, Yannick J.

Introduction

Two-dimensional (2D) materials have become an exciting worldwide subject of research as they have triggered the apparition of new applications, mostly in nanoelectronics and energy conversion research field. There are numerous emerging 2D materials, each one with its own properties and applications [START_REF] Dhanabalan | Present perspectives of broadband photodetectors based on nanobelts, nanoribbons, nanosheets and the emerging 2D materials[END_REF][START_REF] He | Emerging 2D materials beyond graphene for ultrashort pulse generation in fiber lasers[END_REF][START_REF] Wang | Emerging 2D materialbased nanocarrier for cancer therapy beyond graphene[END_REF][START_REF] Xie | Solar-Inspired Water Purification Based on Emerging 2D Materials: Status and Challenges[END_REF][START_REF] Bati | Emerging 2D layered materials for perovskite solar cells[END_REF][START_REF] Glavin | Emerging applications of elemental 2D materials[END_REF][START_REF] Qadir | Representative 2D-material-based nanocomposites and their emerging applications: a review[END_REF][START_REF] Shrivastava | A Roadmap for Disruptive Applications and Heterogeneous Integration Using Two-Dimensional Materials: State-of-the-Art and Technological Challenges[END_REF]. For example, graphene, a semimetallic single layer of carbon atoms arranged in a 2D honeycomb lattice, has been intensively studied exploiting its unique mechanical and electronic properties. Hexagonal Boron nitride (hBN), which is made of an alternate arrangement of nitrogen and boron atoms, crystallizes in a similar structure as graphene but presents a large band gap of about 6 eV. It has been used as a potential protecting layer from contamination and oxidation for many 2D materials [START_REF] Man | Protecting the properties of monolayer MoS 2 on silicon based substrates with an atomically thin buffer[END_REF][START_REF] Han | Effects of hexagonal boron nitride encapsulation on the electronic structure of few-layer MoS2[END_REF]. Besides the gapless graphene and the insulator hBN, transition metal dichalcogenides (TMDCs) provide promising alternatives as they exhibit diverse properties that depend on their composition, such as semiconductors (e.g., MoS2, WS2, …), superconductors (e.g., NbSe2, TaS2, …), semimetals (e.g., WTe2, TiSe2, …), and true metals (e.g., NbS2, VSe2, …) [START_REF] Chhowalla | The chemistry of twodimensional layered transition metal dichalcogenide nanosheets[END_REF][START_REF] Choi | Recent development of two-dimensional transition metal dichalcogenides and their applications[END_REF][START_REF] Inoshita | Topological semimetal phases manifested in transition metal dichalcogenides intercalated with 3 d metals[END_REF]. Semiconducting TMDCs have been successfully used for electronics [START_REF] Samadi | Group 6 transition metal dichalcogenide nanomaterials: synthesis, applications and future perspectives[END_REF][START_REF] Choi | Asymmetric 2D MoS2 for Scalable and High-Performance Piezoelectric Sensors[END_REF], however they present some failures, notably, their smaller carriers mobilities compared to graphene, which limits their application in optoelectronic devices [START_REF] Velický | From two-dimensional materials to their heterostructures: An electrochemist's perspective[END_REF]. In this regard, light has been shed on black phosphorene (black phosphorus monolayer) as it preserves its direct bandgap in stacked forms with value that decreases gradually from 1.8 eV to 0.3 eV with the number of layers. In addition, its unique anisotropic structure due to armchair and zigzag edgesand its high carrier mobility up to 1000 cm 2 V -1 s -1 have already ensured novel uses for black phosphorene in optoelectronic and thermoelectric applications [START_REF] Liu | Phosphorene: an unexplored 2D semiconductor with a high hole mobility[END_REF][START_REF] Xia | Rediscovering black phosphorus as an anisotropic layered material for optoelectronics and electronics[END_REF]. Recently, Zhu et al. [START_REF] Zhu | Semiconducting layered blue phosphorus: a computational study[END_REF] have predicted theoretically another phosphorene allotrope called blue phosphorene, which presents a very similar cohesion energy with respect to its black counterpart. Few years later, Zhang et al. [START_REF] Zhang | Epitaxial synthesis of blue phosphorene[END_REF] have synthesized a monolayer of blue phosphorene by epitaxial growth on an Au (111) substrate. Furthermore, Han et al. [START_REF] Han | Prediction of green phosphorus with tunable direct band gap and high mobility[END_REF] reported a new allotrope of phosphorene called green phosphorene, which will be studied and compared to black and blue phosphorene in the following discussion. Geim et al. [START_REF] Geim | Van der Waals heterostructures[END_REF], suggested that 2D materials with such a wide variety of properties could be effectively used and combined to design and build vertical van der Waals (vdW) heterostructures with the exact desired characteristics. In that respect, each layer should see its properties preserved, providing potentially infinite possibilities for new electronics with better performance, and may lead to promising nano-electronic devices [START_REF] Yankowitz | Van der Waals heterostructures combining graphene and hexagonal boron nitride[END_REF][START_REF] Ghosh | Polarity-Tunable Photocurrent through Band Alignment Engineering in a High-Speed WSe2/SnSe2 Diode with Large Negative Responsivity[END_REF]. For instance, hexagonal Boron Nitride (hBN) has been coupled to graphene and phosphorene in vdW heterostructures to protect and preserve their electronic properties [START_REF] Han | Effects of hexagonal boron nitride encapsulation on the electronic structure of few-layer MoS2[END_REF][START_REF] Mansouri | Graphene/Phosphorene nano-heterostructure as a potential anode material for (K/Na)-ion batteries: Insights from DFT and AIMD[END_REF][START_REF] Wang | Graphene, hexagonal boron nitride, and their heterostructures: properties and applications[END_REF]. In addition, TMD/graphene heterostructures have been successfully used for transistors design [START_REF] Li | Engineering graphene and TMDs based van der Waals heterostructures for photovoltaic and photoelectrochemical solar energy conversion[END_REF][START_REF] Lee | Ultrahigh gauge factor in graphene/MoS2 heterojunction field effect transistor with variable Schottky barrier[END_REF][START_REF] Iannaccone | Quantum engineering of transistors based on 2D materials heterostructures[END_REF][START_REF] Tang | Multilayer graphene-Wse2 heterostructures for WSe2 transistors[END_REF]. Finally, C. Li et al. [START_REF] Li | A promising blue phosphorene/C2N van der Waals type-II heterojunction as a solar photocatalyst: a first-principles study[END_REF] have reported blue phosphorene/C2N vdW heterostructure as an efficient model to enhance separation and migration of the photogenerated electrons and holes in C2N and blue phosphorene, leading to an enhanced photocatalytic activity of the heterostructure.

In vdW heterostructures, surface symmetry plays a key role in the interactions at the interface. Controlling this feature might yield numerous interesting characteristics, which are still under discussion so far. In the present study, black, blue, and green phosphorene, each one with different atomic structure and surface symmetry, are combined with monolayer graphene, AAbilayer graphene, and AB-bilayer graphene to construct vdW heterostructures. As a result, a comparative study for the nine interfaces (phosphorene/Ggraphene) is presented, including stability and electronic properties of the three phosphorene allotropes. Then, the charge transfer at the interface between phosphorene allotropes and monolayer and bilayer graphene is discussed. Such comparison is of huge benefice to determine the energetic stability of phosphorene/graphene heterostructures and the mutual electronic exchange at the interface depending on phosphorene atomic structure.

Computational details

All calculations have been performed using the Quantum Espresso (QE) package [START_REF] Giannozzi | QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials[END_REF] based on Density Functional Theory (DFT). Exchange and Correlation energies are described within the Perdew-Burke-Ernzerhof (PBE) functional under the Generalized Gradient Approximation (GGA) [START_REF] Perdew | Generalized gradient approximation made simple[END_REF]. In order to accurately describe the interlayer weak van der Waals vdW interaction, the DFT-D2 method correction of Grimme has been adopted in all the calculations for graphene/phosphorene heterostructures [START_REF] Grimme | Semiempirical GGA-type density functional constructed with a long-range dispersion correction[END_REF]. The energy cutoff of the plane-wave basis set is set to 50 Ry, the convergences of the total energy difference between cycles and atomic forces acting on each atom for all the geometric structures are set to 10 -6 eV and 0.01 eV/Å, respectively. Graphene/phosphorene heterostructures were built from the optimized monolayer and bilayer graphene and monolayer phosphorene unit cells as described in the following section (see Figure .2). To avoid interactions between periodic images along the z-axis, a 20 Å vacuum was added to the heterostructures. The reciprocal space is sampled within the Monkhorst-Pack scheme by (12 × 9 ×1), (12 × 12 ×1), and (12 × 4 ×1) k-point grid for the black-phosphorene/graphene, blue-phosphorene/graphene, and green-phosphorene/graphene interfaces, respectively. The Heyd-Scuseria-Ernzerhof hybrid functional (HSE06) [START_REF] Heyd | Hybrid functionals based on a screened Coulomb potential[END_REF] method was used particularly to obtain accurate bandgap values of the black, blue, and green phosphorene as (HSE06) functional rectifies inaccurate PBE exchange functional by mixing this latter with a fraction of Hartree-Fock exact exchange [START_REF] Heyd | Efficient hybrid density functional calculations in solids: Assessment of the Heyd-Scuseria-Ernzerhof screened Coulomb hybrid functional[END_REF]. The charge transfer analysis has been performed using Bader charge analysis [START_REF] Henkelman | A fast and robust algorithm for Bader decomposition of charge density[END_REF].

Results and discussion

structural and electronic properties of black, blue, and green phosphorene

Side and top view of black, blue, and green phosphorene are presented in Figure 1, exhibiting significant structural differences. Black phosphorene presents a high anisotropy and structural differences that can be observed from a side view, such as armchair and zigzag edges. On another hand, blue phosphorene exhibits a structural pattern similar to graphene from a top view, and a flatter zigzag ridge than black phosphorene in both sides. Consequently, the layer thickness of blue phosphorene is reduced to 1.23 Å compared to 2.11 Å for black phosphorene. Green phosphorene contains three slightly buckled atomic layers instead of two as in the case of black and blue phosphorene. This leads to an increased phosphorene layer thickness (2.94 Å), which consists in zigzag ridges on one side and combined armchair and zigzag ridges on the other side (Fig. 1(c)). As such, it has often been reported as a structural combination of black and blue phosphorene in previous reports [START_REF] Han | Prediction of green phosphorus with tunable direct band gap and high mobility[END_REF]. Calculated band structures for the different phosphorene allotropes presented in Figure 1 indicate that black phosphorene exhibits a direct bandgap of 1.9 eV, which is very interesting for optoelectronic applications [START_REF] Shiri | Reversible modulation of spontaneous emission by strain in silicon nanowires[END_REF][START_REF] Noborisaka | Electric tuning of direct-indirect optical transitions in silicon[END_REF]. Blue phosphorene presents an indirect bandgap of 3.3 eV that is large compared to the visible light energy, which limits its application in photonics. Green phosphorene presents an almost similar electronic behavior as black phosphorene, with a direct bandgap of 2.1 eV.

Table .1 Optimized lattice parameters a and b (Å) (note that a=b for blue phosphorene), corresponding calculated HSE06 band gap energy (eV), and total energy relative to black phosphorene energy per atom (meV/atom). The respective stability of the different phosphorene allotropes are summarized in Table .1. Total energies of green and blue phosphorene relative to black phosphorene are 11.92 meV/atom and 36.6 meV/atom respectively. However, that energy difference is considered small compared to the impact of external parameters such as substrate and temperature. Our calculated lattice parameters, electronic properties, and order of stability of black, blue, and green phosphorene are consistent with previous reports [START_REF] Han | Prediction of green phosphorus with tunable direct band gap and high mobility[END_REF][START_REF] Zhu | Semiconducting layered blue phosphorus: a computational study[END_REF][START_REF] Garrison | Size and strain effects on mechanical and electronic properties of green phosphorene nanoribbons[END_REF]. As the three phosphorene allotropes exhibit different structural and electronic properties, their interaction with graphene in an vdW heterostructure might present different behavior for each phosphorene allotrope. Thus, our objective is to provide insights in the effect of surface symmetry of phosphorene on its interaction with graphene.

a (Å) b (Å) Height (Å) Band gap (eV

Energy, stability, and electronic properties of phosphorene/monolayer graphene heterostructures

We now turn to the study of phosphorene/graphene interfaces. In order to simulate these heterostructures, two types of configurations for each phosphorene allotrope are considered. First we consider the interaction of one phosphorene layer on top of one graphene layer, and second on top of a graphene bilayer. This second configuration has been considered in the present study to take advantage from different electronic features that might arise from contact of phosphorene with a semimetallic (graphene) or potentially semiconductor (graphene bilayer) substrate. For all these configurations, a common set of lattice vectors has been considered. Hence, the supercell sizes have been chosen to limit, as much as possible, the mismatch strain between graphene and phosphorene lattice parameters, knowing that an exact matching would require a huge supercell, beyond our calculation possibilities. As illustrated in Figure 2 and Figure 7 (discussed in section 3.3 for phosphorene/bilayer graphene), black phosphorene/graphene heterostructures (BP/Gr and BP/2Gr) consist in a 3×2 black phosphorene supercell on top of a 4×2 rectangular graphene supercell. In the same manner, blue phosphorene/graphene heterostructures (blP/Gr and blP/2Gr) consist in a 3×3 blue phosphorene supercell on top of a 4×4 hexagonal graphene supercell. Finally, green phosphorene/graphene heterostructures (GP/Gr and GP/2Gr) consist in a 3×1 green phosphorene supercell on top of a 4×3 rectangular graphene.

Figure 2 Top and side views of the atomic structures of black phosphorene/graphene (BP/Gr), blue phosphorene/graphene (blP/Gr), and green phosphorene/graphene (GP/Gr) heterostructures following phosphorene lattice vectors.

The interaction energy IE per unit atom that measures a configuration stability is defined by

IE = ((𝐸 𝑝ℎ𝑜𝑠𝑝ℎ𝑜𝑟𝑒𝑛𝑒/𝑔𝑟𝑎𝑝ℎ𝑒𝑛𝑒 -(𝐸 𝑝ℎ𝑜𝑠𝑝ℎ𝑜𝑟𝑒𝑛𝑒 + 𝐸 𝑔𝑟𝑎𝑝ℎ𝑒𝑛𝑒 ))/𝑁 𝑃 , (1)
where 𝐸 𝑝ℎ𝑜𝑠𝑝ℎ𝑜𝑟𝑒𝑛𝑒/𝑔𝑟𝑎𝑝ℎ𝑒𝑛𝑒 , 𝐸 𝑝ℎ𝑜𝑠𝑝ℎ𝑜𝑟𝑒𝑛𝑒 , 𝐸 𝑔𝑟𝑎𝑝ℎ𝑒𝑛𝑒 are the total energies of the phosphorene/grapheneinterface, phosphorene monolayer and graphene monolayer, respectively. 𝑁 𝑃 is the number of phosphorous atoms in the heterostructure. According to definition (1), a negative value of IE reflects an energetically favorable configuration. We note that for each phosphorene/graphene heterostructure, several stacking modes between phosphorene (black, blue, and green phosphorene) and graphene (monolayer graphene, AA-, and AB-bilayer graphene) have been tested and no energetically preferred stacking mode have been found. This is consistent with weak van der Waals forces which are much less sensitive to local corrugation.

From a theoretical point of view, the application of strain on each monolayer in order to reach a common lattice parameter is an unavoidable restriction to simulate heterostructures. The ratio of applied strain varies depending on the studied systems [START_REF] Garrison | Size and strain effects on mechanical and electronic properties of green phosphorene nanoribbons[END_REF]. For instance, in the present study, black phosphorene/graphene and green phosphorene/graphene heterostructures present a large strain along armchair ridges (≥ 7%) and a small strain along zigzag ridges (~1%), while blue phosphorene/graphene heterostructures present a small strain (≤0.7%). Therefore, as reported in previous studies [START_REF] Di Felice | Angle dependence of the local electronic properties of the graphene/MoS2 interface determined by ab initio calculations[END_REF], besides the mutual interaction between the constituents of the heterostructure, there is an effect of the applied strain on the electronic properties of each layer. However, phosphorene/graphene heterostructures present the same electronic behavior following both phosphorene and graphene lattice vectors. Thus, considering the flexibility of graphene under tensile strain, the phosphorene lattice vectors have been adopted to describe the electronic properties of phosphorene/graphene heterostructures.

The corresponding interlayer distances and interaction energies for phosphorene/graphene interfaces according to phosphorene and graphene lattice vectors are summarized in Table .2.

As discussed in Section 3.1, phosphorous (P) atoms in the black, blue, and green phosphorene allotropes are not arranged as a single flat plane like in graphene, but belong to separate atomic planes along the z-axis. This implies a corrugated armchair/zigzag shape lateral configuration with different thicknesses. According to the presented results, two key comparisons can be performed. First, the heterostructures that follow graphene lattice vectors exhibit lower total energies and interaction energies compared to those that follow phosphorene lattice vectors. This could be related to the energetic response to applied strain, that is, according to the calculated total energies, higher under larger applied strain following phosphorene lattice vectors than that following graphene lattice vectors. Second, blue phosphorene/graphene heterostructures present the lowest total energies and interaction energies, and the largest interlayer distances, while green phosphorene/graphene heterostructures present the highest total energies and interaction energies, and consequently the shortest interlayer distances. The difference in interaction energy and interlayer distances trend can be explained by the difference in structural properties of phosphorene allotropes. Blue phosphorene/graphene heterostructure exhibits 9 atoms in the bottom plan (phosphorene plan in contact with graphene) and the lowest layer thickness. Black phosphorene/graphene exhibits 12 atoms and the higher layer thickness of black phosphorene. Green phosphorene/graphene exhibits 6 atoms and the highest layer thickness. Consequently, blue phosphorene/graphene heterostructure following graphene lattice vectors is the most stable configuration, while green phosphorene/graphene heterostructure following phosphorene lattice vectors is the less stable. We present in Figure 3 the bandstructure and projected density of states (PDOS) of black phosphorene/graphene heterostructures alongside the superposed bandstructures and density of states (DOS) of free-standing black phosphorene and graphene monolayers. For heterostructures (right panels), both black phosphorene direct band gap and Dirac cone of graphene have been preserved, which is characteristic of the weak van der Waals interaction. Though, the graphene Dirac cone shifts down below the Fermi level by 33.75 meV, corresponding to a small n-doping in graphene. This is representative of a small charge transfer from phosphorene to graphene as summarized in Table 3. These results are consistent with previously reported results [START_REF] Liu | Tailoring sample-wide pseudo-magnetic fields on a graphene-black phosphorus heterostructure[END_REF]. Figure 5 presents the bandstructures of green phosphorene/graphene heterostructures. As for the previous heterostructures, both green phosphorene and graphene electronic behavior have been preserved. Namely, the bandgap energy of green phosphorene and the location of the graphene Dirac cone with respect to the Fermi level remain unchanged . This is due to the zerocharge transfer at the green phosphorene/graphene interface (see Table .3). Table .3 Calculated Bader charge transfer for phosphorene/graphene heterostructures.

According to Bader charge analysis (see Table . 3), the estimated amount of charge transfer is around 0.04 electrons from graphene to blue phosphorene, which is a bit higher than what is calculated in the case of black phosphorene/graphene. This difference in charge transfer is consistent with the difference in Fermi level shift observed between black phosphorene/graphene and blue phosphorene/graphene.

In summary, no bandgap opening at the Dirac cone has been observed in all phosphorene/graphene heterostructures studied here, as expected from the weak van der Waals interactions. Blue phosphorene/graphene heterostructure presents the lowest interaction energy and highest charge transfer from graphene to blue phosphorene. It is followed by black phosphorene/graphene heterostructure that exhibits higher interaction energy, and lower charge transfer from black phosphorene to graphene, and then green phosphorene/graphene heterostructure that presents the highest interaction energy, and almost zero charge transfer.

Energy, stability, and electronic properties of phosphorene/bilayer graphene heterostructures

Figure 7 illustrates the atomic structures of black, blue, and green phosphorene/bilayer graphene heterostructures following phosphorene lattice vectors. The interlayer distances, total energies, and interaction energies for phosphorene/bilayer graphene heterostructures according to both (BP) and (Gr) lattice vectors are summarized in Table 4. Our first observation is that phosphorene/AB-graphene heterostructures exhibit lower interaction energies and shorter interlayer distances than phosphorene/AA-graphene heterostructures for the three phosphorene allotropes. This is related to the fact that bilayer graphene in AB stacking mode is energetically more stable than in AA staking mode [START_REF] Mostaani | Quantum Monte Carlo Calculation of the Binding Energy of Bilayer Graphene[END_REF]. Total and interaction energies for the three studied phosphorene allotropes follow the same trend as for phosphorene/monolayer graphene.

Table .4 Calculated strain ratio 𝜀(%) applied on bilayer graphene (phosphorene) following phosphorene (graphene) lattice vectors, interlayer distances (Å), total energy per number of phosphor atoms (eV/P-atom) of phosphorene/bilayer graphene heterostructures, and interaction energies per number of phosphor atoms (meV/P-atom) of phosphorene/bilayer graphene heterostructures. In order to have clear observation on bilayer graphene band structure in the vicinity of the Fermi level, lattice vectors of graphene are adopted in phosphorene/bilayer graphene heterostructures. Figure 8 presents the bandstructures and DOS of black phosphorene/bilayer graphene heterostructures. As in the case of monolayer graphene both black phosphorene and graphene band structures have been preserved. However, some features have been observed near the Fermi level due to the charge transfer. In the case of AA-stacked bilayer graphene, the graphene Dirac cone is opened by 34.8 meV. The opening of the Dirac cone is related to the charge transfer between phosphorene and bilayer graphene. As indicated in Table .5, the Top (T) layer that interacts directly with phosphorene is differently charged with respect to the bottom (B) layer, which breaks the symmetry between the two graphene planes (top and bottom layers) and opens a gap in the bilayer structure. In the case of AB-stacked bilayer graphene, a Fermi level shift has been observed representing an n-doping in graphene, in addition to the opening of a very small bandgap. As in the case of AA-bilayer graphene, the opening of the Dirac cone is related to symmetry breaking between the two graphene layers due to the difference in charge transfer from black phosphorene to the two graphene layers as indicated in Table .5, which is consistent with various reported studies on bilayer graphene-based interfaces [START_REF] Pierucci | Self-organized metal-semiconductor epitaxial graphene layer on off-axis 4H-SiC[END_REF][START_REF] Dau | Beyond van der Waals interaction: the case of MoSe2 epitaxially grown on few-layer graphene[END_REF][START_REF] Dappe | Charge transfers and charged defects in WSe2/graphene-SiC interfaces[END_REF]. Better illustration of this behavior is presented in Figure 11(a) and Figure 12(a), where the charge distribution shows charge accumulation and depletion only near the top layer of the bilayer graphene (layer in contact with black phosphorene). In that respect, one can obviously notice the charge difference between top and bottom layers in bilayer graphene. Figure 8 presents the bandstructures and DOS of blue phosphorene/bilayer graphene heterostructures. As observed in the case of blue phosphorene/monolayer graphene, blue phosphorene preserves its band structure at the interface with graphene, with a Fermi level shift indicating a p-doping in the bilayer graphene. A higher charge transfer is observed in the case of AA-stacked bilayer graphene, which is in contrast with the black phosphorene/bilayer graphene heterostructure, where AB-stacked bilayer graphene encounters larger charge transfer than AA-stacked bilayer graphene. As mentioned for black phosphorene/bilayer graphene heterostructures, the charge difference between top and bottom layers of the bilayer graphene at the interface with blue phosphorene for AA and AB stacking modes yields a symmetry breaking, resulting in a very small bandgap opening of 10 meV and 11.24 meV respectively.

Lattice vectors

Indeed, as presented in Figure 11 Finally, in the case of green phosphorene/bilayer graphene heterostructures, we use the green phosphorene lattice vectors, similarly to the monolayer case. Also, both green phosphorene and bilayer graphene electronic bandstructures are preserved. According to Bader charge analysis (Table 5), green phosphorene/bilayer graphene heterostructure exhibits a smaller charge transfer compared to that in black phosphorene and blue phosphorene/bilayer graphene heterostructures. This yields a smaller Fermi level shift, indicating an n-doping in graphene bilayer in both AA-and AB stacking, with a more important charge transfer from green phosphorene to AB-stacked bilayer graphene than to AA-stacked bilayer graphene. According to the results presented in Figure 11(c) (Figure 12(c)), as in the case of green phosphorene/monolayer graphene, the charge distribution in green phosphorene/AA-graphene (green phosphorene/AB-graphene) is much smaller compared to the charge density in black phosphorene and blue phosphorene/bilayer graphene.

Conclusion

In summary, a comparative study of black, blue, green phosphorene/graphene is presented. For all the configurations of phosphorene/monolayer graphene, no gap opening near the graphene Dirac cone has been observed. Blue phosphorene/graphene heterostructure presents the lowest interaction energy, and highest charge transfer from graphene to blue phosphorene. Black phosphorene/graphene heterostructure exhibits a higher interaction energy, and a lower charge transfer from black phosphorene to graphene, whereas green phosphorene/graphene heterostructure presents the highest interaction energy. Stability and interaction energies in phosphorene/bilayer graphene heterostructures follow the same trend as in phosphorene/monolayer graphene. Also, a more important charge transfer has been obtained from phosphorene to AB-stacked bilayer graphene than to AA-stacked bilayer graphene for black and green phosphorene. A more important charge transfer is observed from AA-stacked bilayer to blue phosphorene than from AB-stacked bilayer graphene. These charge transfers lead to small gap opening in the bilayer graphene bandstructures due to the charge difference between the top and bottom layers. These results show that different phosphorene allotropes allow modulating graphene or bilayer graphene electronic properties, leading to promising perspectives for future nanoelectronics devices.

Figure 1

 1 Figure 1 Top and side views of the atomic structure, and corresponding calculated band structures for (a) black, (b) blue, and (c) green phosphorene.

Figure 3

 3 Figure 3 Calculated band structures and DOS of superposed free-standing black phosphorene and graphene (left), and black phosphorene/graphene (right) following black phosphorene lattice vectors. The bottom panels show the zoom-in band structure and DOS near the Dirac point. Black and red dashed lines present Fermi level and Dirac cone energy respectively.

Figure 4

 4 Figure 4 presents the bandstructures of free-standing blue phosphorene and graphene monolayers, and blue phosphorene/graphene heterostructures. Contrarily to the black phosphorene/graphene heterostructure, the Dirac cone shifts up with respect to the Fermi level by 113.55 meV, corresponding to a p-doping in graphene.

Figure 4

 4 Figure 4 Calculated bandstructures and DOS of free-standing blue phosphorene and graphene (left), and blue phosphorene/graphene (right) following blue phosphorene lattice vectors. The bottom panels show the zoom-in band structure and DOS near the Dirac point. Black and red dashed lines present Fermi level and Dirac cone energy respectively.

Figure 5

 5 Figure 5 Calculated bandstructures and DOS of free-standing green phosphorene and graphene (left), and green phosphorene/graphene (right) following green phosphorene lattice vectors. Black dashed line presents Fermi level.

Figure 6

 6 Figure 6 Difference in charge distribution and planar averaged charge density along z-axis in BP/Gr (a), blP/Gr (b), and BP/Gr (c) heterostructures. The cyan and red regions represent charge depletion and accumulation, respectively. The isosurface value is 0.0001 e/Å 3 and the horizontal dashed-dot lines denote the locations of atomic layers of graphene and phosphorene.

Figure 7

 7 Figure 7 Top and side views of the atomic structures of black phosphorene/bilayer graphene (BP/2Gr), blue phosphorene/bilayer graphene (blP/2Gr), and green phosphorene/bilayer graphene (GP/2Gr) heterostructures following phosphorene lattice vectors.

Strain

  𝐺𝑟 ) = 0.98 𝜀(𝑏 𝐺𝑟 ) = 7.35 Gr-Gr = 3.47 BP-Gr = 3.34 -642.00 -105.46 Gr 𝜀(𝑎 𝐵𝑃 ) = -0.97 𝜀(𝑎 𝐵𝑃 ) = -

Figure 8

 8 Figure 8 Calculated bandstructures and DOS of (a) black phosphorene/AA-graphene (right), (b) and black phosphorene/AB-graphene. Right panels show the zoom-in band structure near Fermi level. Black and red dashed lines present Fermi level and mid-gap respectively.

  (b) and Figure 12(b), the charge distribution shows a charge transfer only between the top layer of bilayer graphene and blue phosphorene.

Figure 9

 9 Figure 9 Calculated bandstructures and DOS of (a) blue phosphorene/AA-graphene (right), (b) and blue phosphorene/AB-graphene. Right panels show the zoom-in band structure near Fermi level. Black and red dashed lines present Fermi level and mid-gap respectively.

Figure 10 Figure 11

 1011 Figure 10 Calculated bandstructures and DOS of (a) green phosphorene/AA-graphene (right), (b) and green phosphorene/AB-graphene. Right panels show the zoom-in band structure near Fermi level. Black and red dashed lines present Fermi level and mid-gap respectively.

Figure 12

 12 Figure 12 Difference in charge distribution and planar averaged charge density along z-axis in BP/AB-Gr (a), blP/AB-Gr (b), and BP/AB-Gr (c) heterostructures. The cyan and red regions represent charge depletion and accumulation, respectively. The isosurface value is 0.0001 e/Å 3 , and horizontal dashed-dot lines denote the locations of atomic layers of graphene and phosphorene.

Table . 2

 . Calculated strain percent 𝜀(%) applied on graphene (phosphorene) following phosphorene (graphene) lattice vectors, interlayer distances (Å), total energy per number of phosphorous atoms (eV/P-atom) of phosphorene/graphene heterostructures, and interaction energies per number of phosphorous atoms (meV/P-atom) of phosphorene/graphene heterostructures.

		Lattice	Strain 𝜺 (%)	Interlayer	Total energy	Interaction Energy
		vectors		distance (Å)	(eV/P-atom)	(meV/P-atom)
	BP/Gr	BP	𝜀(𝑎 𝐺𝑟 ) = 1.05	3.37	-416.59	-51.75
			𝜀(𝑏 𝐺𝑟 ) = 7.1
		Gr	𝜀(𝑎 𝐵𝑃 ) = -	3.32	-416.76	-58.54
			1.04
			𝜀(𝑏 𝐵𝑃 ) = -6.6
	blP/Gr	blP	𝜀(𝑎 𝐺𝑟 ) = 0.70	3.44	-491.94	-58.89
		Gr	𝜀(𝑎 𝑏𝑙𝑃 ) = -	3.39	-491.94	-59.61
			0.43
	GP/Gr	GP	𝜀(𝑎 𝐺𝑟 ) = 0.86	3.17	-416.42	-39.97
			𝜀(𝑏 𝐺𝑟 ) = 10.34
		Gr	𝜀(𝑎 𝐺𝑃 ) = -	3.08	-416.47	-43.24
			0.85
			𝜀(𝑏 𝐺𝑃 ) = -
			9.37

Acknowledgment

The research leading to these results has received funding from OCP grant AS70 "Towards phosphorene-based materials and devices".

Computational resources for this study were provided by the computing facilities of High Performance Computing simlab-cluster, of Mohammed VI Polytechnic University at Benguerir.


the distance (hence the path) followed by stray light ...next talk ! Coherent techniques: can be implemented after the assembly of the system under test, using the system's detectors Well-known method in radar techniques ("FMCW", frequency-modulated continuous wave) Commercial reflectometers for the monitoring of faults in telecom networks ...but not adapted to measuring stray light in LISA -stray light in LISA is not just optical return (scattered light, diffraction, ghosts, .. to all the detectors) Plan M. Lintz, WITSO, ESTEC, 2023The LISA mission in one slide General approach for the measurement and identification of coherent stray light Measurement of stray light in the LISA's "MOSA"The frequency-ramped laser source, and the characterization of the instrumentConclusion and perspectivesMeasures the variation of the 2.5 Mkm arm lengths 10pm/Hz -records gravitational waves in the 20µHz -1Hz band -trous noirs supermassive black holes, primordial universe,...The basic LISA instrument is the "moving optical sub-assembly" (MOSA) laser's opt. frequency -record all the exiting signals -process the Fourier transform of all the signals same with Beam 2, Beam 3..

M•• 6 •

 6 measurement in LISA's MOSA -Laser source produces two beams: -one powerful, -the other 1mW, low power -beam emitted => beam dump required Need for the "calibrator" unit and signal M. Lintz, GWADW, May 2021 CAL additional The frequency-ramped laser source: monitoring the ramp Frequency ramp must be linear (<10^-4), with a known and reproducible value => The "calibrator" is a fibered interferometer which monitors -the linearity of the frequency ramp -the reproducibility of the ramp rate -the absence of stray frequency modulations and more => 7 nominal peaks sharp enough to appreciate the ramp to << 10 -4 allows real-time fine monitoring of the ramp Trick to identify parasitic peaks: -first scan with scan rate SR1 -second scan with rate SR2 => only true optical contributions give overlapping peaks ! , GWADW, May 2021 Phase-lock with offset demodulation allows for the linear ramp of the laser frequency For each component the "acceptable fractional SL amplitude"  accept-SL stems from the performance model: -noise in the LISA measurement should not exceed 10 pm/√Hz with less than 1 pm/√Hz from stray light the allocation can be broken to 0.1 pm/√Hz for each contribution to stray light • Then the acceptable fractional amplitude is given by  accept-SL = [Allocation for stray light] / [SL path length noise] • Then the measurement floor must be < [ accept-SL ] smallest with a margin (SNR) of 30 • Presently this leads to a fractional noise floor of 2x10^-6 in the Fourier transform data. If an excess is observed with one component, the final check is globally, at MOSA level, against the Performance Model nom. amplitude =  SL  SL  SL  2x10^-Presently no showstopper with the prototype • OK for the measurement of scattered light • Noise floor at OPD < 1m to be improved by normalization of the signals • "Polarization wobbling" reduces the effective dynamics • Residual modulation in the laser's optical frequency scan (=> small, reproducible stray peak) to be reduced • The large number of signals can lead to tedious, slow interpretation of the signals' Fourier transforms • how far the post-processing can be automated is an open question • The prototype was recently coupled to a LISA-similar optical interferometer • to deal with more representative signals (20 simultaneous signals) • => develop automatic post-processing routines • => check for the difference tests in vacuum vs tests in ambient air No striking difference apart from the index of air =>preliminary<=