Winka Le Clec'h

Fre ´de ´ric

D Chevalier

Lise Genty

Joanne Bertaux

Didier Bouchon

Mathieu Sicard
email: mathieu.sicard@univ-poitiers.fr

Cannibalism and Predation as Paths for Horizontal Passage of Wolbachia between Terrestrial Isopods

The alpha-proteobacteria Wolbachia are the most widespread endosymbionts in arthropods and nematodes. Mainly maternally inherited, these so-called sex parasites have selected several strategies that increase their vertical dispersion in host populations. However, the lack of congruence between the Wolbachia and their host phylogenies suggests frequent horizontal transfers. One way that could be used for horizontal Wolbachia transfers between individuals is predation. The aim of this study was to test whether horizontal passage of Wolbachia is possible when an uninfected terrestrial isopod eats an infected one. After having eaten Armadillidium vulgare harbouring Wolbachia, the predator-recipients (the two woodlice A. vulgare and Porcellio dilatatus dilatatus) that were initially Wolbachia-free were tested positive for the presence of Wolbachia both by quantitative PCR and Fluorescence in situ Hybridization (FISH). Even if the titers were low compared to vertically infected individuals, this constitutes the first demonstration of Wolbachia occurrence in various organs of an initially uninfected host after eating an infected one.

Introduction

Wolbachia pipientis are endocytoplasmic alpha-proteobacteria widespread among arthropods [START_REF] Werren | Biology of Wolbachia[END_REF][START_REF] Hilgenboecker | How many species are infected with Wolbachia? A statistical analysis of current data[END_REF] and filarial nematodes [START_REF] Bandi | Phylogeny of Wolbachia in filarial nematodes[END_REF]. These symbionts are mainly maternally inherited and several extended phenotypes have been naturally selected to increase their vertical transmission through generations. The extended phenotypes of the Wolbachia in their hosts that lead to an increased number of infected females are cytoplasmic incompatibility [START_REF] Werren | Biology of Wolbachia[END_REF][START_REF] Yen | The etiological agent of cytoplasmic incompatibility in Culex pipiens[END_REF][START_REF] Serbus | The genetics and cell biology of Wolbachia-host interactions[END_REF], male killing [START_REF] Hurst | Male-killing Wolbachia in two species of insect[END_REF][START_REF] Jaenike | Fighting back against male-killers[END_REF], thelytokous parthenogenesis [START_REF] Stouthamer | Antibiotics cause parthenogenetic Trichogramma (hymenoptera/trichogrammatidae) to revert to sex[END_REF][START_REF] Stouthamer | Inherited microorganisms and arthropod reproduction[END_REF][START_REF] Huigens | Infectious parthenogenesis[END_REF] and feminization of genetic males [START_REF] Martin | Mise en e ´vidence d'un micro-organisme intracytoplasmique symbiote de l'oniscoide Armadillidium vulgare dont la pre ´sence accompagne l'intersexualite ´ou la fe ´minisation totale des ma ˆles ge ´ne ´tiques de la ligne ´e the ´lyge `ne[END_REF][START_REF] Rigaud | Feminizing endocytobiosis in the terrestrial crustacean Armadillidium vulgare latr. (isopoda): recent acquisitions[END_REF][START_REF] Bouchon | Infection in isopod crustaceans: molecular identification and host feminization[END_REF]. Even if the vertical transmission corresponds to the main transmission route for Wolbachia, several co-phylogenetic studies have revealed a lack of congruence between host and symbiont phylogenies, showing the ability of these symbionts to jump horizontally from one host to another [START_REF] O'neill | 16S rRNA phylogenetic analysis of the bacterial endosymbionts associated with cytoplasmic incompatibility in insects[END_REF][START_REF] Stouthamer | Molecular identification of microorganisms associated with parthenogenesis[END_REF][START_REF] Werren | Evolution and phylogeny of Wolbachia: reproductive parasites of arthropods[END_REF][START_REF] Zhou | Phylogeny and PCR-based classification of Wolbachia strains using wsp gene sequences[END_REF][START_REF] Vavre | Phylogenetic evidence for horizontal transmission of Wolbachia in host-parasitoid associations[END_REF][START_REF] Cordaux | Wolbachia infection in crustaceans: novel hosts and potential routes for horizontal transmission[END_REF][START_REF] Baldo | Multilocus sequence typing system for the endosymbiont Wolbachia pipientis[END_REF][START_REF] Raychoudhury | Modes of acquisition of Wolbachia: horizontal transfer, hybrid introgression, and codivergence in the Nasonia species complex[END_REF][START_REF] Kraaijeveld | Clonal genetic variation in a Wolbachia-infected asexual wasp: horizontal transmission or historical sex?[END_REF]. Experimentally, it is possible to mimic such horizontal transfers (i.e. infection of individuals that were born without Wolbachia) by injecting Wolbachia in asymbiotic individuals [START_REF] Rigaud | Wolbachia bacteria effects after experimental interspecific transfers in terrestrial isopods[END_REF][START_REF] Kageyama | Transfection of feminizing Wolbachia endosymbionts of the butterfly, Eurema hecabe, into the cell culture and various immature stages of the silkmoth, Bombyx mori[END_REF][START_REF] Riegler | Wolbachia transfer from Rhagoletis cerasi to Drosophila simulans: investigating the outcomes of host-symbiont coevolution[END_REF][START_REF] Zabalou | Wolbachia-induced cytoplasmic incompatibility as a means for insect pest population control[END_REF][START_REF] Xi | Wolbachia establishment and invasion in an Aedes aegypti laboratory population[END_REF][START_REF] Xi | Interspecific transfer of Wolbachia into the mosquito disease vector Aedes albopictus[END_REF][START_REF] Ruang-Areerate | Wolbachia transinfection in Aedes aegypti: a potential gene driver of dengue vectors[END_REF][START_REF] Mcmeniman | Stable introduction of a life-shortening Wolbachia infection into the mosquito Aedes aegypti[END_REF][START_REF] Apostolaki | Transinfection of the olive fruit fly Bactrocera oleae with Wolbachia: towards a symbiont-based population control strategy[END_REF]. However, the paths used by Wolbachia to pass horizontally from one individual to another in the wild are not well understood. It is obvious that such transfers would be more likely to occur between individuals that are ecologically connected. For instance, one path for Wolbachia to infect a new species is the hybridization process that can occur between two host species as demonstrated in the Nasonia species complex [START_REF] Raychoudhury | Modes of acquisition of Wolbachia: horizontal transfer, hybrid introgression, and codivergence in the Nasonia species complex[END_REF]. Interspecific interactions such as host-parasite relationships can also open a gate for Wolbachia to pass from one host species to another. In this context, Huigens et al. [START_REF] Huigens | Infectious parthenogenesis[END_REF][START_REF] Huigens | Natural interspecific and intraspecific horizontal transfer of parthenogenesisinducing Wolbachia in Trichogramma wasps[END_REF] have experimentally demonstrated natural inter-and intraspecific horizontal transfers of partheno-genesis-inducing Wolbachia between parasitoid wasps of the genus Trichogramma sharing a same host egg. Furthermore, Heath et al. [START_REF] Heath | Horizontal transfer of Wolbachia between phylogenetically distant insect species by a naturally occurring mechanism[END_REF] showed that Wolbachia could pass from Drosophila simulans to the parasitoid wasp Leptopilina boulardi. Blood contact between two injured individuals is another possible path for horizontal transfer of Wolbachia as experimentally demonstrated for the terrestrial crustacean Armadillidium vulgare [START_REF] Rigaud | Success and failure of horizontal transfers of feminizing Wolbachia endosymbionts in woodlice[END_REF].

Another important ecological link between hosts that can potentially be used by Wolbachia to pass horizontally from one host to another is their trophic connection within the food chain. Several previous studies sought to investigate the capacity of Wolbachia to pass between individuals of different species via predation. This has been tested for spiders [START_REF] Cordaux | Wolbachia infection in crustaceans: novel hosts and potential routes for horizontal transmission[END_REF][START_REF] Yun | Wolbachia screening in spiders and assessment of horizontal transmission between predator and prey[END_REF], mites [START_REF] Enigl | Negative evidence of Wolbachia in the predaceous mite Phytoseiulus persimilis[END_REF] and for some mosquito predators that were infected by the pathogenic Wolbachia strain wMelpop [START_REF] Hurst | Impacts of Wolbachia infection on predator prey relationships: evaluating survival and horizontal transfer between wMelpop infected Aedes aegypti and its predators[END_REF]. Despite these efforts, no successful horizontal transfer via predation could be demonstrated to date. In one case, predators became Wolbachia-positive when Phytoseiulus persimilis mites were experimentally fed with symbiotic larvae of the spider mite Tetranychus urticae [START_REF] Enigl | Negative evidence of Wolbachia in the predaceous mite Phytoseiulus persimilis[END_REF]. However, the Wolbachia were restricted to the predator gut and starvation sufficed to erase all trace of infection. These results as well as those obtained on ticks that were thought to be infected by Wolbachia but were in fact infected by endoparasitoids that hosted the symbionts [START_REF] Plantard | Detection of Wolbachia in the tick Ixodes ricinus is due to the presence of the hymenoptera endoparasitoid Ixodiphagus hookeri[END_REF] point out that the detection of Wolbachia in specimens collected from the wild is not always a proof of an actual infection of the focal species. Indeed, the detected Wolbachia can be restricted to the intestine containing prey during digestion or to parasites infecting this species. Testing a potential route of horizontal passage of Wolbachia from one individual to another thus requires experiments with lineages controlled for their infection status.

Here, we used our controlled lineages of woodlice to test whether predation and cannibalism could constitute a path for Wolbachia transmission between individuals. Woodlice are of interest to address this question for several reasons: First of all, even if the main diet of these crustaceans is detritivorous, they can easily turn into herbivores [START_REF] Farmer | Detritivorous crustaceans become herbivores on jasmonate-deficient plants[END_REF] or even carnivores. They can prey on other woodlice from the same species or from different species, especially during social interactions [START_REF] Warburg | The effect of climate on the distribution and abundance of isopods[END_REF]. The probability to be eaten by congenerics or conspecifics increases for individuals that are weak, for example being injured or in the middle of a molting period [START_REF] Pokarzhevskii | Microbial links and element flows in nested detrital food-webs[END_REF]. Another advantage of using terrestrial isopods is their relatively long lifespan (a few years) that allows the monitoring of the infection status in the same individuals for months after the initial infection. Furthermore, their size makes it possible to test different organs separately for the presence of Wolbachia. The ability of woodlice to get infected by eating their congeners has previously been tested by Juchault et al. [START_REF] Juchault | Action interspe ´cifique du facteur e ´pige ´ne ´tique fe ´minisant responsable de la the ´yge ´nie et de l'intersexualite ´du crustace ´Armadillidium vulgare (isopode oniscoı ¨de)[END_REF], who fed some uninfected A. vulgare with pieces of individuals infected with Wolbachia. They concluded that this was not a path used by Wolbachia as they found no infection in the recipients. However, in that case, the presence of Wolbachia in the recipients was only tested in ovaries by transmission electron microscopy, which offers only limited sample prospection and is thus not convenient for the detection of low Wolbachia quantities.

In the present study, we tested the occurrence of horizontal passages of Wolbachia via (i) cannibalism between two A. vulgare, one of which being naturally infected with Wolbachia, and (ii) predation where an uninfected Porcellio dilatatus dilatatus eats an infected A. vulgare. To do so, we designed an experiment that increased the probability of predation and cannibalism for the woodlice [START_REF] Edney | Predation by terrestrial isopods[END_REF]: Before putting predator and prey together, infected ''prey'' individuals were weakened by withdrawing a large amount of hemolymph while uninfected ''predator'' individuals were starved. Using this approach, all ''prey'' individuals were eaten by ''predator'' individuals within two days. In the months following the predation event, the presence and quantities of Wolbachia in the tissues of the ''predators'' were assessed by quantitative PCR and Fluorescence in situ Hybridization. Thereby, we show for the first time the occurrence of Wolbachia in various organs of an initially uninfected host after eating an infected one.

Materials and Methods

Ethic Statement

All experimental procedures and animal manipulations did not require an ethics statement.

Biological Materials

All the animals used in these experiments were reared at 20uC in plastic breeding boxes, in natural photoperiod, on a moistened potting mix derived from peat from sphagnum moss (pH = 6.4 and conductivity = 50.0 mS/m) with dead lime-tree leaves as a food source. The ''predators'' (i.e. animals eating an infected terrestrial isopod) for all experiments came from controlled asymbiotic (i.e. Wolbachia-free) lineages of Armadillidium vulgare and Porcellio dilatatus dilatatus. The animals used to create these asymbiotic A. vulgare and P. d. dilatatus control lineages were collected in Nice (France) in 1967 and in Rom (France) in 1988, respectively, and have since been reared in the laboratory. Wolbachia donors, hereafter called the ''preys'' (i.e. animals eaten by the ''predators''), were A. vulgare infected with the wVulC Wolbachia strain, from a controlled infected lineage created with animals sampled in Niort (France) and reared in the laboratory since 1961.

Cannibalism and Predation Experiments

Thirty asymbiotic one year-old A. vulgare and P. d. dilatatus females were starved during three months in rearing boxes with no other food source than the substrate (i.e. no dead lime-tree leaves). After three months, starved A. vulgare or P. d. dilatatus ''predators'' were individually placed in boxes with one A. vulgare ''prey''. Before being put together with the ''predator'', the A. vulgare ''preys'' were weakened by collecting 10 mL of their hemolymph after piercing their cuticle with a thin needle [START_REF] Braquart-Varnier | Wolbachia mediate variation of host immunocompetence[END_REF]. A fraction of the collected hemolymph was used to check the Wolbachia infection status of the ''prey''. After 48 hours, all the ''preys'' had been eaten by the ''predators''. ''Predators'' were then maintained in individual boxes with substrate and lime-tree leaves at libitum as a food source. For each ''predator'' species, animals were dissected at both 90 days and 180 days post-ingestion (PI) for DNA extraction and FISH experiments.

Tissue Samples and DNA Extractions for Wolbachia Quantification

Total DNA was extracted from the hemocytes (i.e immune cells) collected from each ''prey'' and the ovaries, central nervous system (i.e. nerve cells and neighbouring adipocytes) and hemocytes of each ''predator'' after dissection at 90 days and 180 days PI as described by Kocher et al. [START_REF] Kocher | Dynamics of mitochondrial DNA evolution in animals: amplification and sequencing with conserved primers[END_REF]. For each sample, concentration and quality (OD ratios 260/280 nm and 260/230 nm) of the extracted DNA were measured using the Nanodrop 1000 spectrophotometer (Thermo) to remove any low quality DNA sample.

Quantification of Wolbachia in Host's Tissues by qPCR

The quantification of Wolbachia by quantitative PCR (qPCR) was performed on (i) 10 ''predators'' per species (i.e. A. vulgare and P. d. dilatatus) at t = 0 before any contact of asymbiotic animals with infected ''prey'', (ii) 15 ''predators'' per species at 90 days PI and (iii) 13 ''predators'' for P. d. dilatatus and only two for A. vulgare at 180 days PI. Moreover, Wolbachia quantification was performed on the hemocytes collected from all 60 A. vulgare ''prey'' individuals.

qPCR reactions were performed using the LightCycler 480 system (Roche) as follows: 10 min at 95uC followed by 45 cycles [10 sec at 95uC, 10 sec at 60uC, 20 sec at 72uC]. A melting curve (65uC to 97uC) was recorded at the end of each reaction in order to check the specificity of the PCR product. The reaction mixture consisted of 5 mL of SYBRGreen MasterMix (Roche), 0.5 mL of each 10 mM specific primers [wsp208f (59-TGG-TGC-AGC-ATT-TAC-TCC-AG-39) and wsp413r (59-TCG-CTT-GAT-AAG-CAA-AAC-CA-39)], amplifying 205 bp of the single-copy Wolbachia surface protein (wsp) gene, 3 mL of sterile water and 1 mL of template DNA (between 10 ng and 80 ng of DNA). A Standard curve was plotted using seven dilutions of a purified wsp PCR product (wsp copies.mL 21 : 2.63610 0 , 2.63610 1 , 2.63610 2 , 2.63610 3 , 2.63610 4 , 2.63610 5 , 2.63610 6 , 2.63610 7 ). The number of wsp copies was estimated according to the standard curve. The total DNA quantity (i.e. host+Wolbachia) of each sample was used to normalize the resulting wsp gene copy counts. The results are thus given in number of wsp copies per ng of total DNA.

Wolbachia Localization in ''Predator'' Hemocytes Using Fluorescence in situ Hybridization (FISH)

Hemocytes were sampled from ''predators'' of each species (i.e. two A. vulgare females and five P. d. dilatatus females) 180 days PI. Each animal yielded ,10 mL of hemolymph that were pooled for each species in a microtube kept on ice. Fluorescence in situ Hybridization was performed according to Chevalier et al. [START_REF] Chevalier | The immune cellular effectors of terrestrial isopod Armadillidium vulgare: meeting with their invaders, Wolbachia[END_REF] on a total of 4 mL for each pool fixed with 1% paraformaldehyde-PBS solution (137 mM NaCl, 8 mM Na 2 HPO 4 , 12H 2 O, 1.5 mM KH 2 PO 4 , 3 mM KCl, pH 7.3), at 35% formamide with the probes W1-Cy3 (59-AATCCGGCCGARCCGACCC-39) and W2-Cy3 (59-CTTCTGTGAGTACCGTCATTATC-39) (30 ng.mL 21 each) targeting Wolbachia 16S rRNA [START_REF] Heddi | Four intracellular genomes direct weevil biology: nuclear, mitochondrial, principal endosymbiont and Wolbachia[END_REF]. As in Chevalier et al. [START_REF] Chevalier | The immune cellular effectors of terrestrial isopod Armadillidium vulgare: meeting with their invaders, Wolbachia[END_REF] the samples were further stained with FITC-phalloidin (20 ng, Sigma) mixed into the hybridization buffer and with DAPI (Sigma) mixed into the mounting medium (AF1 antifading, Citifluor, England, 2.5 mg.mL 21 ). Detection was performed with an epifluorescent microscope (Axio Observer-A1, Zeiss) with Apotome (structured illumination) equipped with a 63X/ 1.25 objective (oil immersion) and with the AxioVision 4.8.1 software (Zeiss). The number of hemocytes and their Wolbachia colonization status were counted on ten random images per pool, using ImageJ software (version 1.45; [START_REF] Rasband | Imagej[END_REF]). Hemocytes touching the image borders, i.e. incomplete ones, were ignored.

Statistical Analysis

All statistical analyses were performed using R software (version 2.10.1). Since data distribution did not follow a normal distribution (Shapiro test, p,0.05), Wolbachia titers in tissues were compared with a Kruskal-Wallis followed by Dunn's multiple comparison test or simple pairwise comparison Wilcoxon-Mann-Whitney tests.

Results

Wolbachia Quantification in the Different Host Tissues of ''Predators''

The Wolbachia were quantified by qPCR in hemocytes of the symbiotic ''preys'' and in three ''predator'' tissues: ovaries, central nervous system (CNS) and hemocytes at 90 and 180 days postingestion (PI). All the ''preys'' harboured high titers of Wolbachia (mean of Wolbachia in hemocytes 6 se/ng DNA: 4.62610 3 64.57610 2 , Fig. 1), which is in accordance with titers previously reported in Le Clec'h et al. [START_REF] Clec | High virulence of Wolbachia after host switching: when autophagy hurts[END_REF]. All the ''predators'' tested at t = 0 before any contact with the ''preys'' were completely asymbiotic since not a single Wolbachia was detected by qPCR in all tested tissues.

At 90 days PI, all tested ''predators'' from both species (i.e. A. vulgare and P. d. dilatatus) exhibited Wolbachia in all tested tissues but at low titers comprised between one and 100 Wolbachia per ng DNA (Figure 1). In both ovaries and CNS, Wolbachia titers were higher in A. vulgare, the native host of wVulC, than in P. d. dilatatus (Wilcoxon-Mann-Whitney test: U = 26; p = 0.0147 and U = 14; p = 0.0009, respectively), while no difference was found between species regarding Wolbachia titers in hemocytes (Wilcoxon-Mann-Whitney test: U = 64; p = 0.9730). A global comparison of Wolbachia titers between the different tissues of P. d. dilatatus highlighted heterogeneity between them (Kruskal-Wallis test: K = 14.583, df = 2, p = 0.0007). This heterogeneity was due to higher titers of Wolbachia in hemocytes than in ovaries (Dunn Multiple comparison test: p,0.001). On the contrary, global comparison of Wolbachia titers between the different tissues of A. vulgare revealed no difference (Kruskal-Wallis test: K = 2.818, df = 2, p = 0.2440).

At 180 days PI, many organs were found uninfected by Wolbachia, suggesting an overall decrease of the infection compared to 90 days PI (Table 1). However, at this time point, most A. vulgare individuals were dead (Table 1). We assume that this high mortality rate was due to their isolation and the lack of social contacts that are strongly required for this species exhibiting an important gregarious lifestyle [START_REF] Warburg | The effect of climate on the distribution and abundance of isopods[END_REF]. The comparison of Wolbachia titers in the different tissues of P. d. dilatatus between 90 and 180 days PI showed that the infection was stable in ovaries (Wilcoxon-Mann-Whitney test: U = 10; p = 0.1818) and CNS (Wilcoxon-Mann-Whitney test: U = 5; p = 0.2286) but decreased in hemocytes (Wilcoxon-Mann-Whitney test: U = 11.5; p = 0.0019; Figure 1).

Detection of Wolbachia in the ''Predator'' Hemocytes from Both Species Using Fluorescence in situ Hybridization (FISH)

Wolbachia quantification by qPCR revealed that ''predators'' were infected by Wolbachia at a low level after the ingestion of symbiotic (i.e. Wolbachia-positive) ''preys''. This was confirmed by FISH detection of Wolbachia with specific probes on one pool of hemolymph per species, with two animals for A. vulgare and five for P. d. dilatatus at 180 days PI. Hemocytes of both P. d. dilatatus (Figures 2A andB) and A. vulgare (Figures 2C andD) ''predators'' were colonized (3 and 8%, respectively). The fact that the probes target the transcript of the 16S rRNA gene further indicates that the Wolbachia were alive.

Discussion

Predation, though a brief interaction between living individuals of two species, is used by many parasites that pass horizontally from one host to another [START_REF] Combes | Interactions durables, e ´cologie et e ´volution du parasitisme[END_REF]. Cannibalism, which is one peculiar case of predation that occurs between individuals belonging to the same species, can also lead to horizontal parasite transmission [START_REF] Khan | Studies of pathogens of termites of Pakistan[END_REF]. The horizontal passage of Wolbachia from one individual to another by the predation route was tested unsuccessfully in several studies [START_REF] Enigl | Negative evidence of Wolbachia in the predaceous mite Phytoseiulus persimilis[END_REF][START_REF] Hurst | Impacts of Wolbachia infection on predator prey relationships: evaluating survival and horizontal transfer between wMelpop infected Aedes aegypti and its predators[END_REF]. Phylogenetic analyses of the Wolbachia infecting spiders and their prey in the same ecosystem also indicated that Wolbachia would not frequently navigate between species using this route [START_REF] Yun | Wolbachia screening in spiders and assessment of horizontal transmission between predator and prey[END_REF]. On a different note, some Endosymbiont Based Control Strategies rely on the principle that after introduction into a new host and release in the environment, Wolbachia will not escape and potentially spread along the food chain through predators. Indeed, when artificially introduced into the mosquito Aedes aegypti, the Wolbachia strain wMelPop was not found in the five natural predator species tested after preying on larvae or adults [START_REF] Hurst | Impacts of Wolbachia infection on predator prey relationships: evaluating survival and horizontal transfer between wMelpop infected Aedes aegypti and its predators[END_REF]. In one case, predators became Wolbachia-positive when Phytoseiulus persimilis mites were experimentally fed with symbiotic larvae of the spider mite Tetranychus urticae [START_REF] Enigl | Negative evidence of Wolbachia in the predaceous mite Phytoseiulus persimilis[END_REF]. However, the Wolbachia were restricted to the predator gut and starvation sufficed to erase all trace of infection, showing that, in this case, the Wolbachia did not cross the intestine wall.

Here, we show that after ingestion of an A. vulgare ''prey'', wVulC Wolbachia cells were detected in organs and blood of two different ''predator'' species. This indicates for the first time that some Wolbachia were able to resist the digestive process, to pass through the intestine barrier and to infect the tested tissues (i.e. ovaries, CNS and hemocytes). The efficiency of such a transfer was very high since 100% of the ''predators'' of both species were infected by wVulC, even if all their tested tissues were not always infected at 180 days PI. Overall, the titers of Wolbachia were higher after intraspecific passages in A. vulgare via cannibalism than after interspecific passages in P. d. dilatatus via predation.

However, the wVulC titers in all tested tissues remained very low compared to those recorded in naturally infected A. vulgare or after injection of Wolbachia in the haemocoel of initially asymbiotic individuals of P. d. dilatatus or A. vulgare [START_REF] Clec | High virulence of Wolbachia after host switching: when autophagy hurts[END_REF]. Moreover, the Wolbachia loads did not increase between 90 and 180 days after ingestion, suggesting very low or no multiplication. It can be hypothesized that due to the stress generated by the environment of the digestive tract, the Wolbachia switched to a form that does not multiply or does so at a very low rate. A first hypothesis to further explain this pattern is that only very few Wolbachia variants were able to cross the intestine wall and then multiplied to reach only a low density in the host. Thus, this strong bottleneck would have selected for the Wolbachia that are more resistant while exhibiting lower multiplication rates, according to a growth/ survival trade-off [START_REF] Aertsen | Stress and how bacteria cope with death and survival[END_REF]. A second hypothesis is that many bacteria survived the intestine, crossed the wall and colonized the tissues as a ''non-replicative form'' that slowly decayed over months. The ability of Wolbachia to produce ''non-replicative forms'' has not yet been closely investigated. However, it has been shown previously that Wolbachia is able to survive without replicating in stressful conditions like heat treatment [START_REF] Juchault | Induction par la tempe ´rature d'une physiologie ma ˆle chez les ne ´o-femelles et les intersexue ´s du crustace ´oniscoı ¨de Armadillidium vulgare latr., he ´bergeant un bacte ´roı ¨de a `action fe ´minisante[END_REF][START_REF] Juchault | Effets de la tempe ´rature sur le sex ratio de la descendance et la physiologie sexuelle des femelles d'Armadillidium vulgare latr. (crustacea, oniscidea) he ´bergeant une bacte ´rie fe ´minisante[END_REF] or upon extracellular maintaining for as long as one week [START_REF] Rigaud | Feminizing endocytobiosis in the terrestrial crustacean Armadillidium vulgare latr. (isopoda): recent acquisitions[END_REF][START_REF] Rasgon | Survival of Wolbachia pipientis in cell-free medium[END_REF]. At 180 days PI, we found tissues of some individuals without Wolbachia infection: Ovaries of some P. d. dilatatus and ovaries, CNS and hemocytes of some A. vulgare. We cannot exclude that these tissues had never been infected. However, since all tissues were infected in all animals tested at 90 days PI, we rather suspect that the bacteria died, either because of their inability to recover from the stress encountered during the horizontal passage and/or due to host reactions such as autophagy or apoptosis that are known to be involved in the elimination of Wolbachia from host cells [START_REF] Clec | High virulence of Wolbachia after host switching: when autophagy hurts[END_REF][START_REF] Zhukova | The virulent Wolbachia strain wMelpop increases the frequency of apoptosis in the female germline cells of Drosophila melanogaster[END_REF][START_REF] Voronin | Autophagy regulates Wolbachia populations across diverse symbiotic associations[END_REF].

Among all the tested tissues, the CNS presented an interesting pattern: The infection was low but seemed to be stable until 180 days PI in both species. Regardless of the transinfection mode (i.e. injection or ingestion), the wVulC strain seems to colonize the CNS in a more extensive way than the other tissues [START_REF] Clec | High virulence of Wolbachia after host switching: when autophagy hurts[END_REF]. This tissue seems to constitute a kind of refuge for the Wolbachia, possibly because nerve cells are renewed less frequently compared to hemocytes and oocytes. However, in the nerve cells of individuals infected by the predation route, the infection was stable but low and did not trigger the pathogenic phenotype described in P. d. dilatatus injected with wVulC from A. vulgare ovaries [START_REF] Clec | High virulence of Wolbachia after host switching: when autophagy hurts[END_REF].

In this study, we demonstrate that predation and cannibalism can lead to the ingestion of Wolbachia in terrestrial isopods. Moreover, following this ingestion the presence of Wolbachia is not restricted to the intestine as other organs were tested positive. This demonstrates that Wolbachia wVulC is capable of crossing the intestine barrier and to survive, at least transiently, in a predator's body.

Figure 1 .

 1 Figure 1. Wolbachia loads in CNS, ovaries and hemocytes of the ''predators'' Porcellio d. dilatatus and Armadillidium vulgare. The Wolbachia quantifications performed at 90 and 180 days post-ingestion (PI) revealed that the symbiont colonizes all tissues of the asymbiotic ''predators'' after ingestion of infected ''preys''. Comparison of the Wolbachia titers between the two predator species (i.e. P. d. dilatatus or A. vulgare) revealed that bacterial loads were higher in A. vulgare, the native host of wVulC strain, at 90 days PI. Comparison of Wolbachia titers in the different tissues of P. d. dilatatus between 90 and 180 days PI showed that the infection was stable in ovaries and CNS but decreased in hemocytes. (Nat.titer: The Wolbachia titer in the ''prey'' hemolymph; #: No A. vulgare were infected with Wolbachia among the two tested animals). doi:10.1371/journal.pone.0060232.g001

Figure 2 .

 2 Figure 2. Fluorescence in situ Hybridization (FISH) detection of Wolbachia in circulating hemocytes of the ''predators'' Porcellio d. dilatatus and Armadillidium vulgare 180 days after having ingested of an infected prey. Some hemocytes of P. d. dilatatus (A and B) and of A. vulgare (C and D) were infected with Wolbachia (3 and 8% of hemocytes, respectively). A-D: Wolbachia in red, Actin in green, nuclei in blue. doi:10.1371/journal.pone.0060232.g002

Table 1 .

 1 Wolbachia detection in predators 180 days after ingestion of an infected prey.

				Wolbachia detection in		Wolbachia detection in
		Total	Alive	ovaries	Wolbachia detection in CNS	hemocytes
	Porcellio d. dilatatus	15	13	4/13	13/13	13/13
	Armadillidium vulgare	15	2	0/2	1/2	1/2

doi:10.1371/journal.pone.0060232.t001

PLOS ONE | www.plosone.org

April 2013 | Volume 8 | Issue 4 | e60232

Acknowledgments

We thank all the technical staff of the UMR CNRS 7267. We also thank Jessica Dittmer for comments on previous versions of the manuscript.

This work was supported by the Agence Nationale de la Recherche (ADaWOL ANR-09-JCJC-0109-01 coordinated by Dr Mathieu Sicard). Winka Le Clec'h's work was supported by a grant from Re ´gion Poitou-charentes. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Author Contributions


V Guiot

L Cario

E Janod

B Corraze

V Ta Phuoc

M Rozenberg

P Stoliar

T Cren

D Roditchev

Resistive switching induced by electronic avalanche breakdown in GaTa 4 Se 8-x Te x narrow gap Mott Insulators

Keywords: numbers: 75.47.Gk, 75.50.Dd, 72.80.Ga

Mott transitions induced by strong electric fields are receiving a growing interest. Recent theoretical proposals have focused on the Zener dielectric breakdown in Mott insulators, however experimental studies are still too scarce to conclude about the mechanism. Here we report a study of the dielectric breakdown in the narrow gap Mott insulators GaTa 4 Se 8-x Te x . We find that the I-V characteristics and the magnitude of the threshold electric field (E th ) do not correspond to a Zener breakdown, but rather to an avalanche breakdown. E th increases as a power law of the Mott Hubbard gap (E g ), in surprising agreement with the universal law E th ∝E g 2. 5 reported for avalanche breakdown in semiconductors. However, the delay time for the avalanche that we observe in Mott insulators is over three orders of magnitude longer than in conventional semiconductors. Our results suggest that the electric field induces local insulator-to-metal Mott transitions that create conductive domains which grow to form filamentary paths across the sample.

In many materials with partially filled d bands, the electron motion is frozen as a result of strong repulsive interactions, which drive the system into a Mott insulating state [START_REF] Mott | Metal-Insulator Transitions[END_REF][START_REF] Imada | Metal-insulator transitions[END_REF]. Introduction of carriers in a Mott insulator often leads to exotic properties, such as high-Tc superconductivity in cuprates [START_REF] Bednorz | Possible high Tc superconductivity in the Ba-La-Cu-O system[END_REF] and colossal magnetoresistance in manganites [START_REF] Jin | Thousandfold Change in Resistivity in Magnetoresistive La-Ca-Mn-O Films[END_REF]. A Mott insulator can also be collapsed into a correlated metal by applying pressure. Notable examples are V 2 O 3 [START_REF] Limelette | Universality and Critical Behavior at the Mott Transition[END_REF] and organics [START_REF] Kagawa | Unconventional critical behaviour in a quasi-two-dimensional organic conductor[END_REF]. Another important type of Mott transition, which is receiving a great deal of attention, is the dielectric breakdown caused by strong electric fields. Many recent theoretical studies have focused on the Zener mechanism of breakdown for Mott insulators. For instance, calculations were performed in 1D Hubbard chains using exact diagonalization [START_REF] Oka | Ground-State Decay Rate for the Zener Breakdown in Band and Mott Insulators[END_REF][START_REF] Oka | Dielectric breakdown in a Mott insulator: Many-body Schwinger-Landau-Zener mechanism studied with a generalized Bethe ansatz[END_REF][START_REF] Oka | Breakdown of a Mott Insulator: A Nonadiabatic Tunneling Mechanism[END_REF][START_REF] Oka | Nonlinear transport in a one-dimensional Mott insulator in strong electric fields[END_REF] and time-dependent density matrix renormalization group [START_REF] Heidrich-Meisner | Nonequilibrium electronic transport in a one-dimensional Mott insulator[END_REF], or in the limit of large dimensions using dynamical mean field theory [START_REF] Eckstein | Dielectric Breakdown of Mott Insulators in Dynamical Mean-Field Theory[END_REF]. These theoretical studies predicted a similar non-linear behavior in the current-voltage characteristics, and the existence of a threshold field (E th ) beyond which a field induced metal appears. In the latter case, where the Mott transition occurs beyond a critical value of the Coulomb interaction which is of similar magnitude as the bandwidth, it was found that E th is proportional to ∆ 2 /v F , with ∆ the charge gap, and v F the Fermi velocity. This implies a large threshold field of the order of 10 6 -10 7 V/cm, which is substantially larger than the experimental values observed in dielectric breakdown [START_REF] Taguchi | Dielectric breakdown of onedimensional Mott insulators Sr2CuO3 and SrCuO2[END_REF]. Surprisingly, compared to this significant theoretical effort, experimental studies of Mott insulators under strong electric fields remain quite scarce. Taguchi et al. observed a dielectric breakdown in the quasi-one-dimensional Mott insulators Sr 2 CuO 3 and SrCuO 2 [START_REF] Taguchi | Dielectric breakdown of onedimensional Mott insulators Sr2CuO3 and SrCuO2[END_REF]. More recently a comparable dielectric breakdown was observed in the family of chalcogenide Mott insulators AM 4 Q 8 (A = Ga, Ge; M = V, Nb, Ta, Mo; Q = S, Se) [START_REF] Vaju | Electric-pulse-driven electronic phase separation, insulator-metal transition, and possible superconductivity in a Mott insulator[END_REF][START_REF] Vaju | Electric-Pulse-Induced Resistive Switching and Possible Superconductivity in the Mott Insulator GaTa4Se8[END_REF][START_REF] Dubost | Electric-Field-Assisted Nanostructuring of a Mott Insulator[END_REF][START_REF] Cario | Electric-Field-Induced Resistive Switching in a Family of Mott Insulators: Towards a New Class of RRAM Memories[END_REF][START_REF] Souchier | First evidence of resistive switching in polycrystalline GaV4S8 thin layers[END_REF]. However in both cases E th is of the order of 10 2 -10 4 V/cm which does not match with theoretical predictions for Zener breakdown. This strong discrepancy raises therefore the question of the actual physical origin of the observed breakdown. Here we focus our study on the chalcogenide Mott insulators AM 4 Q 8 and show that the dielectric breakdown is consistent with an electric field induced avalanche phenomenon rather than Zener breakdown. Our work reveals that the I(V) curve, the magnitude of E th and the dependence of E th versus the Mott-Hubbard gap are those expected for an avalanche breakdown, qualitatively similar to what is observed in semiconductors. However, our results also reveal significant differences, for instance, a delay time for the avalanche that is at least three orders of magnitude longer in the Mott insulators AM 4 Q 8 compared to the case of conventional band insulators. The lacunar spinel compounds AM 4 Q 8 , with tetrahedral transition metal clusters (see Fig. 1) [START_REF] Ben Yaich | Nouveaux chalcogénures et chalcohalogénures à clusters tétraédriques Nb4 ou Ta4[END_REF], represents an interesting family of narrow gap Mott insulators. The low Mott gap value makes these compounds highly sensitive to doping or pressure. Doping of GaV 4 S 8 by Ti leads, for example, to a filling control Insulator to Metal Transition (IMT) with the emergence of a ferromagnetic half metal [START_REF] Vaju | Metal-metal bonding and correlated metallic behavior in the new deficient spinel Ga0.87Ti4S8[END_REF][START_REF] Dorolti | Half-Metallic Ferromagnetism and Large Negative Magnetoresistance in the New Lacunar Spinel GaTi3VS8[END_REF]. On the other hand, an external pressure induces a bandwidth controlled IMT and superconductivity in GaTa 4 Se 8 [START_REF] Abd-Elmeguid | Transition from Mott Insulator to Superconductor in GaNb4Se8 and GaTa4Se8 under High Pressure[END_REF][START_REF] Pocha | Crystal Structures, Electronic Properties, and Pressure-Induced Superconductivity of the Tetrahedral Cluster Compounds GaNb4S8, GaNb4Se8, and GaTa4Se8[END_REF]. Recently, we have reported that electric field leads to a striking volatile IMT or dielectric breakdown in GaTa 4 Se 8 [START_REF] Vaju | Electric-pulse-driven electronic phase separation, insulator-metal transition, and possible superconductivity in a Mott insulator[END_REF][START_REF] Vaju | Electric-Pulse-Induced Resistive Switching and Possible Superconductivity in the Mott Insulator GaTa4Se8[END_REF][START_REF] Dubost | Electric-Field-Assisted Nanostructuring of a Mott Insulator[END_REF][START_REF] Cario | Electric-Field-Induced Resistive Switching in a Family of Mott Insulators: Towards a New Class of RRAM Memories[END_REF] which is qualitatively different from the non-volatile resistive switching based on electrochemical effects reported so far in many transition metal oxides [START_REF] Cario | Electric-Field-Induced Resistive Switching in a Family of Mott Insulators: Towards a New Class of RRAM Memories[END_REF][START_REF] Waser | Nanoionics-based resistive switching memories[END_REF][START_REF] Rozenberg | Resistive switching[END_REF].

RESULTS

Mott-Hubbard gap evolution in the

In order to study the origin of this dielectric breakdown and to explore its relationship with the Mott Hubbard gap we have investigated the electric field effects in the series of compounds GaTa 4 Se 8-x Te x (x=0, 4.0, 6.0, 6.5). These compounds were synthesized as described elsewhere [START_REF] Guiot | Control of the electronic properties and resistive switching in the new series of Mott Insulators GaTa4Se8-yTey (0≤y≤6.5)[END_REF]. Optical conductivity and resistivity measurements were subsequently undertaken to evaluate the gap evolution in this series. The room temperature optical conductivity of GaTa 4 Se 8 , shown in Fig. 1b, displays all the expected features of a narrow gap Mott Insulator with a Hubbard energy (U) of the order of 0.55 eV [START_REF] Ta Phuoc | Optical Conductivity Measurements of GaTa4Se8 Under High Pressure: Evidence of a Bandwidth-Controlled Insulator-to-Metal Mott Transition[END_REF]. The low bias resistivities ρ(T) measured with a standard four probes technique for the series of compounds GaTa 4 Se 8-x Te x exhibit a semiconducting-like behavior with a temperature dependence consistent with an activation law at high temperature (see Fig. 1-c). The systematic change of the activation energy observed in Fig. 1 suggests that the substitution of Se per Te permits the bandwidth-control of the Mott Hubbard gap (from 100 to 300 meV) within the GaTa 4 Se 8-x Te x series of compounds, thus enabling the study of the threshold field dependence with the size of the gap.

Dielectric breakdown experiments in the

GaTa 4 Se 8-x Te x Mott insulators Dielectric breakdown was systematically studied in this series of narrow gap Mott insulators using a procedure described in the Methods section. Figure 2 shows that these compounds undergo a sudden volatile dielectric breakdown above a certain threshold electric field (≈1-10 kV/cm). As an example, Fig. 2c depicts the typical temporal evolution of the voltage V S (t) across a GaTa 4 Se 8 crystal while a series of short (10 to 70 µs) voltage pulses (V pulse ) are applied. When the electric field applied to the crystal exceeds a threshold field of ≈ 2.5 kV/cm the crystal systematically undergoes a fast transition to a low resistance state (i.e. from 70 kΩ to 5 kΩ ) called a dielectric breakdown or resistive switching. This transition is volatile and perfectly reproducible. In fact, after the pulse application the low-bias resistance returns to its original value. The delay t delay between the application of the pulse and the dielectric breakdown shifts to smaller values with increasing applied voltage. The voltage drop on the sample V S in the breakdown state is always V S ≈ 9 V (or E th ≈ 2.5 kV/cm) whatever the voltage applied to the sample before the resistive switching. On the other hand, the current flowing through the sample after the dielectric breakdown shows a highly non- ohmic behavior in the transited state in both, pulse or dc measurements (see Fig. 2-b). Thus, we infer that E th (i.e. V th /d where d is the distance between electrodes) corresponds to the breakdown field for the limiting case t delay → ∞. The same qualitative behavior was observed for GaTa 4 Se 1.5 Te 6.5 (see Fig. 2a), all other GaTa 4 Se 8-x Te x compounds, and more generally for all AM 4 Q 8 (A = Ga, Ge; M = V, Nb, Ta, Mo; Q = S, Se) Mott insulator compounds [START_REF] Cario | Electric-Field-Induced Resistive Switching in a Family of Mott Insulators: Towards a New Class of RRAM Memories[END_REF].

Dielectric breakdown mechanism in the

GaTa 4 Se 8-x Te x Mott insulators

For conventional semiconductors the dielectric breakdown is well documented and different mechanisms are proposed such as Zener tunneling [START_REF] Zener | A Theory of the Electrical Breakdown of Solid Dielectrics[END_REF] or avalanche process [START_REF] Levinshtein | Breakdown Phenomena in Semiconductors and Semiconductor Devices[END_REF]. The threshold field observed in the AM 4 Q 8 compounds is at least 3 orders of magnitude smaller than the threshold field of the order of 10 6 -10 7 V/cm expected for Zener breakdown in Mott insulators [START_REF] Oka | Ground-State Decay Rate for the Zener Breakdown in Band and Mott Insulators[END_REF]. This definitively rules out a Zener breakdown mechanism. Conversely, the magnitude of the threshold field in AM 4 Q 8 Mott insulators compares well with the threshold field values of 1 and 40 kV/cm observed for avalanche breakdowns in narrow gap semiconductors InSb and InAs, respectively [START_REF] Hudgins | An Assessment of Wide Bandgap Semiconductors for Power Devices[END_REF][START_REF] Hudgins | Wide and Narrow Bandgap Semiconductors for Power Electronics: A New Valuation[END_REF]. The I(V) characteristics observed in the AM 4 Q 8 compounds and in semiconductors like InSb, InAs, Si or Ge are also very similar [START_REF] Levinshtein | Breakdown Phenomena in Semiconductors and Semiconductor Devices[END_REF]. Indeed, all these compounds exhibit a steep increase of the current at the threshold field, which is almost vertical. In narrow gap semiconductors this is related to the impact-ionization process. An avalanche breakdown indeed occurs when the electrons accelerated by the applied voltage can gain enough energy to ionize by impact other electrons above the band gap and generate electron-hole pairs [START_REF] Levinshtein | Breakdown Phenomena in Semiconductors and Semiconductor Devices[END_REF]. When the creation of electron-hole pair by impactionization overcompensates the electron-hole recombination process (Auger Thermal process) a multiplication of carriers occurs and induces a dielectric breakdown with a steep increase of the current at the threshold field. For high current density the avalanche breakdown is characterised by a negative differential resistance (NDR) in the current-voltage characteristic which is the consequence of the contribution of holes to the field distribution along the sample [START_REF] Levinshtein | Breakdown Phenomena in Semiconductors and Semiconductor Devices[END_REF]. As shown in Fig. 2, such a NDR effect is observed on the I-V curve of GaTa 4 Se 8 measured in DC mode using a current source. Again, this strongly supports an avalanche mechanism as the origin of the dielectric breakdown.

Dependence of the avalanche threshold field in Mott insulators and classical semiconductors

For semiconductors the avalanche threshold field varies as a function of a power law of the band gap [START_REF] Levinshtein | Breakdown Phenomena in Semiconductors and Semiconductor Devices[END_REF] and follows the universal law E th ∝ Eg 2.5 [START_REF] Hudgins | An Assessment of Wide Bandgap Semiconductors for Power Devices[END_REF][START_REF] Hudgins | Wide and Narrow Bandgap Semiconductors for Power Electronics: A New Valuation[END_REF]. For comparison Fig. 3 displays the variation of the threshold field as a function of the Mott-Hubbard gap for all the AM 4 Q 8 compounds. This figure reveals a remarkable power law dependence of the threshold fields with the gap E th ∝ Eg 2.5 (see blue curve in fig 3). The inset of Fig. 3 compares also the threshold fields versus gap dependence for the AM 4 Q 8 compounds and classical semiconductors. This comparison reveals that for all Mott and band insulators or semiconductors the threshold fields line up along a universal law E th ∝ Eg 2.5 . This is again strong

DISCUSSION

This scaling of the Mott-and band-insulators along the same universal law E th = 1.73 E g 2.5 indicates that the threshold field in the avalanche breakdown depends only on the gap whatever its origin and nature. This is rather surprising as the excitation gap in Mott insulators arises from electron-electron repulsions, (i.e. from strong correlation effects), in stark contrast with the case of conventional semiconductors. Despite this similarity, as we mentioned before, the main qualitative difference between the electric breakdown in semiconductors and Mott insulators is the significantly longer t delay of the latter. The origin of the difference may be due to the different coupling to the lattice degrees of freedom. The Mott transition is indeed accompanied of a compressibility anomaly [START_REF] Kotliar | Compressibility Divergence and the Finite Temperature Mott Transition[END_REF][START_REF] Hassan | Sound Velocity Anomaly at the Mott Transition: Application to Organic Conductors and V2O3[END_REF] which leads to a large volume change [START_REF] Mcwhan | Metal-Insulator Transitions in Pure and Doped V2O3[END_REF]. In fact, the giant electromechanical coupling observed during an STM studies by applying electric pulses between the tip and a cleaved GaTa 4 Se 8 crystal surface supports this scenario [START_REF] Dubost | Electric-Field-Assisted Nanostructuring of a Mott Insulator[END_REF]. Therefore, the strong coupling of the electronic and lattice degrees of freedom is likely to slow down significantly the velocity of the avalanche propagation. Interestingly, Fig. 2 shows that the dielectric breakdown in the AM 4 Q 8 Mott insulators occurs with a t delay in the µs range (from a few µs to the ms) for typical sample lengths d=20-40 µm. In contrast, in semiconductors the t delay lies in the ps to the ns range, that is, several orders of magnitude faster [START_REF] Levinshtein | Breakdown Phenomena in Semiconductors and Semiconductor Devices[END_REF]. Figure 4 displays the avalanche velocity v = d/t delay as a function of excess electric field E-E th where E is the electric field applied on the sample. This figure shows that v varies as (E-E th ) 3 . This remarkable power law dependence as well as the magnitude of the velocity in m/s range recall a phase growth mechanism [START_REF] Willnecker | Dislocation velocities, dislocation densities, and plastic flow in lithium fluoride crystals[END_REF] or the propagation of dislocations [START_REF] Messerschmidt | Dislocation Dynamics During Plastic Deformation[END_REF][START_REF] Johnston | Dislocation velocities, dislocation densities, and plastic flow in lithium fluoride crystals[END_REF]. This analysis therefore suggests that the excess electric field triggers the local growth of conducting domains where a Mott transition has taken place, which eventually form filamentary paths across the sample as the avalanche breakdown occurs.

A mathematical modeling of the previous scenario was undertaken to describe the experimental data. This model considers a one dimensional resistive network where each cell may be in one of two states, insulator (I) or metal (M), characterised by their corresponding resistance r I and r M , and their energy E I and E M . This model also assumes that the two states are separated by an energy barrier of height E B -E I . The energy landscape used for the calculation is shown in Supplementary Fig- ure S1. Initially, all cells are in the insulating state, since the system is a Mott insulator. An external voltage pulse V pulse is then applied on the resistor network and the local voltage drops on the cells are computed. The cells may undergo a transition from state I to M by a thermal activation process.The effective activation energy barrier, for an I to M transition of the i-th cell under the action of the applied voltage, is(E B -E I -∆V i ), where ∆V i is the computed voltage drop at the cell. These assumptions lead to non-linear differential equation for the rate of cell transitions per unit time. Further details of the mathematical expressions are provided in the Methods section. The solution of the differential equation is easily obtained by standard numerical integration. The results are shown in Fig. 2(d). We observe that this simple model qualitatively captures the behavior of t delay of the avalanche mechanism. Initially, the conductive path modeled by the resistive network is highly resistive, so there is a small voltage drop on each cell, and the rate of transitions is low. Successive transitions, however, lower the resistance of the path, as r M << r I , therefore increasing the current and also the voltage drop ∆V i in the cells that still remain insulating. The increased ∆V i lowers the local energy activation barriers, thus augmenting the transition rates. A larger fraction of cells undergo a transition and, eventually, a runaway process take place were the rest of the cells rapidly completes their transitions. Interestingly, this simple model also qualitatively accounts for the field dependence of the velocity of the transition as shown in Supplementary Figure S2 and in Fig. 4. However the power law behavior predicted by this simple model is parameter dependent, i.e. is non universal.

To conclude we have reported for the first time an avalanche breakdown in the narrow gap Mott insulators AM 4 Q 8 . The phenomenology of the breakdown (I(V) characteristic) and the magnitude of the threshold electric field are comparable with those reported for avalanche breakdowns in semiconductors. Moreover the threshold field dependence with the width of the Mott Hubbard gap shows a surprising agreement with the universal law E th = 1.73 Eg 2.5 reported for semiconductors, despite the fact that the AM 4 Q 8 are strongly correlated systems. Our experimental and theoretical investigations suggest that, unlike semiconductors, avalanche breakdown in Mott insulators is associated to the growth of conducting filamentary paths of a metallic metastable phase within the sample. The strong coupling of electronic and lattice degrees of freedom due to compressibility anomalies may account for the reduced avalanche speed observed in the Mott insulators compared to conventional band insulators. Finally, our work suggests that avalanche breakdown may be a general feature of narrow gap Mott insulators.

METHODS

Sample preparation

Single crystals of GaTa 4 Se 8-y Te y with y ranging from 0 to 6.5 were prepared using stoichiometric mixtures of elemental gallium, tantalum, selenium and tellurium (purities ≥ 99,5 %) [START_REF] Guiot | Control of the electronic properties and resistive switching in the new series of Mott Insulators GaTa4Se8-yTey (0≤y≤6.5)[END_REF]. These mixtures were loaded in evacuated sealed quartz ampules of about 10 cm and heated up at 300 • C/h to 1000 • C and hold at this temperature during 160h. The quartz tubes were subsequently cooled down, first slowly to 800 • C at 1 • C/h and then faster (300 • C/h) to room temperature. These syntheses yielded black powders containing a high yield of GaTa 4 Se 8-y Te y metallic-gray cubic and tetrahedral crystals (typical size ≤ 300 µm) along with a small amount of impurity phases (e.g. GaTe, TaSe 2 ). Large amounts of tetrahedral or cubic-shaped crystals of all other members of the AM 4 Q 8 family have been obtained using a similar procedure.

Transport measurements

The AM 4 Q 8 crystals used for transport measurements were contacted using 17 µm gold wires and carbon paste (Electrodag PR-406), and then annealed in vacuum at 150 • C during 30 minutes. The low-bias resistance of the AM 4 Q 8 was measured using a source-measure unit (either a Keithley 236 or a Keithley 6430) by a standard two-or four-probe technique. We checked that the contact resistances were much smaller than the sample resistance. Voltage pulses were applied using an Agilent 8114A. During the pulse, the voltage and current across the sample were measured with a Tektronix DPO3034 oscilloscope associated with a IeS-ISSD210 differential probe, using the simple circuit described in the inset of Fig 2-a.

Mathematical Modeling

In order to obtain Figures 2d and4b we numerically integrated

dx dt = ν • exp - E B -E I -V i k B T (1)
by using 4th order Runge-Kutta method (time step = 0.001). Here x is the fraction of cells in metallic state. E B , E I , and V i are defined as displayed in Supplementary Figure S1. We set ν = 0.001, k B T = 1, E B -E I = 1 and

V i = V pulse • r I r I • (1 -x) + r M • x + R L . (2)
For Figure 2d we simulated V pulse = 2.5, 3, 3.5, 4, 4.5, 5 and 5.5. Figure 4b presents the switching times for the 5

GaTa 4

 4 Se 8-x Te x compounds

FIG. 1 :

 1 FIG. 1: Resistivity and optical conductivity measurements. (a) representation of the lacunar spinel structure of the AM4Q8 compounds. Blue, orange and Yellow filled circle represents M, A and Q atoms respectively. The M4 tetrahedral cluster and the AQ4 tetrahedra are highlighted in blue and orange, respectively (b) experimental optical conductivity of GaTa4Se8 (green line) showing that the optical conductivity is that expected for a Mott Insulator with an Hubbard energy U= 0.55eV and a gap close to 0.12 eV. The gray solid line corresponds to the fit of optical conductivity spectrum using two contributions : a broad mid-infrared band (red shaded area) and high-frequencies contributions (thick solid red line). (c) Resistivity as a function of inverse temperature for GaTa4Se8 (filled green triangle), GaTa4Se4Te4 (black open triangle), GaTa4Se2Te6 (blue open square), and GaTa4Se1.5Te6.5 (filled red square).

FIG. 2 :

 2 FIG. 2: Resistive switching experiments and modeling. (a)I-V curves extracted from pulse (open circles and squares) experiments for a crystal of GaTa4Se1.5Te6.5. The circuit used to apply voltage pulses is shown in inset. (b) I-V curves extracted from pulse (open circles and squares) or DC experiments (plain or dashed lines) for a crystal of GaTa4Se8. (c) Evolution of the voltage Vs(t) across a crystal of GaTa4Se8 when short voltage pulses Vpulse (10-70 µs) of increasing magnitude are applied to the circuit. For example, Vpulse = 5V , 35V, 40V, 44V, 50V, 60V and 86V for the gray, blue, black, green, pink, light blue and orange curves, respectively. These curves show a clear evolution of the time (t delay ) at which occurs the transition to a low resistance state (resistive switching) as a function of V pulse . In (a) and (b) the I-V curves are extracted from Vs(t) curves similar to the one shown in (c) and from the corresponding I(t) curves not shown here. In (a) and (b) open circles correspond to the I-V values measured before the resistive switching and open squares correspond to the I-V values measured after the resistive switching. (d) Results of mathematical modeling of Vs(t) using a one dimensional resistive network. The time at which occurs the resistive switching decreases as the applied voltage to the resistor network is increased from the black to the orange curve.

FIG. 3 :

 3 FIG. 3: Dependence of E th in Mott insulators and semiconductors. Threshold Electric field (inducing avalanche breakdown) as a function of the Mott gap for various AM4Q8 compounds. The solid blue curve correspond to a power law dependence E th ∝ Eg 2.5 . Inset : comparison of the threshold fields versus gap dependence for the AM4Q8 compounds and for classical semiconductors. The solid blue line displays the universal law E th [kV/cm] = 173 (Eg[eV]) 2.5 observed for semiconductors.

FIG. 4 :

 4 FIG. 4: Avalanche velocity in Mott Insulators. (a) Avalanche velocity v = d/t delay for various AM4Q8 compounds as a function of excess electric field E-E th where E is the electric field applied on the sample. (b) velocity of the transition 1/t delay extracted from the mathematical modeling of the resistive switching shown in figure 2d.

ACKNOWLEDGMENTS

This work was supported by the French Agence Nationale de la Recherche through the funding of the NV-CER (ANR-05-JCJC-0123-01) and NanoMott (ANR-09-Blan-0154-01) projects.

higher values. The 1D resistivities were set as 10 • r M = R L and r I = 10 • R L . V S was obtained as:

t -1 delay was calculated as the inverse of the number of Runge-Kutta cycles needed for x to arrive to 1. Another output of this numerical simulation is presented in Supplementary Figure S2, the evolution of dx dt in time.

Author Contributions

L.C., E.J. and B.C. initiated the project. V.G., L.C., E.J. and B.C. performed the synthesis and the caracterisations of the crystals, and the resistive switching experiments. V.T.P. did the optical conductivity measurements. P.S. and M.R. did the modeling. L.C., E.J., B.C., V.G., V.T.P., D.R., T.C., P.S. and M.R discussed and wrote the article in the framework of the NanoMott project.

Competing financial interest

the author declare no competing financial interest