Dr Thomas Hueso
email: hueso.th@gmail.com

Anne-Sophie Godron

Emilie Lanoy

Jérôme Pacanowski

Laura Levi

Emmanuelle Gras

Laure Surgers

Amina Guemriche

Jean-Luc Meynard

France Pirenne

Salim Idri

Pierre Tiberghien

Pascal Morel

Caroline Besson

Rémy Duléry

Sylvain Lamure

Olivier Hermine

Amandine Gagneux-Brunon

Nathalie Freymond

Sophie Grabar

Karine Lacombe
email: karine.lacombe2@aphp.fr

Hemoplasm Study Group

Karine Pr

Lacombe

Convalescent plasma improves overall survival in patients with B-cell lymphoid malignancy and COVID-19: a longitudinal cohort and propensity score analysis

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

The HEMOPLASM study group: Thomas Perpoint (Hôpital Croix-Rousse, HCL); Mathieu Mahevas (Hôpital Henri-Mondor, APHP), Arsène Mekinian (Hôpital Saint-Antoine, APHP); Claire Rouzaud (Hôpital Necker, APHP), Satnislas Faguer (CHU Toulouse); Fatiha Merabet (CH Versailles), Philippe Petua

Introduction

Patients with hematological malignancies and SARS-CoV2 infection display a high rate mortality with an estimated risk of death of 34% that reach 39% in hospitalized patients [START_REF] Vijenthira | Outcomes of patients with hematologic malignancies and COVID-19: a systematic review and meta-analysis of 3377 patients[END_REF][START_REF] Robilotti | Determinants of COVID-19 disease severity in patients with cancer[END_REF] . In such patients, several studies highlighted that both underlying cellular or humoral immunosuppression may hamper virus clearance resulting in prolonged shedding and high risk of severe form of COVID-19 [START_REF] Choi | Persistence and Evolution of SARS-CoV-2 in an Immunocompromised Host[END_REF][START_REF] Michot | Severe COVID-19 in patients with hematological cancers presenting with viremia[END_REF] . Furthermore, vaccine response in patients with hematological malignancies is lower compared to general population especially in patients with B-lymphoid disease [START_REF] Herishanu | Efficacy of the BNT162b2 mRNA COVID-19 vaccine in patients with chronic lymphocytic leukemia[END_REF][START_REF] Malard | Weak immunogenicity of SARS-CoV-2 vaccine in patients with hematologic malignancies[END_REF] . Thus, therapeutic approaches to inhibit viral replication and enhance viral clearance are mandatory in this specific population.

Passive immunotherapy by means of COVID-19 convalescent plasma (CCP) has emerged as a promising therapy to target SARS-CoV2 and achieve clinical recovery [START_REF] Bloch | Deployment of convalescent plasma for the prevention and treatment of COVID-19[END_REF][START_REF] Tiberghien | Collecting and evaluating convalescent plasma for COVID-19 treatment: why and how?[END_REF] . In France, CCP has been proposed in a national monitored access program, notably to hospitalized COVID-19 patients with underlying immunosuppression such as patients with hematological malignancy.

While most randomized trials have not reported a benefit of CCP in a general population with COVID-19 [START_REF] Janiaud | Association of Convalescent Plasma Treatment with Clinical Outcomes in Patients with COVID-19: A Systematic Review and Meta-analysis[END_REF] , we observed that B-cell depleted patients with protracted COVID-19 and unable to mount a specific humoral response may benefit from CCP transfusion along with a decrease of all inflammatory parameters, oxygen weaning and viral clearance [START_REF] Hueso | Convalescent plasma therapy for B-cell-depleted patientswith protracted COVID-19[END_REF] . A retrospective propensity score matched analysis of 966 patients with a wide range of haematological malignancies among whom 143 received CPP found that CCP was associated a 40% lower mortality [START_REF] Thompson | Association of Convalescent Plasma Therapy with Survival in Patients with Hematologic Cancers and COVID-19[END_REF] , without however taking into consideration immortal time bias and specificity of each hematological malignancies [START_REF] Calip | Time-Related Biases in Nonrandomized COVID-19-Era Studies Using Real-world Data[END_REF] . Based on these preliminary and encouraging results, we report on the outcome after CPP transfusion in a cohort of COVID-19 patients with hematological malignancies as well as on the results of a nested comparison of the survival among patients with B-cell neoplasm transfused or not with CCP

Methods

Patients and inclusion criteria

We analyzed all patients with hematological malignancies and virologically-documented The subset of patients with B-lymphoid neoplasm was then compared to a cohort of patients with similar disease who were not treated with CCP in French hospitals during the successive COVID-19 outbreaks periods (Figure 1). Both cohorts were treated as per standard of care for COVID- To study the effectiveness of convalescent plasma therapy in patients with B-cell neoplasms, we compared the 81 patients exposed to CCP with B-cell neoplasms of the CCP cohort with 120 patients non-exposed to CCP with B-cell neoplasms were selected from the cohort described in Dulery et al. (standard group) [START_REF] Duléry | Prolonged in-hospital stay and higher mortality after Covid-19 among patients with non-Hodgkin lymphoma treated with B-cell depleting immunotherapy[END_REF] . To estimate the effect of CCP on survival in non-randomized settings where patients' characteristics associated with CCP exposure could differ in the two groups, an inverse probability of treatment weighting (IPTW) approach was retained aiming to control for indication bias in several population analyses. Individual propensity score, ie the probability of treatment by CCP, was retrieved from logistic regression model including potential confounders both prognostic of survival and associated with CCP indication: age ("<65 years" vs." ≥65 years"), comorbidity (high blood pressure or diabetes or BMI>=25kg/m 2 _yes vs. no), corticosteroid therapy (yes vs. no). A pseudopopulation was built by weighting observations by propensity scores. In order to check if weighting improved the comparability of the two groups, absolute standardized differences were estimated in the unweighted and weighted samples. According to IPTW common practice, standardized differences < 0.20 were considered negligible. For each analysis the distribution of probability of receiving CPP in the two groups was examined visually in order to see if overlap existed and positivity assumption was not violated.

Then, hazard ratios (HR) of death associated with CCP were derived from weighted Cox proportional hazards. Estimates of HR of death associated with CCP from univariable and multivariable (adjusted for variables included in the propensity score and described above)

unweighted Cox proportional hazards model were also provided for main and sensitivity analyses population. Of note, the number of variables included in both IPTW and multivariable models was limited by the relative low number of events; therefore, only variables strongly associated with indication of CCP and with sufficient numbers of patients for each modality were kept. Main analysis was restricted to patients previously treated with anti-CD20 therapy and alive 16 days after hospitalization for COVID-19 that corresponded to the median time of CPP transfusion after hospitalization. In order to limit the immortal time bias which can arise because patients treated with CCP had to survive long enough after hospitalization to receive CPP [START_REF] Calip | Time-Related Biases in Nonrandomized COVID-19-Era Studies Using Real-world Data[END_REF] , a landmark approach was chosen. Follow-up of patients who received CCP after more than 16 days following hospitalization was censored at time of CPP initiation. Since the use of CCP could differ in terms of area and period of recruitment, exposure to cancer therapies and to COVID-19 medications that were not accounted for in IPTW, several sensitivity analyses in which baseline was date of hospitalization were conducted to assess for the robustness of the main results: i) in the overall population of exposed and non-exposed patients to CCP, ii) in a population restricted to anti-CD20 therapy pre-treated patients, excluding patients over 85 years, and patients pre-exposed to tocilizumab, remdesevir or azithromycin/hydroxychloroquine, iv) in a population excluding the first epidemic wave from March, 2020 to June, 2020, v) in a population restricted to Parisregion (Ile-de-France area, see Figure 1 and Table S1). Another sensitivity landmark analysis with baseline at date of hospitalization plus 16 days has been carried out in patients alive 16 days after hospitalization. Of note, other sensitivity analyses on overall population were also adjusted for gender. All analyses were done using R software version 3. 1.

No transfusion-related adverse events were reported after CCP infusion. CCP transfusion was associated with decreased of (d+7 vs d0) temperature (p<0.0001), CRP (p<0.0001), ferritin (p=0.0004) and fibrinogen (p=0.07). Conversely, PCR cycle threshold values significantly increased (p=0.001) (Figure 2). The overall survival was 64.9 % (95 % CI= 56.2-74.9), 77. 4).

Propensity score analysis in patients with B-lymphoid neoplasm

The numbers of patients included in each population analysis are provided in the flow chart Figure 1. The main population analysis included 147 patients pre-exposed to anti-CD20

therapy and alive at day 16 after hospitalization for COVID.

The characteristics of patients of each analyzed population are detailed in supplementary table S1. This table shows that patients treated with CPP differ from the untreated ones, including for variables that could not be included in the propensity score. To account for the latter variables, sensitivity analysis populations restricted to specific wave, to pre-exposure to anti-CD20 or to specific area of hospitalization were performed.

In the main IPTW analysis, the exposure to CCP was associated with a 63% (95% CI=31%-80%) decrease in risk of death in the 16 day-anti-CD20 pre-exposed population as shown in table 4. The HR estimated by IPTW varied across the different analysis populations from 40% in waves 2-4 population to 63% in main analysis population. Multivariable models provided similar results to IPTW (Table 4). Addition of gender to propensity score did not modify the estimation of the effect of the convalescent plasma exposure. Hazard ratios of death associated with each variable included in the propensity score are provided in supplementary table S2.

Discussion

Our study reports the effect of CCP in a large and representative cohort of patients with hematological malignancies and hospitalized for severe COVID-19. Overall 90-days survival was 64.9% for all cohort and 77.9 % in B-cell neoplasm. This appears to be lower than previous studies in particularly in the Thompson et al study with a crude rate mortality of 13.3% 28 days after CCP in patients with hematological malignancies and COVID-19 [START_REF] Thompson | Association of Convalescent Plasma Therapy with Survival in Patients with Hematologic Cancers and COVID-19[END_REF][START_REF] Abani | Convalescent plasma in patients admitted to hospital with COVID-19 (RECOVERY): a randomised controlled, open-label, platform trial[END_REF] .

This difference could be explained by a longer follow up (90 days) and a lower representation of B-cell neoplasm in our cohort.

We report also a significant decrease of all inflammatory parameters as well as negativation of PCR in nasopharyngueal swab at d+7 was also observed, consistent with our previous report [START_REF] Hueso | Convalescent plasma therapy for B-cell-depleted patientswith protracted COVID-19[END_REF] . Furthermore, CPP infusion was well tolerated [START_REF] Joyner | Early safety indicators of COVID-19 convalescent plasma in 5000 patients[END_REF] . As previously described, age and comorbidities such as high blood pressure and COVID-19 severity emerged as the most important risk factors of death due to COVID-19 [START_REF] Passamonti | Clinical characteristics and risk factors associated with COVID-19 severity in patients with haematological malignancies in Italy: a retrospective, multicentre, cohort study[END_REF] . Interestingly, although an increased risk of death was associated with B-depletion therapy such as anti-CD20 or CD19 mAbs in a recently published retrospective lymphoma cohort [START_REF] Duléry | Prolonged in-hospital stay and higher mortality after Covid-19 among patients with non-Hodgkin lymphoma treated with B-cell depleting immunotherapy[END_REF] , previous B-cell therapy depletion was strongly associated with better overall survival in patients receiving convalescent plasma even after adjustment for confounding factors. Since in our study most patients (87%) transfused with CCP had a negative serology for COVID-19, we assume that such patients were unable to produce neutralizing SARS-CoV-2 antibodies due to the underlying hematological disease or the previous administered drugs targeting B-cells [START_REF] Murphy | COVID-19, plasma, and hypogammaglobulinemia[END_REF] . Subsequent transfer of neutralizing antibodies in such patients by mean of CCP transfusion resulted in the control of viral replication and allowed for clinical recovery. The poor benefit of CCP transfusion in patients with plasma cell or myeloid neoplasm, who did not commonly receive previous anti-CD20 or CD19 monoclonal antibodies, supports our hypothesis.

To further investigate the effect of CCP, we compared the subset of CCP-treated patients with B-cell lymphoid malignancies and COVID-19 to a similar cohort of patients who were treated with standard of care only. The methodology used aimed at controlling for biases inherent to observational design of this retrospective comparison, included indication and immortal time biases. We showed that patients with B-cell neoplasm and previously pre-exposed to anti-CD20 therapy treated with CCP exhibited a significantly better survival probability that those who did not received CCP. This important result supports the results reported in a USretrospective cohort [START_REF] Thompson | Association of Convalescent Plasma Therapy with Survival in Patients with Hematologic Cancers and COVID-19[END_REF] and confirms the essential role of convalescent plasma in the COVID-19 therapeutics landscape of patients with B-cell malignancies.

However, those results present several limitations and raise several questions. In our longitudinal cohort, the risk of death reaches 80% and 64 % for myeloid neoplasm and plasma cell neoplasm respectively that is twofold higher than reported in previous studies [START_REF] Vijenthira | Outcomes of patients with hematologic malignancies and COVID-19: a systematic review and meta-analysis of 3377 patients[END_REF] . We have to note a higher COVID-19 severity with 34% of patients with myeloid and plasma-cell neoplasm requiring for mechanical ventilation whereas only 13% for B-cell neoplasm at the time of CCP. In the same way, previous studies reported a better outcome after early CCP transfusion in non-hospitalized patients [START_REF] Libster | Early High-Titer Plasma Therapy to Prevent Severe Covid-19 in Older Adults[END_REF] . Of note, we observed a lower overall survival in patients transfused within the first 10 days after symptoms onset in univariable analysis, an association that disappeared in the multivariable analysis. A similar observation was made in the Recovery trial (in the CCP arm as well as the control arm) and may reflect more severe disease in patients hospitalized early in the course of the disease (Recovery, lancet 2021).

Furthermore, 62% of patients transfused earlier (within the first 10 days) presented with myeloid or plasma-cell neoplasm who did not benefit from CCP transfusion in our cohort.

In our retrospective nested analysis, data were collected prospectively from two data sources: one for patients exposed to CPP and another one for patients not exposed to CPP. Such comparison could not identify causal effect of treatment exposure with the level of proof provided by randomized clinical trials. We have tried to limit bias by using statistical methods controlling indication bias (propensity score) and the immortal bias (time-lead analysis). The benefit of CPP appears to be robustly identified in all our sensitivity analysis. In addition, the main analysis which controls more strictly indication and immortal bias (use of 16 day landmark and IPW) identifies the strongest effect. We also have no data on the type of viral strain that infected the patients who received CPP, and thus could not analyze the impact of virological parameters in the response to CPP. However, during the inclusion period, SARS-CoV2 strains circulating in France were mainly the Wuhan original strain and its alpha variant. We cannot therefore extend our results to the variant of concern Delta that is currently getting dominant world-wide. CCP from convalescent and vaccinated donors exhibit high titer crossvariant antibodies that may provide a higher efficacy than CPP used in our study [START_REF] Tauzin | A single dose of the SARS-CoV-2 vaccine BNT162b2 elicits Fc-mediated antibody effector functions and T cell responses[END_REF][START_REF] Stamatatos | mRNA vaccination boosts cross-variant neutralizing antibodies elicited by SARS-CoV-2 infection[END_REF][START_REF] Liu | Reduced neutralization of SARS-CoV-2 B.1.617 by vaccine and convalescent serum[END_REF] .

We presently favor the issuing of such CCP for treatment of immunosuppressed patients with B-cell malignancies.

Although our study brings some strong arguments in favor of the use of CCP in B-cell depleted COVID-19 patients several recent issues need to be considered. Indeed, initiation of the anti-SARS-CoV-2 vaccination [START_REF] Polack | Safety and Efficacy of the BNT162b2 mRNA Covid-19 Vaccine[END_REF] , the availability and use of anti-spike monoclonal antibodies in patients at risk of developing severe form of COVID-19 [START_REF] Horby | Casirivimab and imdevimab in patients admitted to 4 hospital with COVID-19 (RECOVERY): a randomised, 5 controlled[END_REF] patients [START_REF] Weinreich | REGN-COV2, a Neutralizing Antibody Cocktail, in Outpatients with Covid-19[END_REF] . Besides the cost of such an approach (over 2000 euros per administration compared to 120 euros/CPP) and possibly limited availability, immune escape mutations have been described especially in patients with B-cell lymphoid disease justifying a successful treatment rescue with CCP [START_REF] Pommeret | Bamlanivimab + etesevimab therapy induces SARS-CoV-2 immune escape mutations and secondary clinical deterioration in COVID-19 patients with B-cell malignancies[END_REF][START_REF] Lohr | Bamlanivimab Treatment Leads to Rapid Selection of Immune Escape Variant Carrying the E484K Mutation in a B.1.1.7-Infected and Immunosuppressed Patient[END_REF] . In the light of this, emergence of variants due to protracted shedding or therapy-related selection [START_REF] Kemp | SARS-CoV-2 evolution during treatment of chronic infection[END_REF][START_REF] Cutler | Mechanistic approaches for the prevention and treatment of chronic GVHD[END_REF][START_REF] Martinot | Emerging RNA-Dependent RNA Polymerase Mutation in a Remdesivir-Treated B-cell Immunodeficient Patient With Protracted Coronavirus Disease[END_REF] remains the most important challenge to face. In our series, although we did not assess the SARS-CoV-2 lineages we did not observe a difference of overall survival between the three epidemic outbreaks.

In conclusion, among patients with hematological malignancies and COVID-19, CPP represents an interesting approach especially in patients with in B-cell lymphoid malignancies. Importantly, such patients have poor response to vaccination and may present escape variant due to prolonged shedding or anti-spike mAbs administration. The place of CCP in the treatment of COVID-19 patients unable to mount a humoral response could be strengthened if confirmed in a randomized prospective trial, and should also be discussed in light of the increasing availability of anti-spike monoclonal antibodies.

(

  CH Tarbes), Martin Martinot (CH Colmar), Etienne Crickx (Hôpital Henir Mondor, APHP), Tali-Anne Szwebel (Hôpital Cochin, APHP), Caroline Morbieu (Hôpital Cochin, APHP), Elie Azoulay (Hôpital Saint-Louis, APHP), Emilie Piet (CH Annecy), Giovanna Melica (Hôpital Henri-Mondor, APHP), Fabrice Bruneel (CH Versailles), Joy Mootien (CH Mulhouse), Jean-François Timsit (Hôpital Bichat, APHP), Florent Wallet (Hôpital Croix-Rousse, HCL), Benjamin Wyplosz (hôpital Bicêtre, APHP), Hafid Ait Oufella (hôpital Saint-Antoine, APHP), Ines Devred, Hôpital Saint-Antoine, APHP), Laure Crognier (CHU Rangueil, Toulouse), Caroline Protin (CHU Rangueil Toulouse), Georges-Daniel Calcaianu (GHRMSA), Donatien de Seissan De Marignan (CHU Lyon Sud, HCL), Julien Saussereau (Hôpital Saint-Louis, APHP), Marion Calmette (Hôpital Edouard Herriot, HCL), Paul Le Turnier (CHU Nantes), Agnes Chapelet (CHU Nantes), Guillaume Franchineau (CH Poissy), Paul Loubet (CHU Nimes), Guillaume Dumas (hôpital Saint-Louis, APHP), Victor Gerber (CH Colmar), Anne Bergeron (Hôpital Saint-Louis, APHP), Kevin Alexandre (CHU Rouen), Axel Ursenbach (CHU Strasbourg), Elise Yvin (Hôpital Saint-Louis, APHP), Ana Berceanu (CHU Besançon), Charlotte Wemmert (Hôpital Henri Mondor, APHP), Marie-Anne Lafont (CH Albi), Virginie Vitrat (CH Annecy), Mylène Maillet (CH Annecy), Maleka Schenck (CHU Hautepierre, HCL), Maxime Desgrouas (CH Orléans), Adrien Robine (Bourg-en-Bresse), Camille Munck (Hôpital Saint Vincent de Paul, Lille), Jérémy Castanera (CH Lannemezan), Julien Poissy (CHU Lille), Côme Bureau (Hôpital Pitié-Salpêtrière, APHP), Benoit Bailly (CHU Besançon), Nathalie Pansu (CHU Montpellier), Lucas Perez (CHU Montpellier), Caroline Merle de Boever (Clinique du Parc, Montpellier), Julie Abraham (CHU Limoges), Thibault Longval (CH Versailles), Romain Jouffroy (hôpital Ambroise Paré, APHP), Julien Colle (CHU Conception, Marseille), Kevin Bouiller (CHU Besançon), Elodie Rivière (Hôpital Bicêtre, APHP), Caroline Pouplet (CH La Roche sur Yon), Ines Boussen (hôpital Saint-Louis, APHP), Geoffroy Venton (CHU Conception, Marseille), Arthur Pavot (hôpital Bicêtre, APHP), Mai-Anh Nay (CH Orléans), Yannick Brunin (CHU Besançon), Fanny Pommeret (Institut Gustave Roussy), Camille Bigenwald (Institut Gustave Roussy), Otto Hartman (Hôpital Henri Mondor, APHP), Romain Gueneau (Hôpital de Bicêtre, APHP)

COVID- 19

 19 included from May 1st 2020 to April 1st 2021 in a CCP monitored access program implemented in France (CCP cohort). Underlying disease included B lymphoid neoplasm (such as diffuse B-cell lymphoma (DLBCL), chronic lymphoid leukemia (CLL) , follicular lymphoma (FL), mantle cell lymphoma (MCL), marginal zone lymphoma (MZL) or B-acute lymphoblastic leukemia (B-ALL)) plasma cell neoplasm requiring treatment and myeloid neoplasm (myelodysplastic syndrome or acute myeloid leukemia).

  and the emergence of SARS-CoV-2 variants have changed the course of COVID-19 outbreak. Firstly, none of the patients in both cohorts (CCP-treated and non CCP-treated) were vaccinated against SARS-CoV-2. Although prospective randomized trial strongly supports the efficacy of vaccination in general population, results are less favorable in immunosuppressed patients especially patients with CLL or MM who exhibit a lower serological response despite two administrations of BNT162b2 mRNA COVID-19 vaccine 5,25,26 . Further investigations are needed to evaluate the efficacy of vaccination on mortality linked to COVID-19 in such patients. Secondly, use of anti-spike mAb opened a new perspective especially in frail patients with a reduction of related hospitalization or death in mild to moderate COVID-19

Flow chartFigure 2 :

 2 Figure 1. Flow chart

Figure 3 :

 3 Figure 3: Overall survival after COVID-19 convalescent plasma transfusion represented using

Figure 4 :

 4 Figure 4: Forest Plot representing hazard ratio of death obtained in multivariable analysis.

Figure 1 *

 1 Figure 1

Figure 2

 2 Figure 2.

Figure 3 .

 3 Figure 3.

Figure 4 .

 4 Figure 4.

  Figure S2

  p< 0.0001), COVID-19 severity (p= 0.0003) and the time of CCP administration (p=0.002) were significantly associated with overall survival (Table2 andFigure3). In multivariable analysis only age > 70 yrs (HR= 2.63, 95% CI= 1.31-5.27; p=

	0.008), high blood pressure (HR= 2.71, 95% CI= 1.215-6.06; p= 0.015) and COVID-19
	severity (WHO scale 6 & 7) (HR= 5.36, 95% CI= 1.12-25.64 and 6.31, 95% CI= 1.31-30.39;
	p= 0.038 respectively) were associated with lower overall survival whereas previous B-cell
	depletion therapy was strongly associated with better overall survival (HR= 0.22, 95% CI=
	0.09-0.51; p<0.001) (Figure
	5
	% (95 % CI= 68.5-87.7) in patients with B-lymphoid neoplasm, 20 % (95 % CI= 5.8-69.1)
	with myeloid neoplasm and 36.8 % (95% CI= 20.4-66.4) with plasma-cell neoplasm. Deaths

were all associated with COVID-19. In univariable analysis, age > 70 years (p=0.006), high blood pressure (p=0.003), the type of hematological disease (p< 0.0001), a previous B-depletion therapy (

Table 1 .

 1 Convalescent Plasma therapy (CPP cohort) characteristics

	Patients

Lymphocyte count at the time of CCP transfusion, median (IQR)

	B-lymphoid neoplasm	0 (0-0)
	Myeloid neoplasm	9 (0-48)
	Plasma cell neoplasm	7 (1-17)

Serological status for COVID-19, n (%)

	Table 2. Univariable analysis
			Patients		90 days overall survival
	Patients characteristics	n = 112 %	95% CI	HR	95% CI	P
	Overall	112	64.9 56.2-74.9
	Gender					0.02
	Female	33	79.7 66.1-96.0 0.38 0.16-0.90
	Male	79	58.9 48.7-71.3	1
	Age						0.006
	< 70 yrs	77	70.9 60.6-83.0	1
	≥ 70 yrs	35	50.2 36-70.2 2.41 1.26-4.60
	High blood pressure					0.003
	Yes		20	42.9 25.5-72 2.77 1.37-5.62
	No		92	69.5 60.2-80.3	1
	Diabete					0.216
	Yes		7	42.9 18.2-100 1.93 0.68-5.44
	No		105	66.7 57.9-76.9	1
	Body mass index					0.05
	< 25		51	59.7 47.4-75.2	1
	25-30	32	77.6 64.2-93.7 0.48	0.2-1.13
	≥ 30		11	23.3 5.1-100 1.68 0.71-3.99
	Missing data	16	80.4 62.7-100 0.44 0.13-1.49
	Hematological disease					< 0.0001
	B-lymphoid neoplasm	83	77.5 68.5-87.7	1
	Myeloid neoplasm	10	20.0 5.8-69.1 7.79 3.26-18.61
	Plasma cell neoplasm	19	36.8 20.4-66.4 4.6	2.17-9.78
	Previous B-depletion therapy					< 0.0001
	Yes		81	76.9 67.7-87.4 0.21 0.11-0.42
	No		31	35.5 22.1-57	1
	Disease status					0.8
	Complete remission	48	66.5 53.8-82.2	1
	Partial remission/stable disease	29	68.1 52.9-87.7	1	0.44-2.30
	Progressive disease	22	56.4 38.5-82.7 1.45 0.63-3.38
	Positive Missing data	13	69.2 48.2-99.5 1	2 (2) 0.33-3.04
	Negative WHO scale (COVID-19 severity)					98 (87)	0.0004
	Unknown WHO 4	22	90 77.8-100	1	12 (11)
	Previous COVID-19 specific treatment, n (%)* WHO 5 47 71.7 59.8-86 3.35 0.76-14.85
	Steroid WHO 6	22	72 (64) 50 30.4-82.2 4.86 1.05-22.55
	Tocilizumab WHO 7	21	8 (7) 38.1 22.1-65.7 10.9 2.45-48.48
	Remdesivir Steroid administration					13 (12)	0.8
	Others Yes	72	8 (7) 63.7 53.2-76.3 1.12 0.56-2.23
	Nothing No	40	67.5 53.6-84.9	1	32 (29)
	Time from COVID-19 onset to
	CCP	* Some patients may have simultaneous treatment		0.002
	< 10 days	29	43.4 28.3-66.8	1
	> 10 days	83	72.8 63.3-83.6 0.37 0.20-0.72

Table 3 .

 3 Characteristics of patients with B-lymphoid neoplasm according to analyzed population (main analysis, overall population analyses).

		Analyzed population
	16d anti-CD20 population	Overall population
	Group		Group
	CP+	CP-	CP+	CP-
	N (%)	N (%)	N (%)	N (%)

Panel F


Laura Chaix
email: laura.chaix@neel.cnrs.fr

Blair W Lebert

Hu Miao

Alessandro Nicolaou

Flora Yakhou

H Cercellier

Stéphane Grenier

N B Brookes

A Sulpice

S Tsutsui

A Bossak

L Paolasini

D Santos-Cottin

H Yamamoto

I Yamada

M Azuma

T Nishikubo

T Yamamoto

M Katsumata

M P M Dean

M D'astuto

Bulk charge density wave and electron-phonon coupling in superconducting copper oxychlorides

I. INTRODUCTION

Charge density waves (CDWs) have been predicted in cuprates not long after the discovery of high-temperature superconductivity [1,2] and are now considered as a generic property of the high-temperature superconducting (HTS) cuprates, although their microscopic origin and relation with the pseudogap and superconductivity remain unclear. In fact, experimental studies of CDWs in HTS cuprates were initiated with bulk-sensitive scattering measurements of La-based cuprates [3] and surfacesensitive scanning tunnelling microscopy on Bi-based cuprates and copper oxychlorides (Ca 2-x Na x CuO 2 Cl 2 ) [4,5]. Then, the evolution and diversification of the techniques fertilized the experimental field of CDW orders in cuprates, providing deeper insights on a larger scale of compounds [6][7][8][9][10][11][12][START_REF] Li | Proc. Natl. Acad. Sci[END_REF][START_REF] Lee | [END_REF]. While all these studies in-dicate an ubiquitous CDW, they also point toward different characteristics which depend on the material. For instance, experimental observations have shown that, for different cuprate compounds, the CDW is short or longrange, coexists or not with an associated spin-order, or that its wave-vector increases or decreases with doping [9,10]. Such discrepancies have raised substantial questions about the nature of the CDW formation mechanism in HTS cuprates and stimulated scenarios involving either real-space local interactions or Fermi surface nesting [1,3,6,15,16]. Experimental studies have collected evidence for both scenarios and no consensus has been reached so far.

Combining surface and bulk probes on the same material can provide information on the CDW formation mechanism and its relation with both the superconductivity and the pseudogap. This approach, including, for example, scanning tunnelling microscopy, angle-resolved photoemission spectroscopy and resonant X-ray scattering, was applied to the Bi-based family. Such studies revealed a CDW which is consistent in surface and bulk and proposed possible connections to the fermiol-ogy [15,[17][18][19]. Ca 2-x Na x CuO 2 Cl 2 (Na-CCOC), whose surface electronic structure has been thoroughly explored [5,6], is another promising system to combine surface and bulk-sensitive measurements to study the CDW, which exhibits unique characteristics. Interestingly this compound has a simple tetragonal I4/mmm crystal structure [Fig. 1 (a)] without any structural instabilities [20] and presents strong 2D electronic properties [21], representing an ideal test bench to study the intrinsic physics from CuO 2 planes [6]. Although this system was among the first HTS cuprates in which scanning tunnelling microscopy measurements successfully revealed a surface CDW, observed over a doping range from x = 0.08 to x = 0.12 [5,[START_REF] Fujita | Proc. Natl. Acad. Sci[END_REF], the existence of such order in bulk remains an open question. Indeed, a previous X-ray study, in which no bulk CDW was detected, suggested either its short-ranged nature or that the CDW is pinned at the surface [START_REF] Smadici | [END_REF]24]. Despite 25 years of research on bulk CDW in hole-doped cuprates, all converging toward its ubiquity and significance in the phase diagram, Na-CCOC remains an exception. This is an issue that deserves clarification with state-of-the-art X-ray scattering methods such as the highly-sensitive and energy-resolved soft X-ray resonant inelastic X-ray scattering (RIXS) technique.

In this study, we combine high energy-resolution RIXS at the Cu L 3 -edge [Fig. 1 (b)] and non-resonant inelastic X-ray scattering (IXS) measurements to investigate CDW and electron-phonon coupling anomalies in Na-CCOC with x ∼ 0.1. Our results provide the first direct observation of a bulk and incommensurate CDW in this material. Concomitant to this observation, our RIXS and IXS data revealed anomalies on the Cu-O bond-stretching phonon characterized by (i) a softening and broadening at the CDW wave-vector, (ii) a RIXS intensity anomaly at Q A > Q CDW and (iii) a funnel-like RIXS intensity emanating from the CDW. Together these findings, which are not observed in the undoped sample, point toward CDW-induced electron-phonon coupling anomalies that are interpreted in terms of dispersive charge excitations emanating from the CDW and interacting with the Cu-O bond-stretching phonon.

II. METHODS

A. Single-crystal synthesis

Single-crystal synthesis of undoped copper oxychloride, i.e. Ca 2 CuO 2 Cl 2 sample (CCOC), is described in Ref. [25]. For the single-crystal synthesis of Na-doped copper oxychloride, i.e. Ca 2-x Na x CuO 2 Cl 2 samples (Na-CCOC), we used the following precursors: CaCO 3 (99.99%), CuO (99.99%), CaCl 2 (99.99%), NaClO 4 (99.9%) and NaCl (99.99%). First, we prepared a stoichiometric Ca 2 CuO 2 Cl 2 powder by a solid state reaction of CaCO 3 , CuO, and CaCl 2 as described in previous works [26][27][28]. In an argon filled dry box, we mixed the resulting Ca 2 CuO 2 Cl 2 powder with NaClO 4 , NaCl and CuO precursors in a molar ratio of 1:0.2:0.2:0.2. We charged the mixture in cylindrical Pt capsules and then set the capsules in high-pressure cells. Since it was shown that the synthesis pressure is related to the Na content, we compressed the pressure cell between 3.5 to 4 GPa in a cubic anvil type high-pressure apparatus in order to get underdoped Na-CCOC single crystals. The capsules were heated up to 1250 • C at a rate of 10 • C/min, kept at this temperature for 1 h and then slowly cooled down to 1050 • C at a rate of 10-20 • C/h. After heat treatment, we released the pressures. We obtained single crystals with a Na doping concentration of x ∼ 0.1 (T C ∼ 14 K) whose crystal structure is shown on Fig. 1 Resonant inelastic X-ray scattering (RIXS) measurements were performed on the ERIXS spectrometer [29] at the ID32 beamline of the European Synchrotron Radiation Facility (ESRF). To avoid hygroscopic damage of the surface, the samples were cleaved under Ar atmosphere right before loading them into the high-vacuum chamber containing the four-circle diffractometer. All RIXS data shown in this report have been recorded with the incident photon energy tuned to the maximum of the Cu L 3 -edge absorption curves, i.e. at the resonance [see Appendix A, Fig. 7 (b) for the corresponding absorption curve near the Cu L 3 -edge], except data shown in Fig. 1 (d), which were recorded off-resonance. The energy resolution was approximately ∆E ∼ 50 meV for negative Q measurements of Na-CCOC, ∆E ∼ 60 meV for positive Q measurements of Na-CCOC, except for the five first scans (Q = 0.15 to Q = 0.25 r.l.u.), where the energy resolution was ∆E ∼ 80 meV, and ∆E ∼ 65 meV for negative Q measurements of CCOC. The energy resolution was checked by recording RIXS spectra on silver paint at each Q position. The experimental geometry is sketched in Fig. 1 (b).

For all the RIXS data shown in this manuscript, we used a linear vertical x-ray polarization (σ-polarization), i.e. perpendicular to the scattering plane. Na-CCOC sample was oriented with the ac-plane parallel to the scattering plane. In order to have the sample precisely aligned, the Na-CCOC orientation matrix was obtained by measuring the (0 0 2) Bragg peak at 932 eV and the (-1 0 1) Bragg peak at 1680 eV using the four-circle diffractometer inside the high-vacuum RIXS chamber. During the RIXS measurements, the scattering angle was fixed at 2θ= 149.5 • giving a total momentum transfer |Q| = 0.91 Å-1 with Q = k i -k f . Its component in the abplane, that is the projected momentum transfer Q , was changed by rotating the sample around the b-axis, allowing to probe the dispersion of the excitations within the CuO 2 plane. Therefore, the projected momentum transfer Q was along the < 100 > direction, varying from (0.1, 0) to (0.5, 0) in reciprocal lattice units (2π/a). All the RIXS data shown in this manuscript are plotted as function of the projected in-plane momentum transfer Q (along the a-axis) in reciprocal lattice units (r.l.u.).

We chose a convention where negative (positive) Q measurements correspond to grazing-incidence (emission) geometry. Note that we mainly measured RIXS spectra at negative Q , i.e. grazing-incidence geometry. Positive Q measurements, i.e. grazing-emission geometry, were also performed on Na-CCOC at 25 K to confirm the results (see Appendix C). For the low-temperature data, RIXS spectra were recorded at 25 K, whereas, for the high-temperature measurements, RIXS spectra were measured at 245 K.

C. Inelastic X-ray scattering measurements

High-resolution inelastic X-ray scattering (IXS) was performed at the ID28 beamline of the ESRF [30,31], with complementary measurements performed at the BL35XU beamline of SPring-8 [32]. Note that one data point at Q = (3.065, 0.003, -0.073) has been recorded at the BL35XU beamline (SPring-8), whereas the data taken on the ID28 beamline (ESRF) concern the full dispersion along Q = (3 0 0) -(q 0 0). 9 in-line analyzers were installed in the IXS spectrometer of ID28, while BL35XU uses a 3 x 4 analyzer. The Si(9 9 9) backscattering setup was chosen: the incident X-ray energy was 17.793 keV and the energy resolution was 3 meV on average, with small variations (< 10%) depending on the analyzer. In particular we found 2.96 (7) meV for analyzer 2 of ID28, from the fit of the elastic line width of our own data. To reduce the tails of the low energy modes and avoid multiple scattering, the IXS spectra were measured at 25 K using a closed cycle refrigerator. The resolution (∼ 3 meV) is decoupled from the incident energy, i.e. depends from the Darwin width of the main monochromator and is constant over all the exchanged energy range. This guarantee that the broadening of the optic phonon is effective. Background observed between 60 and 100 meV mostly comes from elastic scattering from the sample. Grease was used to protect the hygroscopic samples from air and to mount them on the copper sample holders in the cryostat.

III. RESULTS

A. Bulk charge density wave in Na-CCOC

The RIXS technique has recently emerged as decisive to detect incipient electronic orders such as CDW and its corresponding excitations/fluctuations [9,[11][12][START_REF] Li | Proc. Natl. Acad. Sci[END_REF][START_REF] Lee | [END_REF][33][START_REF] Miao | Proc. Natl. Acad. Sci[END_REF][START_REF] Arpaia | [END_REF][36]. It is suitable to detect weak signals. This is due to the combination of the resonant process, which increases the sensitivity to the valence electrons, and the high energy-resolution now available, which can discriminate low-energy excitations from quasi-elastic contributions. Figure 1 (c) displays a RIXS intensity map recorded onresonance and at 25 K in Na-CCOC. Enhanced quasielastic intensity peaking at an in-plane momentum transfer of Q ∼ -0.26 r.l.u. (reciprocal lattice units) is detected. In contrast, the intensity drops by two orders of magnitude in the same energy-and momentum-range, when the incident photon energy is off-resonance [Fig. 1 (d)]. The observed quasi-elastic peak is therefore dominated by the resonant process, indicating that it is associated with the electronically active Cu states.

More quantitative assessments can be achieved by analyzing the high-resolution (∆E ∼ 50 meV) and high statistics RIXS intensity map displayed in Fig. 2 (a). The RIXS intensity integrated over a small energy window (-25 meV < E < 25 meV) around the zero-energy loss is shown in Fig. 2 (b). A quasi-elastic peak is confirmed. The peak position is found at Q CDW ∼ -0.27±0.01 r.l.u., while its FWHM ∼ 0.08 ± 0.01 r.l.u., indicates a correlation length of ξ ∼ 15 -20 Å. Note that measurements at positive Q confirm these observations (see Appendix C). This peak is the signature of an incommensurate shortrange CDW, that is static or quasi-static in nature (on a timescale of ∼ 160 fs, limited by the experimental energy resolution). Upon increasing the temperature to 245 K, the CDW peak is absent, as shown in Fig. 2 (b), and only the specular scattering background remains, indicating that the CDW correlation increases when decreasing the temperature.

B. Cu-O bond-stretching phonon and electron-phonon coupling anomalies

We now focus on the inelastic features and investigate the interplay between the lattice excitations and the CDW. Indeed, the study of the phonon spectra can provide insight on the driving force behind its formation mechanism, possibly revealing Kohn anomaly resulting from Fermi surface nesting or any momentum-dependent electron-phonon coupling [START_REF] Zhu | Proc. Natl. Acad. Sci[END_REF]. Inelastic neutron scattering and IXS have identified anomalies in the phonon spectra close to the CDW wave-vectors in several HTS cuprates, suggesting an intimate relation with the lattice [START_REF] Uchiyama | [END_REF][39][40][41][42][43][44][45][46]. These anomalies could be connected to the origin of the CDW, and have been discussed in term of CDW-induced modification of the lattice [33], hybridization between different phonon modes [40,45] or even the presence of collective charge excitations [47]. Despite of being intensively studied over the past 30 years, the very nature of these phonon anomalies remains puzzling in HTS cuprates, calling for a new paradigm in phonon investigation. Because of its sensitivity to electron-phonon coupling and the recent technical progress made on its energy-resolution, the RIXS is now becoming a key complementary technique to investigate phonon spectra and electron-phonon coupling in HTS cuprates.

As presented in Fig. 3, the energy-loss RIXS spectra at 25 K show an excitation centered at ∼ 60 meV, between the elastic peak and the tails of the magnetic excitations observed at higher energy. The dispersion of this excitation is shown on Fig. 5 (a) and was obtained by plotting the peak position (see red ticks on Fig. 3) as function of Q . To identify this excitation, we have performed IXS measurements on another Na-CCOC sample from the same batch. As shown in Fig. 4 displaying IXS spectra at 25 K, a peak corresponding to a phonon mode is observed at 60 meV, whose dispersion is plotted in Fig. 5 (c). Its energy and dispersion agree well with the 60 meV excitation observed in the RIXS data, indicating that both excitations, i.e. the one seen in RIXS and the one seen in IXS, have common origin. A comparison to density functional theory calculations shown on Fig. 5 (a) and(c) and other HTS cuprates indicate that this mode corresponds to the Cu-O BS phonon [38-43, 48, 49]. Interestingly, as seen by both RIXS and IXS, the BS phonon dispersion softens. This softening presents two components. First, a doping-induced softening in a form of a cosine-like dispersion along (q 0 0), which has been already reported in a earlier IXS study [43] and reproduced well by the density functional theory. Then, a pronounced dip is observed at Q ∼ 0.3 r.l.u., i.e. close to the CDW wave-vector, which is not captured by the density functional theory [50,51]. This dip co-incides with a peak width broadening occurring between 0.2 and 0.4 r.l.u. [Fig. 5 (d)] and resembles the phonon anomaly observed in conventional metallic systems such as NbSe 2 , where the electron-phonon coupling is known to have a substantial implication on the formation of the CDW [START_REF] Zhu | Proc. Natl. Acad. Sci[END_REF]. Note that the Q of the RIXS dispersion minimum is not exactly coinciding with Q CDW , as also observed in La 2-x Sr x CuO 4 [33]. This could indicate that the phonon softening and CDW wave-vector relationship is more complex than expected. This could also originate from the Q -dependent electron-phonon coupling which is higher at larger Q and tends to displace the minimum of the BS phonon dispersion [33]. Note also that a previous IXS study on Bi2201 revealed a second phonon mode in the 40-80 meV energy range, whose dispersion crosses or anticrosses the BS phonon at q = (0.25 0 0) [40]. However, our IXS data do not indicate the presence of another mode in this energy range, which should be well separated to the BS phonon for spectra away from the crossing point (for instance for those close to the Brillouin zone center) and should display a significant dispersion [see Figure 9]. Our results suggest that the CDW affects the lattice dynamics, and in the present case the BS mode, by renormalizing its frequency and linewidth. This points toward an intimate connection between the electron-phonon coupling and the CDW that deserves further examination.

To study the role of the electron-phonon coupling, we can examine the RIXS phonon intensity. Indeed, this technique has recently been used to quantify the electronphonon coupling strength λ in several HTS cuprates, confirming a momentum dependent electron-phonon coupling that is strongest at the zone boundary for the BS mode [52,53]. This is due to the intrinsic nature of the RIXS process, in which the phonons are excited through the electron-phonon coupling interaction [54,55]. Consequently, the RIXS phonon intensity is proportional to the electron-phonon coupling strength and can thereby reflect interactions between phonons and underlying charge excitations [12][START_REF] Li | Proc. Natl. Acad. Sci[END_REF][START_REF] Lee | [END_REF]. As a function of the momentum, the electron-phonon coupling should scale as I(Q) ∝ sin 2 (πH) + sin 2 (πK) for the BS mode [55], i.e. sin 2 (πQ ) for our scattering geometry. However, Fig. 5 (e) shows that a deviation is observed in our data. Indeed, the momentum-dependence of the BS phonon integrated intensity presents an anomaly at |Q A | > |Q CDW |, as indicated by the difference plot shown in the bottom panel of Fig. 5 (e), and confirmed by the analysis of the positive Q data (see Appendix C). A Lorentzian fit of the difference gives Q A ∼ -0.36 ± 0.02 r.l.u. This deviation confirms the presence of electron-phonon coupling anomalies in the vicinity of the CDW. Similar electron-phonon coupling anomalies have been observed in La 1.8-x Eu 0.2 Sr x CuO 4+δ [56,57] and Bibased cuprates [12][START_REF] Li | Proc. Natl. Acad. Sci[END_REF][START_REF] Lee | [END_REF] using RIXS. The former seems to occur in a narrow momentum region near the CDW wave-vector and has been discussed in term of enhanced electron-phonon coupling within the CDW phase that further stabilizes the CDW modulation [56]. The latter however occurs for |Q| > |Q CDW | and has been at-tributed to originate from an interference between the BS phonon and charge excitations emanating from the CDW [12][START_REF] Li | Proc. Natl. Acad. Sci[END_REF][START_REF] Lee | [END_REF]. Due to their dispersive nature, these excitations broaden in momentum with increasing energy to form a funnel-like intensity emanating from the CDW. Once crossing the BS phonon, an interference occurs that leads to an intensity anomaly in the RIXS data. Since this interference is dictated by the electron-phonon coupling, which increases monotonically with the momentum for the BS mode, the intensity anomaly is more visible for |Q| > |Q CDW |, i.e. where the electron-phonon coupling is strong [12][START_REF] Li | Proc. Natl. Acad. Sci[END_REF][START_REF] Lee | [END_REF]. Our observation of an intensity anomaly occurring at |Q A | > |Q CDW | therefore favors the second scenario, i.e. the interference between the BS phonon and charge excitations dispersing from the CDW. This is further supported by the RIXS intensity map presented in Fig. 2 (a) showing an additional scattering intensity smoothly connecting the CDW and the BS phonon and forming a funnel-like intensity emanating from the CDW [Fig. 5 (b)]. Together, these observations point toward the existence of dispersive excitations associated with the CDW. By connecting Q CDW and Q A , we determined a velocity for these excitations: v CDW ∼ 0.4 eV• Å, consistent with the velocities found in Bi-based cuprates [12,[START_REF] Li | Proc. Natl. Acad. Sci[END_REF]. This result differs from a recent RIXS study on La 2-x Sr x CuO 4 , in which the phonon softening has been attributed to a CDW-induced modification of the lattice without any coupling to electronic excitations [33]. This might be an indication of the different elec-tronic character of the CDW in La 2-x Sr x CuO 4 relative to Na-CCOC.

The CDW nature of the observed anomalies is confirmed by recording RIXS spectra on the undoped Ca 2 CuO 2 Cl 2 (CCOC) sample. Fig. 6 (a) presents the energy-momentum intensity map, with the fitted elastic peak and magnons subtracted. As expected, a good agreement is obtained by comparing the dispersion of the 70 meV RIXS excitation (white diamonds) to the one of the BS phonon measured by IXS on another CCOC sample from the same batch (black diamonds) [51]. The CCOC BS phonon is almost dispersionless, with no softening in the probed momentum range. In addition, the momentum-dependence of the quasi-elastic peak confirms the absence of the CDW in CCOC [Fig. 6 (b)]. As anticipated, the phonon integrated intensity shown in Fig. 6 (c) increases monotonically with Q . More importantly, its momentum-dependence is well captured by the sin 2 (πQ ) trend, consistent with predictions due to electron-phonon coupling for the BS phonon [52,55]. These observation confirm that the phonon and electronphonon coupling anomalies observed in Fig. 5 exist only in doped CCOC, where the CDW is present.

IV. DISCUSSION

To visualize our results, the temperature-hole doping phase diagram of Na-CCOC is displayed in Fig. 6 (d). Sodium substitution for calcium in CCOC dopes the Mott insulating state,inducing a metallic state with no long-range magnetic order and superconductivity at higher doping [58][59][60]. Our study unambiguously reveals a bulk CDW at 25 K in the underdoped region of the phase diagram, i.e. close to the doping concentration of x ∼ 0.1. Our results suggest that the CDW is short-ranged (∼ 15 -20 Å), comparable to the correlation lengths found in Bi-based cuprates, known for exhibiting chemical disorder and inhomogeneity [10]. They also indicate that the CDW is incommensurate with Q CDW ∼ -0.27 ± 0.01 r.l.u.

Our estimation of Q CDW from RIXS in Na-CCOC is slightly different than the one claimed in scanning tunnelling microscopy studies, discussing a commensurate CDW (Q CDW = 0.25), which is observed over a doping range from x = 0.08 to x = 0.12 [5]. In the following, we discuss several scenarios that could explain this discrepancy. First, it is important to note that the scanning tunnelling microscopy CDW wave-vector, estimated from the Fourier transform of the conductance maps, was given without error bars, contrary to our case. We cannot judge their error, but a closer inspection of their data indicates that, while the overall scanning tunnelling microscopy peaks seem centered on commensurate positions for the (2π, 0) directions, it is not the case for the (0, 2π) directions, where the maximums are peaked on incommensurate positions, close to the CDW wavevector found in our RIXS study [5]. It is therefore possi- ble that the scanning tunnelling microscopy data are not precise enough to distinguish if the surface CDW is precisely commensurate or incommensurate as found in our case. Another possibility is that the scanning tunnelling microscopy CDW is commensurate and that the difference between RIXS and scanning tunnelling microscopy lies in the difference between surface and bulk properties. In this scenario, the commensurate CDW would not be representative of the bulk electronic properties and would only be located at the surface, possibly stabilized by a soft surface phonon [24]. While we cannot exclude the possibility of a material-specific feature here, such discrepancy was however not observed in Bi-based compounds, where combined X-ray and scanning tunnelling microscopy studies showed consistency between surface and bulk properties [15,18]. An alternative scenario would be that the CDW is locally commensurate, locked to a 4a 0 periodicity as probed by scanning tunnelling microscopy [5], but appears incommensurate in Xray studies, through discommensuration effects [START_REF] Mesaros | Proc. Nat. Acad. Sci[END_REF]. This last proposal comes from recent analysis of the scanning tunnelling microscopy data in Bi-based cuprates where they revealed a doping independent local commensurate CDW with a 4a 0 periodicity while scattering measurements identified an incommensurate global modulation with a wave-vector decreasing with increasing doping [START_REF] Mesaros | Proc. Nat. Acad. Sci[END_REF][START_REF] Webb | [END_REF][63]. Similar recent observations have been made on the high-magnetic phase of YBCO using nuclear magnetic resonance [64]. This scenario, which may be consistent with the doping-independent commensurate CDW wave-vector seen in Na-CCOC with scanning tunnelling microscopy [5], requires however more studies to be confirmed. We therefore believe that our results will motivate further in depth investigations of the CDW in Na-CCOC combining both bulk and surface probes, as it has been done in Bi-based compounds [15,18,[START_REF] Mesaros | Proc. Nat. Acad. Sci[END_REF][START_REF] Webb | [END_REF][63].

Concerning the inelastic features, our IXS measurements revealed anomalies in the BS phonon, resulting in a peak width broadening and a dip in its dispersion at Q CDW , which is not reproduced by the density functional theory. We also evidenced that such lattice anomalies are concomitant to RIXS intensity anomalies which are characterized by a momentum-dependent electronphonon coupling that deviates from the predictions for the Cu-O bond stretching mode and a funnel-like intensity emanating from the CDW. Together, these results point toward the existence of additional charge excitations dispersing from the short-range CDW at 25 K and interacting with the Cu-O bond stretching phonon at 60 meV. This extends the observation of such excitations outside the Bi-based family [12][START_REF] Li | Proc. Natl. Acad. Sci[END_REF][START_REF] Lee | [END_REF], whose nature has been discussed in term of a collective mode corresponding to SU(2) fluctuations [65] or a continuum of quantum fluctuations that could melt the CDW below T C [START_REF] Lee | [END_REF]. This last scenario might open a new route for the CDW and superconductivity relationship, beyond the simple competing picture. It also points toward the presence of quantum critical points, which could be responsible for many unconventional properties found in these systems. By demonstrating that CDW excitations also exist in Na-CCOC, we offer another playground to study this scenario.

V. CONCLUSION

To summarize our main finding, the study we described in the present work :

• it unambiguously reveals a bulk CDW at 25 K and close to the doping concentration of x ∼ 0.1, which is short-ranged (∼ 15 -20 Å),and incommensurate with Q CDW ∼ -0.27 ± 0.01 r.l.u.;

• it shows that the phonon anomalies seen by IXS, directly probing the S(q, ω), are concomitant to RIXS intensity anomalies showing that electronphonon coupling originates them;

• as previously observed only in the Bi-based family [12][START_REF] Li | Proc. Natl. Acad. Sci[END_REF][START_REF] Lee | [END_REF], a funnel-like inelastic intensity emanate from the CDW.

Together, these results point toward the existence of additional charge excitations dispersing from the shortrange CDW at 25 K and interacting with the Cu-O bond stretching phonon at 60 meV

VI. APPENDIX A. Sample preparations and characterizations

For this study, we choose Ca 2-x Na x CuO 2 Cl 2 (Na-CCOC) samples with a doping concentration of x ∼ 0.1 [T C ∼ 14 K, see Fig. 7 (a)], similarly to the previous scanning tunnelling microscopy studies in which a surface CDW was successfully reported. We used four differ-ent samples of Ca 2-x Na x CuO 2 Cl 2 : three doped samples called Na-CCOC samples 1, 2 and 3, as well as one undoped one called CCOC sample. The three doped ones (Na-CCOC samples 1, 2 and 3) were from the same batch. The Na-CCOC sample 1 and CCOC sample were used to perform the RIXS measurements whereas the Na-CCOC sample 2 and 3 were used for the IXS measurements at ID28 beamline of ESRF and BL35XU beamline of SPring-8 respectively. The samples were pre-aligned before the measurements using single-crystal X-ray diffraction. Ca 2-x Na x CuO 2 Cl 2 is sensitive to humidity, so to avoid hygroscopic damages of the surface, they were encapsulated within two Kapton foils during the X-ray diffraction measurements. For the RIXS measurements, the samples were glued with silver paint on the sampleholders. Their manipulations and preparations were done inside glove-boxes. 8 (d)]. RIXS spectra shown in this report have been extracted with a Single Photon Counting algorithm using the RixsToolBox software [66], except for Fig. 1 (c) and 1 (d), which display spectra extracted with traditional algorithm. The data have been normalized to I 0 and corrected to self-absorption effects using the formalism described in Ref. [53,67], except for Fig. 1 (c) and 1 (d), where only I 0 normalization has been applied. The zero-energy loss position was precisely determined using the procedure described in Ref. [12]: each spectrum taken on the samples has been roughly align by a comparison to a spectrum acquired on silver paint near the samples, then the zero-energy position was finely adjusted through the fit of the elastic peak. The model used to fit each RIXS spectrum involves four components, convoluted with the Gaussian energy resolution function: a Gaussian function for the elastic peaks, a Lorentzian function for the Cu-O bond stretching phonons, an anti-symmetrized Lorentzian function for the magnetic excitations and a Gaussian background to account for the tail of the excitations at higher energy. Fig. 3 demonstrates the quality of the fits. Note that the plotted fits are already convoluted with the energy resolution function. Similar fitting procedures and analysis are commonly found in the literature [12,[START_REF] Li | Proc. Natl. Acad. Sci[END_REF]68]. Error bars for the RIXS phonon dispersion are estimated by the uncertainty in determining the zero energy loss [Fig. 5 (a)]. Those for the RIXS integrated intensity plots are determined by Poisson statistics.

B. RIXS and IXS data analysis

Negative Q data Positive Q data CDW QCDW ∼ Q † CDW ∼ wave-
The IXS spectra recorded on ID28 and BL35XU were normalized to to their respective beamline monitor. Fig. 9 summarizes the corresponding IXS data. The spectra have been analyzed using a similar fitting procedure than the one described in [69]. Pseudo-Voigt line shapes were used to fit the Cu-O bond stretching phonon mode. We also checked the results using a damped-harmonicoscillator model [70] for the Cu-O bond stretching phonon mode, which overlap well within error-bars with the pseudo-Voigt model. Fig. 4 demonstrates the quality of the fits. I summarizes the CDW and intensity anomaly wave-vectors, found from the analysis of the positive Q data. This comparison between positive and negative Q data enables solid crosschecking of the observations in two independent measurements.

FIG. 1 :

 1 FIG. 1: (a) Crystal structure of Na-CCOC [25]. a, b and c are the lattice axes of the sample. Cl ions are located on the apical sites. The four surrounding O form the square coordination of Cu, which is highlighted in blue. (b) Sketch of the RIXS scattering geometry with respect to the crystal structure of Na-CCOC and with a CDW. (c), (d) RIXS intensity maps recorded on-(c) and off-(d) resonance (top panels) as function of the energy and Q . The integrated intensities in the quasi-elastic regions (indicated with black arrows on the RIXS intensity maps) are plotted on the bottom panels.

  (a). The samples were characterized by X-ray diffraction and magnetic susceptibility measurements [see Appendix A, Fig.7 (a)].

FIG. 2 :

 2 FIG. 2: (a) RIXS intensity maps recorded at 25 K, as function of the energy and Q . (b) Momentum-dependence of the integrated quasi-elastic intensity at 25 K (top) and 245 K (bottom). The quasi-elastic region is defined as between the two blue arrows on (a). The black solid line is a fit to the data consisting of two Lorentzians, one for the CDW (in blue) and the other for the tail of the specular reflection peak at Q = 0 (dotted line), plus a constant. QCDW is indicated with a vertical solid line.

FIG. 3 :

 3 FIG. 3: Fits of the RIXS spectra measured at 25 K in Na-CCOC. Energy-loss spectra plotted over the low-energy region demonstrating the quality of the fits. The model used takes into account a Gaussian for the elastic peak, a Lorentzian for the Cu-O bond-stretching phonon and an anti-symmetrized Lorentzian for the magnetic excitations, convoluted with the Gaussian energy resolution function (∆E ∼ 50 meV). The data are shown with markers and the resulting fits are displayed with black solid lines. The fitted Cu-O bond-stretching phonons are highlighted with filled areas. The red vertical lines indicate the fitted phonon position.

FIG. 4 :

 4 FIG. 4: Fits of the IXS spectra measured at 25 K at the ID28 beamline of ESRF in Na-CCOC plotted over the Cu-O bondstretching phonon energy region demonstrating the quality of the fits. Pseudo-Voigt line shapes were used to fit the BS phonon mode. The data are shown with markers and the resulting fits are displayed with black solid lines. The fitted BS phonons are highlighted with red lines. Normalized Intensity corresponds to the ratio of IXS Intensity with the beam monitor.

FIG. 5 :

 5 FIG. 5: (a) RIXS BS phonon dispersion at 25 K. density functional theory calculations, extracted from ref. [51], are shown with a grey solid line. (b) RIXS intensity map at 25 K, with subtracted elastic and paramagnon peaks. The raw data are the same than those shown in Fig. 2 (a). (c), (d) IXS BS phonon dispersion (c) and width (d) at 25 K. IXS spectra have been measured at both BL35XU (SPring-8) and ID28 (ESRF) beamlines (see Methods). Note that in contrast to the peak position, the fitted FWHM at q = (0.5 0 0) was a parameter not stable in the fit (with very large error bars), which strongly depends on the model used (either pseudo-Voigt or damped harmonic-oscillator). (e) Momentum-dependence of the RIXS integrated intensity of the elastic/paramagnon-subtracted data at 25 K with sin 2 (πQ ) curve (black solid line). The integrated energy window corresponds to the white dashed lines in (b). The bottom panel represents the difference between the integrated intensity and the sin 2 (πQ ) curve, with Lorentzian fit (solid line). QCDW and QA are indicated with a dashed line and arrow respectively.

FIG. 6 :

 6 FIG. 6: (a) Elastic and magnons-subtracted RIXS intensity map of CCOC at 25 K. The RIXS BS phonon dispersion is displayed with white diamonds. The black diamonds show the IXS BS phonon dispersion, from ref. [51]. (b) Momentumdependence of the integrated quasi-elastic RIXS intensity of the CCOC data. The integrated energy window corresponds to the blue arrows on Fig. 2 (a). (c) Momentum-dependence of the integrated RIXS intensity of the elastic and magnonsubtracted data of CCOC with sin 2 (πQ ) curve (black solid line). The integrated energy window corresponds to the white dashed lines in (a). (d) Temperature-doping phase diagram of Na-CCOC. The onset temperatures, i.e. TN (antiferromagnetic, AFM) and Tc (superconducting, SC), are from ref. [58-60]. The different doping concentrations and temperatures probed in our study are reported with filled diamonds.

FIG. 7 :

 7 FIG. 7: (a) Zero-field-cooling (ZFC) and field-cooling (FC) magnetization measurements vs temperature with a magnetic field of 46.3 Oe of the Na-CCOC sample 1 (sample measured with RIXS) across the superconducting transition. The TC corresponds to the onset of the diamagnetic signal. Insert shows an enlarged view of the signal within the blue box near TC . (b) X-ray absorption spectrum (XAS) near the Cu L3edge of Na-CCOC.

Fig. 8

 8 Fig.8summarizes the RIXS spectra of our study, recorded on Na-CCOC at 25 K and 245 K at negative Q [Fig.8(a) and (c)] and positive Q [Fig.8 (b)] and on CCOC at 25 K [Fig.8 (d)]. RIXS spectra shown in this report have been extracted with a Single Photon Counting algorithm using the RixsToolBox software[66], except for Fig.1 (c) and 1 (d), which display spectra extracted with traditional algorithm. The data have been normalized to I 0 and corrected to self-absorption effects using the formalism described in Ref.[53,67], except for Fig.1 (c) and 1 (d), where only I 0 normalization has been applied. The zero-energy loss position was precisely determined using the procedure described in Ref.[12]: each spectrum taken on the samples has been roughly align by a comparison to a spectrum acquired

FIG. 8 :

 8 FIG. 8: RIXS spectra of Na-CCOC sample 1 recorded at 25 K at negative Q with an energy resolution of ∆E ∼ 50 meV (a) and positive Q with an energy resolution of ∆E ∼ 60 meV (except for the five first scans, i.e. Q = 0.15 to Q = 0.25 r.l.u., where the energy resolution was ∆E ∼ 80 meV) (b). (c) RIXS spectra of Na-CCOC recorded at 245 K at negative Q with an energy resolution of ∆E ∼ 50 meV. (d) RIXS spectra of CCOC recorded at 25 K at negative Q with an energy resolution of ∆E ∼ 65 meV. The spectra are shifted vertically for clarity.

C

  FIG.9: IXS spectra measured for different Q = (3 -q, 0, 0) and at 25 K in Na-CCOC sample 2. The data have been recorded on the ID28 beamline of ESRF. The intensity for each wave-vector below q=0.5 are shifted of 0.2x10 -2 , so that the Brillouin zone center is at the top, and the zone boundary at the bottom. Fig.4in the main text show a zoom of the same data, focussing on the details around the Cu-O bondstretching mode energy range.

FIG. 10 :

 10 FIG. 10: (a) RIXS intensity map recorded at 25 K with low statistics, as function of the energy and Q . (b) Momentumdependence of the integrated quasi-elastic intensity of the positive Q data at 25 K. The quasi-elastic region is defined as between the two purple arrows on (a). The black solid line is a fit to the data consisting of two Lorentzians, one for the CDW and the other for the tail of the specular reflection peak at Q = 0, plus a constant. The fit of the CDW peak is highlighted in purple. The CDW wave-vector is indicated with a vertical solid line. The background corresponding to the tail of the specular reflection peak is shown with a black dotted line. (c) Momentum-dependence of the RIXS integrated intensity of the elastic/paramagnon-subtracted positive Q data at 25 K. The integrated energy window is 0-100 meV. The black solid line is the sin 2 (πQ ) curve. The bottom panel represents the difference between the integrated intensity and the sin 2 (πQ ) curve, with Lorentzian fit (solid line). The dashed line indicates Q † CDW . The arrow highlights the anomaly wave-vector Q † A .

TABLE I :

 I Comparison

	vector (r.l.u.)	-0.27 ± 0.01	0.28 ± 0.01
	CDW	FWHM ∼	FWHM † ∼
	width (r.l.u.)	0.08 ± 0.01	0.06 ± 0.01
	Correlation	ξ ∼ 15	ξ † ∼ 20
	length ( Å)
	Phonon	QA ∼	Q † A ∼
	anomaly (r.l.u.)	-0.36 ± 0.02	0.34 ± 0.02

of the wave-vectors, widths and correlation lengths of the CDW, as well as the wave-vectors of the phonon intensity anomalies from the analysis of the RIXS data recorded at negative and positive Q .

Acknowledgments

RIXS experiment was performed at the ID32 beamline of the European Synchrotron Radiation Facility (ESRF, Grenoble, France) supported by a beamtime allocation under the proposal HC-3884. IXS measurements were performed at the ID28 beamline of ESRF supported by a beamtime allocation under the proposal HC-4310. Additional IXS measurements were conducted at BL35XU of SPring-8 (Japan) under the SPring-8 Budding Researchers Support Program (proposal No. 2019B1779). We thank O. Leynaud for access to the X'Press diffractometer platform as well as L.-M. Chamoreau and B. Baptiste for access to the "Plateforme Diffraction" at IPCM, Paris, and providing help for the single-crystal X-ray diffraction experiments. We thank L. Del-Rey and D. Dufeu for conceiving the sample holders and J. Debray for his help for the preparation of the RIXS experiment. We thank L. Laversenne and N. Bendiab for access to the glove-boxes. We thank P. Rodière and M.-H. Julien for fruitful discussions. We acknowledge financial support from ANR-DFG grant ANR-18-CE92-0014-03 "Aperiodic", IRS IDEX/UGA and Grants-in-Aid for Scientific Research 18H05208, and 19H05625, from the Japan Society for the Promotion of Science (JSPS).