A recent report that sulfur hydride under pressure is an electron-phonon superconductor with a Tc of 190 K has been met with much excitement although it is yet to be confirmed. Based on several electron-phonon spectral density functions already available from density functional theory, we find that the electron-phonon spectrum is near optimum for Tc with a particularly large value of its characteristic phonon energy omega_ln which is due to the small hydrogen mass. We find that the thermodynamic universal BCS ratios are near those for Pb and Nb3Sn. We suggest that optical measurements could be a useful tool to establish the existence and nature of the superconductivity in this system. Conventional superconductors are in the impurity-dominated dirty limit. By contrast sulfur hydride will be in the clean limit because of its large energy gap scale. The AC optical conductivity will display distinct and separate signatures of the superconducting gap in the low-energy impurity-dominated range of the optical spectrum and additional phonon structures at higher energies where the clean limit applies.
This article reports the experimentally clarified crystal structure of a recently discovered sulfur hydride in high temperature superconducting phase which has the highest critical temperature Tc over 200 K which has been ever reported. For understanding the mechanism of the high superconductivity, the information of its crystal structure is very essential. Herein we have carried out the simultaneous measurements electrical resistance and synchrotron x-ray diffraction under high pressure, and clearly revealed that the hydrogen sulfide, H2S, decomposes to H3S and its crystal structure has body-…
A recent experiment has shown a macroscopic quantum coherent condensate at 203 K, about 19 degrees above the coldest temperature recorded on the Earth, 184 K, in pressurized sulfur hydride. This discovery is relevant not only in material science and condensed matter but also in other fields ranging from quantum computing to quantum physics of living matter. It has given the start to a gold rush looking for other macroscopic quantum coherent condensates in hydrides at the temperature range of living matter 200<Tc<400K. We present here a review of the experimental results and the theoretical wor…
Capitani and coworkers [1] reported that infrared optical reflectance measurements provided evidence for a superconducting transition in sulfur hydride [2] under 150 GPa pressure, and that the transition is driven by the electron-phonon interaction. Here we argue that the measured data did not provide evidence that the system undergoes a transition to a superconducting state, nor do the data support any role of phonons in driving a transition. Rather, the data are consistent with the system remaining in the normal state down to temperature 50K, the lowest temperature measured in the experiment…
Due to the value of the isotope shift in sulfur hydrides, a phonon-mediated pairing scenario of superconductivity is generally accepted for these high-temperature superconductors which is consistent with the Bardeen-Cooper-Schrieffer (BCS) framework. Knowing that a large electronic density of states enhances $T_c$, generalized Fermi surface topologies are used to increase it. A multi-band model within the BCS framework is proposed in this work for the description of sulfur hydride superconductors. This model is used to describe some properties of the $H_3S$ superconductor. Strong coupling effe…
Remarkable feature of the phase diagram of sulfur hydrides is a sharp increase in critical temperature from 120K up to200K. This increase is a signature of the structural transition. The study described below is concerned with the nature of this phase transition. One can demonstrate that the symmetry analysis along with an analysis of the impact of lattice deformations lead to the conclusion that we are dealing with the first order transition. It leads to an abrupt appearance of small pockets on the Fermi surface and to the two-gap energy spectrum.
Due to its low atomic mass hydrogen is the most promising element to search for high-temperature phononic superconductors. However, metallic phases of hydrogen are only expected at extreme pressures (400 GPa or higher). The measurement of a record superconducting critical temperature of 190 K in a hydrogen-sulfur compound at 200 GPa of pressure[1], shows that metallization of hydrogen can be reached at significantly lower pressure by inserting it in the matrix of other elements. In this work we re-investigate the phase diagram and the superconducting properties of the H-S system by means of mi…
The rapid variation of the superconductivity Tc in hydride sulfur (H3S) under high pressure [A. Drozdov et al, Nature 525, 73 (2015); M. Einaga et al, arXiv: 1509.03156] in a vicinity Pcr=123GPa is interpreted in terms of the 1st order transition, possibly related to a CDW-instability with a non-zero structural vector. The superconductivity mechanisms in high-Tc phase be discussed, ordinary methods of calculating Tc are shown not applicable in H3S because, beside the acoustic branches, its phonon spectrum contains hydrogen modes with much higher frequency. A modified approach provides realisti…
Room-temperature superconductivity was recently discovered in carbonaceous sulfur hydride (C-S-H) close to 3\,Mbar. We report significant differences in the superconducting response of C-S-H, with a maximum $T_{C}$ of 191(1)\,K, below a 1\,Mbar. Variations in intensity of the C-H Raman modes reveal carbon content can vary between crystals synthesized with the same photo-induced method. Synchrotron single crystal x-ray diffraction identifies polymorphism with increasing degrees of covalency. These unique metastable states are highly sensitive to thermodynamic pathways.
We theoretically give an infinite number of metastable crystal structures for the superconducting sulfur hydride H$_{x}$S under pressure. It has been thought that theoretically predicted structures of H$_{2}$S and H$_{3}$S exhibit low and high $T_{\rm c}$ in the experiment, respectively. The newly found structures are long-period modulated crystals where slab-like H$_{2}$S and H$_{3}$S regions intergrow in a microscopic scale. The extremely small formation enthalpy for the H$_{2}$S--H$_{3}$S boundary indicated with the first-principles calculations suggests possible alloying of these phases th…
The recent report of superconductivity under high pressure at the record transition temperature of Tc=203K in sulfur hydride has been identified as conventional in view of the observation of an isotope effect upon deuteration. Here it is demonstrated that conventional theories of superconductivity in the sense of BCS or Eliashberg formalisms can neither account for the observed values of Tc nor the pressure dependence of the isotope coefficient. The only way out of the dilemma is a multi-band approach of superconductivity where already small interband coupling suffices to achieve the high valu…
Observation of high-temperature superconductivity in sulfur hydrides at megabar pressures has generated an irresistible wave on searching for new superconductors in other compressed hydrogen-rich compounds. An immediate effort is towards exploration of the relevant candidate of tellurium hydrides, where tellurium is isoelectronic to sulfur but it has a heavier atomic mass and much weaker electronegativity. The hitherto unknown phase diagram of tellurium hydrides at high pressures was investigated by a first-principles swarm structure search. Four energetically stable and metallic stoichiometri…
It is demonstrated that resistive transition at 203 K observed in metallic sulfur hydride system at high pressure can be magnetic (rather than superconducting (SC)) in nature. The onset temperature of genuine superconducting transition in these compounds appears to be essentially lower on temperature. The normal-state magnetic (AF SDW) phase transition preceding a superconducting one (Tc < Tm) is characteristic for HTSC cuprates, pnictides (selenides) and organic superconductors. The resistive drop is provided by disappearing of magnetic (AF spin fluctuation) scattering of conduction electrons…
A diamond anvil cell (DAC) which can generate extremely high pressure of multi-megabar is promising tool to develop a further physics such a high-transition temperature superconductivity. However, electrical transport measurements, which is one of the most important properties of such functional materials, using the DAC is quite difficult because the sample space is very small and a deformation of electrodes under extreme condition. In this study, we fabricated a boron-doped diamond micro-electrode and an undoped diamond insulation on a beveled culet surface of the diamond anvil. By using the …
Recently, Snider et al (2020 Nature 586 373) reported on the observation of superconductivity in highly-compressed carbonaceous sulfur hydride, $H_x$$(S,C)_y$. The highest critical temperature in $H_x$$(S,C)_y$ by 5 K exceeds previous record of Tc = 280 K reported by Somayazulu et al (2019 Phys. Rev. Lett. 122 027001) for highly-compressed $La$$H_{10}$. In this paper we analyze experimental temperature dependent magnetoresistance data, R(T,B), reported by Snider et al. The analysis shows that $H_x$$(S,C)_y$ compound exhibited Tc = 190 K (P = 210 GPa) has the electron-phonon coupling constant $…
A new experimental study by Snider et al. [Nature 586, 373-377 (2020)] reported behavior in a high-pressure carbon-sulfur-hydrogen system that has been interpreted by the authors as superconductivity at room temperature. The sudden drop of electrical resistance at a critical temperature and the change of the R vs. T behavior with an applied magnetic field point to superconductivity. This is a very exciting study in one of the most important areas of science, hence, it is crucial for the community to investigate these findings and hopefully reproduce these results. In this comment, we present c…
Recent discovery of high-temperature superconductivity (Tc = 190 K) in sulfur hydrides at megabar pressures breaks the traditional belief on the Tc limit of 40 K for conventional superconductors, and open up the doors in searching new high-temperature superconductors in compounds made up of light elements. Selenium is a sister and isoelectronic element of sulfur, with a larger atomic core and a weaker electronegativity. Whether selenium hydrides share similar high-temperature superconductivity remains elusive, but it is a subject of considerable interest. First-principles swarm structure predi…
The phenomenon of high temperature superconductivity, approaching room temperature, has been realized in a number of hydrogen-dominant alloy systems under high pressure conditions1-12. A significant discovery in reaching room temperature superconductivity is the photo-induced reaction of sulfur, hydrogen, and carbon that initially forms of van der Waals solids at sub-megabar pressures. Carbonaceous sulfur hydride has been demonstrated to be tunable with respect to carbon content, leading to different superconducting final states with different structural symmetries. A modulated AC susceptibili…
To understand the most-recent experiment on room-temperature superconductivity in carbonaceous sulfur hydride (CSH) systems under high pressure, we have performed extensive stoichiometry and structure searches of ternary CSH compounds using generic evolutionary algorithms. Judged from the formation enthalpy of different CSH compounds, our studies conclude that certain levels of carbon doping (~5%-6%) in sulfur hydride (H$_3$S) in its R3m and phases gives rise to the most-stable structure (second to the H$_3$S itself) among the various CSH systems found. The replacement of a small amount of sul…
The maximum critical temperature for superconductivity in pressurized hydrides appears at the top of superconducting domes in Tc versus pressure curves at a particular pressure, which is not predicted by standard superconductivity theories. The a high-order anisotropic van Hove singularity near the Fermi level observed in band structure calculations of pressurized sulfur hydride, typical of a supermetal, has been associated with the array of metallic hydrogen wires modules forming a nanoscale heterostructure at atomic limit called superstripes phase. Here we propose that pressurized sulfur hyd…
The recent discovery of room temperature superconductivity (283 K) in carbonaceous sulfur hydride (C-S-H) has attracted lots of interests in ternary hydrogen rich materials. In this report, ternary hydride P-S-H has been synthesized through photochemical reaction from elemental sulfur (S), phosphorus (P) and molecular hydrogen (H2) at high pressures and room temperature. The Raman spectroscopy under pressure shows that H2S and PH3 compounds are synthesized after laser heating at 0.9 GPa and a ternary van der Waals compound P-S-H is synthesized with a further compression to 4.6 GPa. The P-S-H c…
We calculate superconducting transition temperatures ($T_{\rm c}$) in sulfur hydrides H$_{2}$S and H$_{3}$S from first principles using the density functional theory for superconductors. At pressures of $\lesssim$150 GPa, the high values of $T_{\rm c}$ ($\gtrsim$130 K) observed in the recent experiment [A. P. Drozdov, M. I. Eremets, and I. A. Troyan, arXiv:1412.0460] are accurately reproduced by assuming that H$_{2}$S decomposes into $R3m$-H$_{3}$S and S. For the higher pressures, the calculated $T_{\rm c}$s for $Im3m$-H$_{3}$S are systematically higher than those for $R3m$-H$_{3}$S and the ex…
The recent discovery of superconductivity at 190~K in highly compressed H$_{2}$S is spectacular not only because it sets a record high critical temperature, but because it does so in a material that appears to be, and we argue here that it is, a conventional strong-coupling BCS superconductor. Intriguingly, superconductivity in the observed pressure and temperature range was predicted theoretically in a similar compound H$_{3}$S. Several important questions about this remarkable result, however, are left unanswered: (1) Does the stoichiometry of the superconducting compound differ from the nom…
Emerets's experiments on pressurized sulfur hydride have shown that H3S metal has the highest known superconducting critical temperature Tc=203K. The Emerets data show pressure induced changes of the isotope coefficient between 0.25 and 0.5, in disagreement with Eliashberg theory which predicts a nearly constant isotope coefficient. We assign the pressure dependent isotope coefficient to Lifshitz transitions induced by pressure and zero point lattice fluctuations. It is known that pressure could induce changes of the topology of the Fermi surface, called Lifshitz transitions, but were neglecte…
The superconducting state in Carbonaceous Sulfur Hydride (C-S-H) system is characterized by the record-high critical temperature of $288$~K experimentally observed at $\sim$267 GPa. Herein, we determined the properties of the \mbox{C-S-H} superconducting phase within the scope of both classical Eliashberg equations (CEE) and the Eliashberg equations with vertex corrections (VCEE). We took into account the scenarios pertinent to either the intermediate or the high value of electron-phonon coupling constant ($λ\sim 0.75$ or $λ\sim 3.3$, respectively). The scenario for the intermediate value, how…
The Meissner effect, magnetic field expulsion, is a hallmark of superconductivity. Associated with it, superconductors exclude applied magnetic fields. Recently Minkov et al. presented experimental results reportedly showing "definitive evidence of the Meissner effect" in sulfur hydride and lanthanum hydride under high pressure [1], and more recently Eremets et al. argued that "the arguments against superconductivity (in hydrides) can be either refuted or explained" [2]. Instead, we show here that the evidence presented in those papers does not support the case for superconductivity in these m…
Motivated by the recent report of superconductivity above 200 K in ultra-dense hydrogen sulfide, we search for high-\tc\ conventional superconductivity in the phase diagram of the binary Li-S system, using {\em ab-initio} methods for crystal structure prediction and linear response calculations for the electron-phonon coupling. We find that at pressures higher than 20 GPa, several new compositions, besides the known Li$_2$S, are stabilized; many exhibit electride-like {\em interstitial} charge localization observed in other alkali metal compounds. Of all predicted phases, only Li$_3$S at P > 6…
In this review article we consider theoretically and give experimental support to the models of the Fermi-Bose mixtures and the BCS-BEC crossover compared with the strong-coupling approach, which can serve as the cornerstones on the way from high-temperature to room-temperature superconductivity in pressurized metallic hydrides. We discuss some key theoretical ideas and mechanisms proposed for unconventional superconductors (cuprates, pnictides, chalcogenides, bismuthates, diborides, heavy-fermions, organics, bilayer graphene, twisted graphene, oxide hetero-structures), superfluids and balance…
Recently superconductivity has been discovered at around 200~K in a hydrogen sulfide system and around 260~K in a lanthanum hydride system, both under pressures of about 200 GPa. These record-breaking transition temperatures bring within reach the long-term goal of obtaining room temperature superconductivity. We have used first-principle calculations based on density functional theory (DFT) along with Migdal-Eliashberg theory to investigate the electron-phonon mechanism for superconductivity in the $Fm\bar{3}m$ phase proposed for the LaH$_{10}$ superconductor. We show that the very high trans…
Recently YH6, compound from a group of theoretically predicted stable compressed MH6 hydrides (M/ Ca, Mg, Y, Sc) with bcc Im-3m crystal structure, was successfully experimentally realized. Superconductivity of pressurized YH6 was confirmed experimentally, Tc / 224 K at 166 GPa, but with critical temperature considerably lower than value predicted by Migdal-Eliashberg (ME) theory. Here we present theoretical reinvestigation of superconductivity in MH6 hydrides. Our results confirm that YH6 and ScH6 with Im-3m structure at corresponding GPa pressures are superconductors but with an antiadiabatic…
The multiple scattering-based theory of Gaspari and Gyorffy for the electron-ion matrix element in close packed metals is applied to Im-3m H3S, which has been predicted by Duan {\it et al.} and Bernstein {\it et al} to be the stable phase at this stoichiometry around 190 GPa, thus is the leading candidate to be the phase observed to superconduct at 190K by Drozdov, Eremets, and Troyan. The nearly perfect separation of vibrational modes into those of S and of H character provides a simplification that enables identification of contributions of the two atoms separately. The picture that arises i…
Hydrogen-rich compounds have been extensively studied both theoretically and experimentally in the quest for novel high-temperature superconductors. Reports on sulfur-hydride attaining metallicity under pressure and exhibiting superconductivity at temperatures as high as 200 K have spurred an intense search for room-temperature superconductors in hydride materials. Recently, compressed phosphine was reported to metallize at pressures above 45 GPa, reaching a superconducting transition temperature (T$_{c}$) of 100 K at 200 GPa. However, neither the exact composition nor the crystal structure of…
In this work, we show that the same theoretical tools that successfully explain other hydrides systems under pressure seem to be at odds with the recently claimed conventional room temperature superconductivity of the carbonaceous sulfur hydride. We support our conclusions with I) the absence of a dominant low-enthalpy stoichiometry and crystal structure in the ternary phase diagram. II) Only the thermodynamics of C-doping phases appears to be marginally competing in enthalpy against H$_3$S. III) Accurate results of the transition temperature given by ab initio Migdal-Eliashberg calculations d…
Hydrogen-based superconductors provide a route to the long-sought goal of room-temperature superconductivity, but the high pressures required to metallize these materials limit their immediate application. For example, carbonaceous sulfur hydride, the first room-temperature superconductor, can reach a critical temperature (Tc) of 288 K only at the extreme pressure of 267 GPa. The next recognized challenge is the realization of room-temperature superconductivity at significantly lower pressures. Here, we propose a strategy for the rational design of high-temperature superconductors at low press…
High pressure serves as a path finding tool towards novel structures, including those with very high Tc.The superconductivity in sulfur hydrides with record value (203 K) is caused by the phonon mechanism. However, the picture differs from the conventional one in important ways. The phonon spectrum in sulfur hydride is both broad and has a complex structure. High value of Tc is mainly due to strong coupling to the high-frequency optical modes, although the acoustic phonons also make a noticeable contribution. New approach is described;it generalizes the standard treatment of the phonon mechani…
The highest critical temperature of superconductivity Tc has been achieved in cuprates: 133 K at ambient pressure and 164 K at high pressures. As the nature of superconductivity in these materials is still not disclosed, the prospects for a higher Tc are not clear. In contrast the Bardeen-Cooper-Schrieffer (BCS) theory gives a clear guide for achieving high Tc: it should be a favorable combination of high frequency phonons, strong coupling between electrons and phonons, and high density of states. These conditions can be fulfilled for metallic hydrogen and covalent hydrogen dominant compounds.…
In our desire to give a new suggestion for H-based superconductors experiments we present a theoretical framework for understanding the impact of an applied electric field on pressured hydride superconductors. We study a material at pressure $p$, when it possesses insulator-superconductor transition, at the respective superconducting critical temperature $T_{cr}$. The theory shows the applied electric field penetrates the material and forces the Cooper pairs to Bose condensate. If one applies an electric field and then increases the temperature, the theory predicts novel critical temperature $…
We examine the superconducting solution in the Holstein model, where the conduction electrons couple to the dispersionless Boson fields, using the Migdal-Eliashberg theory and Dynamical Mean Field Theory. Although different in numerical values, both methods imply the existence of an optimal Boson energy for superconductivity at a given electron-Boson coupling. This non-monotonous behavior can be understood as an interplay between the polaron and superconducting physics, as the electron-Boson coupling is the origin of the superconductor, but at the same time traps the conduction electrons makin…
A superconductor is a material that can conduct electricity with no resistance below its critical temperature (Tc). The highest Tc that has been achieved in cuprates1 is 133 K at ambient pressure2 and 164 K at high pressures3. As the nature of superconductivity in these materials has still not been explained, the prospects for a higher Tc are not clear. In contrast, the Bardeen-Cooper-Schrieffer (BCS) theory gives a guide for achieving high Tc and does not put bounds on Tc, all that is needed is a favorable combination of high frequency phonons, strong electron-phonon coupling, and a high dens…
Since pivotal experimental discovery of the near-room-temperature superconductivity (NRTS) in highly-compressed sulphur hydride by Drozdov et al (2015 Nature 525 73-76), more than a dozen of binary and of ternary hydrogen-rich phases exhibited superconducting transition above 100 K have been discovered to date. There is a widely accepted theoretical point of view that primary mechanism governing the emergence of superconductivity in hydrogen-rich phases is the electron-phonon pairing. However, our recent analysis of experimental temperature dependent resistance in $H_{3}S$, $LaH_{x}$, $PrH_{9}…
The discovery of a superconducting phase in sulfur hydride under high pressure with a critical temperature above 200 K has provided a new impetus to the search for even higher $T_c$. Theory predicted and experiment confirmed that the phase involved is H$_3$S with Im-3m crystal structure. The observation of a sharp drop in resistance to zero at $T_c$, its downward shift with magnetic field and a Meissner effect confirm superconductivity but the mechanism involved remains to be determined. Here, we provide a first optical spectroscopy study of this new superconductor. Experimental results for th…
