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A recent ab initio investigation of Na-C binary compounds under moderate pressures has uncovered a possible stable NaC$_4$ superconductor with an estimated critical temperature up to 41K. We revisit this promising binary system by performing a more focused exploration of Na-intercalated graphite configurations, assessing the sensitivity of their thermodynamic stability to density functional approximations at different (T,P) conditions, and examining their superconducting properties with the anisotropic Migdal-Eliashberg formalism. The combinatorial screening of possible Na arrangements reveals additional stable stoichiometries, i.e., Na$_3$C$_{10}$, NaC$_8$, NaC$_{10}$, and NaC$_{12}$, that redefine the previously proposed convex hulls for pressures up to 10 GPa. The evaluation of formation enthalpies with different van der Waals functionals indicates that the proposed compounds might not be thermodynamically stable at zero temperature but some of them could stabilize due to the vibrational entropy or form via cold compression if graphite is used as a starting material. Our more rigorous modeling of the electron-phonon coupling in NaC$_4$ confirms the material's potential for high-temperature superconductivity, with a critical temperature reaching 48 K at 10 GPa, and reveals a well-defined two-gap structure unusual for an electron-doped compound. By tracking the position of the intercalant nearly free electron states with respect to the Fermi level in viable Na-C compounds, we map out the range of pressures and compositions needed for strong electron-phonon coupling and identify Na$_3$C$_{10}$ as an equally promising superconductor., Comment: 12 pages, 10 figures

We employ ab initio modeling to investigate the possibility of attaining high-temperature conventional superconductivity in ambient-pressure materials based on the known MgB$_2$C$_2$ and recently proposed thermodynamically stable NaBC ternary compounds. The constructed $(T,P_M)$ phase diagrams (M = Mg or Na) indicate that these layered metal borocarbides can be hole-doped via thermal deintercalation that has been successfully used in previous experiments to produce Li$_y$BC ($y=1>x\gtrsim0.5$) samples. The relatively low temperature threshold required to trigger NaBC desodiation may help prevent the formation of defects shown recently to be detrimental to the electron-phonon coupling in the delithiated LiBC analog. According to our numerical solutions of the anisotropic full-bandwidth Migdal-Eliashberg equations, the proposed Mg$_x$B$_2$C$_2$ and Na$_x$BC materials exhibit superconducting critical temperatures between 43 K and 84 K. At the same time, we demonstrate that buckling of defect-free honeycomb BC layers, favored in heavily-doped Na$_x$BC compounds, can substantially reduce or effectively suppress the materials' potential for MgB$_2$-type superconductivity., Comment: 11 pages, 8 figures and 1 table

In this study, we combine the ab initio Migdal-Eliashberg approach with the intermediate representation for the Green's function, enabling accurate and efficient calculations of the momentum-dependent superconducting gap function while fully considering the effect of the Coulomb retardation. Unlike the conventional scheme that relies on a uniform sampling across Matsubara frequencies - demanding hundreds to thousands of points - the intermediate representation works with fewer than 100 sampled Matsubara Green's functions. The developed methodology is applied to investigate the superconducting properties of three representative low-temperature elemental metals: aluminum (Al), lead (Pb), and niobium (Nb). The results demonstrate the power and reliability of our computational technique to accurately solve the ab initio anisotropic Migdal-Eliashberg equations even at extremely low temperatures, below 1 Kelvin., Comment: 13 pages, 8 figures

Delithiation of the known layered LiBC compound was predicted to induce conventional superconductivity at liquid nitrogen temperatures but extensive experimental work over the past two decades has detected no signs of the expected superconducting transition. Using a combination of first-principles stability analysis and anisotropic Migdal-Eliashberg formalism, we have investigated possible Li$_x$BC morphologies and established what particular transformations of the planar honeycomb BC layers are detrimental to the material's superconductivity. We propose that Li$_x$BC reintercalation with select alkali and alkaline earth metals could lead to synthesis of otherwise inaccessible metastable Li$_x$M$_y$BC superconductors with critical temperatures ($T_{c}$) up to 73 K. The large-scale exploration of metal borocarbides has revealed that NaBC and Li$_{1/2}$Na$_y$BC layered phases are likely true ground states at low temperatures. The findings indicate that this compositional space may host overlooked synthesizable compounds with potential to break the $T_{c}$ record for conventional superconductivity in ambient-pressure materials., Comment: 15 pages, 10 figures

Over the last two decades, following the early developments on maximally localized Wannier functions, an ecosystem of electronic-structure simulation techniques and software packages leveraging the Wannier representation has flourished. This environment includes codes to obtain Wannier functions and interfaces with first-principles simulation software, as well as an increasing number of related post-processing packages. Wannier functions can be obtained for isolated or extended systems (both crystalline and disordered), and can be used to understand chemical bonding, to characterize electric polarization, magnetization, and topology, or as an optimal basis set, providing very accurate interpolations in reciprocal space or large-scale Hamiltonians in real space. In this review, we summarize the current landscape of techniques, materials properties and simulation codes based on Wannier functions that have been made accessible to the research community, and that are now well integrated into what we term a \emph{Wannier function software ecosystem}. First, we introduce the theory and practicalities of Wannier functions, starting from their broad domains of applicability to advanced minimization methods using alternative approaches beyond maximal localization. Then we define the concept of a Wannier ecosystem and its interactions and interoperability with many quantum simulations engines and post-processing packages. We focus on some of the key properties and capabilities that are empowered by such ecosystem\textemdash from band interpolations and large-scale simulations to electronic transport, Berryology, topology, electron-phonon couplings, dynamical mean-field theory, embedding, and Koopmans functionals\textemdash concluding with the current status of interoperability and automation. [...], Comment: Review article, revised version, 60 pages, 12 figures, references in alphabetical order. To appear in Rev. Mod. Phys. https://journals.aps.org/rmp/accepted/e3072EabZ471ee0bd0ff81e5ef7e01214bbaff57a

We apply a novel chemical capacitor setup to facilitate metallization of ionic hydrides, LiH and MgH2. It turns out that the amount of holes doped to a single layer of these materials may reach 0.72 per H atom without structure collapse; concomitant maximum TC values exceed 17 K in the absence of external pressure for 0.31-hole-doped LiH supported on the LiBaF3 perovskite., Comment: 6 pages, 1 table, 5 figures and graphical entry figure plus electronic supplement of 65 pages

EPW is an open-source software for $\textit{ab initio}$ calculations of electron-phonon interactions and related materials properties. The code combines density functional perturbation theory and maximally-localized Wannier functions to efficiently compute electron-phonon coupling matrix elements on ultra-fine Brillouin zone grids. This data is employed for predictive calculations of temperature-dependent properties and phonon-assisted quantum processes in bulk solids and low-dimensional materials. Here, we report on significant new developments in the code that occurred during the period 2016-2022, namely: a transport module for the calculation of charge carrier mobility and conductivity under electric and magnetic fields within the $\textit{ab initio}$ Boltzmann transport equation; a superconductivity module for the calculation of critical temperature and gap structure in phonon-mediated superconductors within the $\textit{ab initio}$ anisotropic multi-band Eliashberg theory; an optics module for calculations of phonon-assisted indirect transitions; a module for the calculation of small and large polarons without supercells using the $\textit{ab initio}$ polaron equations; and a module for calculating electron-phonon couplings, band structure renormalization, and temperature-dependent optical spectra using the special displacement method. For each capability, we outline the methodology and implementation, and provide example calculations. We describe recent code refactoring to prepare EPW for exascale architectures, we discuss efficient parallelization strategies, and report on extreme parallel scaling tests., Comment: 61 pages, 9 figures

Prediction of high-$T_{\rm{c}}$ superconductivity in hole-doped Li$_x$BC two decades ago has brought about an extensive effort to synthesize new materials with honeycomb B-C layers, but the thermodynamic stability of Li-B-C compounds remains largely unexplored. In this study, we use density functional theory to characterize well-established and recently reported Li-B-C phases. Our calculation of the Li chemical potential in Li$_x$BC helps estimate the ($T$,$P$) conditions required for delithiation of the LiBC parent material, while examination of B-C phases helps rationalize the observation of metastable BC$_3$ polymorphs with honeycomb and diamond-like morphologies. At the same time, we demonstrate that recently reported BC$_3$, LiBC$_3$, and Li$_2$B$_2$C phases with new crystal structures are both dynamically and thermodynamically unstable. With a combination of evolutionary optimization and rational design, we identify considerably more natural and favorable Li$_2$B$_2$C configurations that, nevertheless, remain above the thermodynamic stability threshold.

Gold is one of the most inert metals, forming very few compounds, some with rather interesting properties, and only two of them currently known to be superconducting under certain conditions (AuTe$_2$ and SrAuSi$_3$). Compounds of another noble element, Ag, are also relatively rare, and very few of them are superconducting. Finding new superconducting materials containing gold (and silver) is a challenge - especially having in mind that the best high-$T_c$ superconductors at normal conditions are based upon their rather close ''relative'', Cu. Here we report combined X-ray diffraction, Raman, and resistivity measurements, as well as first-principles calculations, to explore the effect of hydrostatic pressure on the properties of the sylvanite mineral, AuAgTe$_4$. Our experimental results, supported by density functional theory, reveal a structural phase transition at $\sim$5 GPa from a monoclinic $P2/c$ to $P2/m$ phase, resulting in almost identical coordinations of Au and Ag ions, with rather uniform interatomic distances. Further, resistivity measurements show the onset of superconductivity at $\sim$1.5 GPa in the $P2/c$ phase, followed by a linear increase of $T_c$ up to the phase transition, with a maximum in the $P2/m$ phase, and a gradual decrease afterwards. Our calculations indicate phonon-mediated superconductivity, with the electron-phonon coupling coming predominantly from the low-energy phonon modes. Thus, along with the discovery of a new superconducting compound of gold/silver, our results advance understanding of the mechanism of the superconductivity in Au-containing compounds, which may pave the way to the discovery of novel ones.

LiB, a predicted layered compound analogous to the MgB$_2$ superconductor, has been recently synthesized via cold compression and quenched to ambient pressure, yet its superconducting properties have not been measured. According to prior isotropic superconductivity calculations, the critical temperature ($T_{\rm{c}}$) was expected to be only 10$-$15 K. Using the anisotropic Migdal-Eliashberg formalism, we show that the $T_{\rm{c}}$ may actually exceed 32 K. Our analysis of the contribution from different electronic states helps explain the detrimental effect of pressure and doping on the compound's superconducting properties. In the search for related superconductors, we screened Li-Mg-B binary and ternary layered materials and found metastable phases with $T_{\rm{c}}$ close to or even 10$-$20% above the record 39 K value in MgB$_2$. Our reexamination of the Li-B binary phase stability reveals a possible route to synthesize the LiB superconductor at lower pressures readily achievable in multianvil cells.

Molybdenum ditelluride (MoTe$_2$) is attracting considerable interest since it is the archetypal type-II Weyl semimetal and a candidate for topological superconductivity. We investigate the superconducting phase diagram of two MoTe$_2$ polymorphs using the $ab~initio$ anisotropic Migdal-Eliashberg theory, and we show that the superconducting dome originates from the synergistic contribution of the density of states at the Fermi level and the transverse acoustic Te modes in the 1T$^\prime$ phase. We find that the electron and hole pockets carry trivial $s$-wave order parameters of slightly different magnitude, reminiscent of a two-gap structure as suggested by recent experiments. We suggest that a possible route for enhancing the superconducting critical temperature, and realizing $s_{+-}$ pairing, in the T$_d$ phase is to exploit its non-trivial band topology via electron doping., Comment: 10 pages, 8 figures, and contains supplemental material

The tin-selenide and tin-sulfide classes of materials undergo multiple structural transitions under high pressure leading to periodic lattice distortions, superconductivity, and topologically non-trivial phases, yet a number of controversies exist regarding the structural transformations in these systems. We perform first-principles calculations within the framework of density functional theory and a careful comparison of our results with available experiments on SnSe$_2$ reveals that the apparent contradictions among high-pressure results can be attributed to differences in experimental conditions. We further demonstrate that under hydrostatic pressure a $\sqrt{3} \times \sqrt{3} \times 1$ superstructure can be stabilized above 20 GPa in SnS$_2$ via a periodic lattice distortion as found recently in the case of SnSe$_2$, and that this pressure-induced phase transition is due to the combined effect of Fermi surface nesting and electron-phonon coupling at a momentum wave vector $\mathbf{q}$ = $(1/3, 1/3, 0)$. In addition, we investigate the contribution of nonadiabatic corrections on the calculated phonon frequencies, and show that the quantitative agreement between theory and experiment for the high-energy $A_{1g}$ phonon mode is improved when these effects are taken into account. Finally, we examine the nature of the superconducting state recently observed in SnSe$_2$ under nonhydrostatic pressure and predict the emergence of superconductivity with a comparable critical temperature in SnS$_2$ under similar experimental conditions. Interestingly, in the periodic lattice distorted phases, the critical temperature is found to be reduced by an order of magnitude due to the restructuring of the Fermi surface., Comment: accepted manuscript, 15 pages, 11 figures, and supplemental material

We performed high pressure x-ray diffraction (XRD), Raman, and transport measurements combined with first-principles calculations to investigate the behavior of tin diselenide (SnSe$_2$) under compression. The obtained single-crystal XRD data indicate the formation of a $(1/3,1/3,1)$-type superlattice above 17 GPa. According to our density functional theory results, the pressure-induced transition to the commensurate periodic lattice distortion (PLD) phase is due to the combined effect of strong Fermi surface nesting and electron-phonon coupling at a momentum wave vector $\mathbf{q}=(1/3,1/3,1)$. In contrast, similar PLD transitions associated with charge density wave (CDW) orderings in transition metal dichalcogenides (TMDs) do not involve significant Fermi surface nesting. The discovered pressure-induced PLD is quite remarkable, as pressure usually suppresses CDW phases in related materials. Our findings, therefore, provide new playgrounds to study the intricate mechanisms governing the emergence of PLD in TMD-related materials., Comment: 6 pages, 4 figures + Supplemental (12 pages, 14 figures)

We probe the accuracy limit of {\it ab initio} calculations of carrier mobilities in semiconductors, within the framework of the Boltzmann transport equation. By focusing on the paradigmatic case of silicon, we show that fully predictive calculations of electron and hole mobilities require many-body quasiparticle corrections to band structures and electron-phonon matrix elements, the inclusion of spin-orbit coupling, and an extremely fine sampling of inelastic scattering processes in momentum space. By considering all these factors we obtain excellent agreement with experiment, and we identify the band effective masses as the most critical parameters to achieve predictive accuracy. Our findings set a blueprint for future calculations of carrier mobilities, and pave the way to engineering transport properties in semiconductors by design., Comment: 11 pages and 8 figures

We elucidate the origin of the phonon-mediated superconductivity in 2$H$-NbS$_2$ using the ab initio anisotropic Migdal-Eliashberg theory including Coulomb interactions. We demonstrate that superconductivity is associated with Fermi surface hot spots exhibiting an unusually strong electron-phonon interaction. The electron-lattice coupling is dominated by low-energy anharmonic phonons, which place the system on the verge of a charge density wave instability. We also provide definitive evidence for two-gap superconductivity in 2$H$-NbS$_2$, and show that the low- and high-energy peaks observed in tunneling spectra correspond to the $\Gamma$- and $K$-centered Fermi surface pockets, respectively. The present findings call for further efforts to determine whether our proposed mechanism underpins superconductivity in the whole family of metallic transition metal dichalcogenides., Comment: 6 pages, 5 figures and Supplemental Material

The recent discovery of topologically protected surface states in the noncentrosymmetric $\alpha$-BiPd and the centrosymmetric $\beta$-Bi$_{2}$Pd has renewed the interest in the Bi-Pd family of superconductors. Here, we employ first-principles calculations to investigate the structure, electronic, and topological features of $\beta$-Bi$_{2}$Pd, in bulk and in thin films of various thicknesses. We find that the Van der Waals dispersion corrections are important for reproducing the experimental structural parameters, while the spin-orbit interaction is critical for properly describing the appearance of topological electronic states. By increasing the thickness of the slab, the Dirac-cone surface states and the Rashba-type surface states gradually emerge at 9 and 11 triple-layers., Comment: 8 pages, 6 figures

The EPW (Electron-Phonon coupling using Wannier functions) software is a Fortran90 code that uses density-functional perturbation theory and maximally localized Wannier functions for computing electron-phonon couplings and related properties in solids accurately and efficiently. The EPW v4 program can be used to compute electron and phonon self-energies, linewidths, electron-phonon scattering rates, electron-phonon coupling strengths, transport spectral functions, electronic velocities, resistivity, anisotropic superconducting gaps and spectral functions within the Migdal-Eliashberg theory. The code now supports spin-orbit coupling, time-reversal symmetry in non-centrosymmetric crystals, polar materials, and $\mathbf{k}$ and $\mathbf{q}$-point parallelization. Considerable effort was dedicated to optimization and parallelization, achieving almost a ten times speedup with respect to previous releases. A computer test farm was implemented to ensure stability and portability of the code on the most popular compilers and architectures. Since April 2016, version 4 of the EPW code is fully integrated in and distributed with the Quantum ESPRESSO package, and can be downloaded through QE-forge at http://qe-forge.org/gf/project/q-e., Comment: 24 pages and 22 figures