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Designing new, technologically relevant superconductors has long been at the forefront of solid-state physics and chemistry research. However, developing efficient approaches for modeling the thermodynamics of superconducting alloys while accurately evaluating their physical properties has proven to be a very challenging task. To fill this gap, we propose an ab initio thermodynamic statistical method, the Extended Generalized Quasichemical Approximation (EGQCA), to describe off-stoichiometric superconductors. Within EGQCA, one can predict any computationally accessible property of the alloy, such as the critical temperature in superconductors and the electron-phonon coupling parameter, as a function of composition and crystal growth conditions by computing the cluster occurrence probabilities that minimize the overall mixing Gibbs free energy. Importantly, EGQCA incorporates directly chemical ordering, lattice distortions, and vibrational contributions. As a proof of concept, we applied EGQCA to the well-known Al-doped MgB$_2$ and to niobium alloyed with titanium and vanadium, showing a remarkable agreement with the experimental data. Additionally, we model the near-room temperature sodalite-like Y$_{1-x}$Ca$_x$H$_6$ superconducting solid solution, demonstrating that EGQCA particularly possesses a promising potential for designing in silico high-$T_{\text{c}}$ superhydride alloys. Our approach notably enables the high-throughput screening of complex superconducting solid solutions, intrinsically providing valuable insights into the interplay between synthesis, thermodynamics, and physical properties.

Migdal-Eliashberg theory is one of the state-of-the-art methods for describing conventional superconductors from first principles. However, widely used implementations assume a constant density of states around the Fermi level, which hinders a proper description of materials with distinct features in its vicinity. Here, we present an implementation of the Migdal-Eliashberg theory within the EPW code that considers the full electronic structure and accommodates scattering processes beyond the Fermi surface. To significantly reduce computational costs, we introduce a non-uniform sampling scheme along the imaginary axis. We demonstrate the power of our implementation by applying it to the sodalite-like clathrates YH$_6$ and CaH$_6$, and to the covalently-bonded H$_3$S and D$_3$S. Furthermore, we investigate the effect of maximizing the density of states at the Fermi level in doped H$_3$S and BaSiH$_8$ within the full-bandwidth treatment compared to the constant-density-of-states approximation. Our findings highlight the importance of this advanced treatment in such complex materials., Comment: 16 pages, 4 figures. Revised manuscript with minor changes. Supplemental Information available on the journal website (open access)

In this work, we resolve conflicting experimental and theoretical findings related to the dynamical stability and superconducting properties of $Fm\overline{3}m$-LuH$_3$, which was recently suggested as the parent phase harboring room-temperature superconductivity at near-ambient pressures. Including temperature and quantum anharmonic lattice effects in our calculations, we demonstrate that the theoretically predicted structural instability of the $Fm\overline{3}m$ phase near ambient pressures is suppressed for temperatures above $200\,\text{K}$. We provide a $p\,\unicode{x2013}\,T$ phase diagram for stability up to pressures of $6\,\text{GPa}$, where the required temperature for stability is reduced to $T>80\,\text{K}$. We also determine the superconducting critical temperature $T_\text{c}$ of $Fm\overline{3}m$-LuH$_3$ within the Migdal-Eliashberg formalism, using temperature- and quantum-anharmonically-corrected phonon dispersions, finding that the expected $T_\text{c}$ for electron-phonon mediated superconductivity is in the range of $50$ $\unicode{x2013}$ $60\,\text{K}$, i.e., well below the temperatures required to stabilize the lattice. When considering moderate doping based on rigidly shifting the Fermi level, $T_\text{c}$ decreases for both hole and electron doping. Our results thus provide evidence that any observed room-temperature superconductivity in pure or doped $Fm\overline{3}m$-LuH$_3$, if confirmed, cannot be explained by a conventional electron-phonon mediated pairing mechanism., Comment: 9 pages, 5 figures. Revised manuscript. Supplemental Information available on the journal website (open access)

The quantum nature of the hydrogen lattice in superconducting hydrides can have crucial effects on the material's properties. Taking a detailed look at the dynamic stability of the recently predicted BaSiH$_8$ phase, we find that the inclusion of anharmonic quantum ionic effects leads to an increase in the critical dynamical pressure to $20\,\text{GPa}$ as compared to $5\,\text{GPa}$ within the harmonic approximation. We identify the change in the crystal structure due to quantum ionic effects to be the main driving force for this increase and demonstrate that this can already be understood at the harmonic level by considering zero-point energy corrections to the total electronic energy. In fact, the previously determined critical pressure of kinetic stability $p_\text{kin} = 30\,\text{GPa}$ still poses a stricter bound for the synthesizability of BaSiH$_8$ and similar hydride materials than the dynamical stability and therefore constitutes a more rigorous and accurate estimate for the experimental realizability of these structures., Comment: 10 pages, 5 figures. Revised manuscript with minor changes. Supplemental Material available on the journal website (open access)

We report the theoretical prediction of two high-performing hydride superconductors BaSiH$_8$ and SrSiH$_8$. They are thermodynamically stable above pressures of $130$ and $174\,\text{GPa}$, respectively, and metastable below that. Employing anharmonic phonon calculations, we determine the minimum pressures of dynamical stability to be around $3\,\text{GPa}$ for BaSiH$_8$ and $27\,\text{GPa}$ for SrSiH$_8$, and using the fully anisotropic Migdal-Eliashberg theory, we predict $T_\text{c}$'s around $71$ and $126\,\text{K}$, respectively. We also introduce a method to estimate the lowest pressure of synthesis, based on the calculation of the enthalpy barriers protecting the BaSiH$_8$ $Fm\bar{3}m$ structure from decomposition at various pressures. This $kinetic$ pressure threshold is sensibly higher than the one based on $dynamic$ stability, but gives a much more rigorous limit for synthesizability., Comment: 9 pages, 6 figures. Revised manuscript with minor changes. Supplemental Material available on the journal website (open access)

In this work we explore the phase diagram of the binary Nb-S system from ambient pressures up to 250 GPa using $ab$ $initio$ evolutionary crystal structure prediction. We find several new stable compositions and phases, especially in the high-pressure regime, and investigate their electronic, vibrational, and superconducting properties. Our calculations show that all materials, besides the low-pressure phases of pure sulfur, are metals with low electron-phonon coupling strengths and critical superconducting temperatures below 15 K. Furthermore, we investigate the effects of phonon anharmonicity on lattice dynamics, electron-phonon interactions, and superconductivity for the novel high-pressure phase of $\mathrm{Nb}_2\mathrm{S}$, demonstrating that the inclusion of anharmonicity stabilizes the lattice and enhances the electron-phonon interaction., Comment: 9 pages, 6 figures and Supplemental Material

We evaluate the non-equilibrium single particle Green's functions in the steady state of the interacting resonant level model (IRLM) under the effect of an applied bias voltage. Employing the so-called auxiliary master equation approach, we present accurate nonperturbative results for the non-equilibrium spectral and effective distribution functions, as well as for the current-voltage characteristics. We find a drastic change of these spectral properties between the regimes of low and high bias voltages and discuss the relation of these changes to the negative differential conductance (NDC), a prominent feature in the non-equilibrium IRLM. The anomalous evolution of the distribution function next to the impurity shown by our calculations suggests a mechanism whereby the impurity gets effectively decoupled from the leads at voltages where the NDC sets in, in agreement with previous renormalization group approaches. This scenario is qualitatively confirmed by a Hartree-Fock treatment of the model.