Periodic Trends and a Physics-Based Multistage Search for High-$T_c$ Hydride Superconductors

Abstract

Hydrogen-rich materials under pressure are candidates for conventional phonon-mediated superconductivity, but first-principles electron--phonon-coupling (EPC) calculations are computationally demanding. We develop an interpretable multistage workflow for prioritizing binary hydride superconductors before full EPC calculations. Using controlled cubic $X_m$H$_n$ prototypes at 200~GPa, we introduce the spectral moment $A_1$ as an intermediate measure of electron--phonon perturbation strength. In its linewidth-based construction, $A_1$ remains finite as harmonic phonons soften, allowing related structures with imaginary harmonic modes to be screened; it does not establish superconductivity or physical realizability for unstable structures. For dynamically stable cubic systems, $A_1$ correlates strongly with the H-$1s$ density-of-states fraction at the Fermi level, $\alpha$, a projected Fermi-surface descriptor, $\beta$, and atomic number density, $\rho$. These trends are summarized heuristically by $A_1\approx h\alpha\beta\rho$, where $h$ is framework- and pressure-dependent; the descriptor is used for ranking, not as a universal $T_c$ predictor. We incorporate $\alpha\beta\rho$ and enthalpic competitiveness into a three-stage evolutionary search comprising multiobjective structural screening, harmonic-phonon stability filtering, and coarse density-functional perturbation-theory (DFPT) EPC calculations. Application to more than 100,000 binary hydride structures at 50 and 200~GPa identifies candidates and prioritizes NaH$_6$ structural families. Higher-accuracy calculations show that $Pm\bar{3}m$ NaH$_6$ is dynamically stable down to 50~GPa and has a harmonic Allen--Dynes estimate of $T_c\approx230$~K. The framework combines electronic descriptors with progressively more expensive stability and EPC calculations for scalable hydride exploration.