Enhanced Coulomb pseudopotentials in high-pressure hydrides from first principles

Abstract

In the Eliashberg theory of superconductivity, Coulomb interactions oppose the phonon-mediated attraction and suppress the superconducting critical temperature $T_{\mathrm{c}}$. However, most first-principles predictions continue to treat this repulsion with an empirical Coulomb pseudopotential ${\mu }_{\text{ME}}^{\ast }$ in the range 0.1-0.15. Here we present first-principles calculations of the Coulomb parameter $\mu$ and pseudopotential ${\mu }_{\text{ME}}^{\ast }$ in superconducting hydrides across a range of pressures. The screened Coulomb interaction is evaluated at the random phase approximation level with the Mantel code. We demonstrate that several hydride systems, including H${}_3$S, YSbH${}_6$ and Mg${}_2$IrH${}_6$, have strong Coulomb repulsions driven by a large density of states at the Fermi energy, $N_{\mathrm{F}}$. For Mg${}_2$IrH${}_6$ we obtain $\mu =0.62$ and ${\mu }_{\text{ME}}^{\ast }\approx 0.39$, leading to a 40 K suppression in $T_{\mathrm{c}}$ relative to a standard ${\mu }_{\text{ME}}^{\ast }=0.16$. Our obtained ${\mu }_{\text{ME}}^{\ast }$ is far above the conventional range and, accounting for the energy dependence of the density of states, resolves the factor-of-two discrepancy between $T_{\mathrm{c}}$ estimates of previous studies. Across all systems and pressures studied, we find that $\mu$ closely tracks $N_{\mathrm{F}}$, suggesting that commonly used ${\mu }_{\text{ME}}^{\ast }$ values lead to overestimated $T_{\mathrm{c}}$ in materials where the density of states at the Fermi energy is large.

arXiv comment13 pages, 7 figures