The possible role of van Hove singularities in the high $T_c$ of superconducting H$_3$S

TL;DR

This paper investigates how van Hove singularities influence the high critical temperature in superconducting H$_3$S, showing that peaks in the density of states can enhance superconductivity even with modest coupling.

Contribution

It demonstrates that a robust peak in the density of states, caused by van Hove singularities, can significantly boost $T_c$ in H$_3$S, and provides analytical solutions across coupling regimes.

Findings

Van Hove singularities create peaks in the density of states.

Enhanced $T_c$ is achievable with modest coupling strengths.

Nesting is reduced, minimizing competing instabilities.

Abstract

We observe that H$_3$S has a bcc structure and, with nearest neighbour hopping only, a strong singularity occurs at zero energy. This singularity is accompanied with a highly nested Fermi surface, which is {\it not} conducive to a stable superconducting instability. Introduction of next-nearest-neighbour hopping removes the singularity, but a `robust' peak remains in the electron density of states. Solution of the BCS equations shows an enhanced superconducting $T_c$ due to this peak. Furthermore, nesting is no longer present, so other instabilities will not compete effectively with superconductivity. We find high critical temperatures are possible, even with very modest coupling strengths. We also examine a limit of the $T=0$ equations (in an Appendix) where an analytical solution is possible over the entire range of coupling strengths, and therefore the BCS-BEC crossover is fully covered.