Electronic structure theory of H$_{3}$S: Plane-wave-like valence states, density-of-states peak and its guaranteed proximity to the Fermi level

Abstract

Superconductivity in sulfur superhydride H$_{3}$S under extreme pressures has been explained theoretically, but it requires a peaked concentration of the electronic density of states (DOS), which has been found in first-principles calculations. The mechanism of this peak formation, though vital for its high transition temperature, has however remained obscure. We address this problem through detailed analysis of the first-principles electronic wave functions. The valence wave functions are shown to be significantly plane-wave-like. From the Fourier-mode analysis of the self-consistent potential and atomic pseudopotentials, we extract the nearly uniform models that accurately reproduce the first-principles band structure with very few parameters. The DOS peak is shown to be the consequence of the hybridization of specific plane waves. Adjacency of Jones' large zone to the plane-wave spherical Fermi surface is posited to be the root cause of the multiple plane-wave hybridization, the DOS peak formation and its proximity to the Fermi level. The present theory resolves the minimal modeling problem of electronic states in H$_{3}$S, as well as establishes a mechanism that may help to boost the transition temperatures in pressure induced superconductors.