Proton Quantum Effects in H$_3$S Electronic Structure: A Multicomponent DFT study via Nuclear-Electronic Orbital Method

TL;DR

This study uses Nuclear-Electronic Orbital DFT to assess how proton quantum effects influence the electronic structure and phonons of high-pressure H$_3$S, revealing minimal impact on $T_c$ from electronic changes but significant phonon modifications.

Contribution

First-principles NEO-DFT calculations show proton quantum effects mainly affect phonons, with minor electronic structure modifications, clarifying their role in high-pressure H$_3$S superconductivity.

Findings

NQEs cause subtle electronic band structure modifications near the Fermi level.

Phonon dispersion calculations show large changes in hydrogen-dominated phonons due to NQEs.

Changes in the DOS would only slightly increase $T_c$, while phonon effects explain the $T_c$ reduction upon deuteration.

Abstract

We investigate the impact of the quantum effects of protons on the electronic structure of high-pressure H$_3$S, a benchmark hydrogen-rich superconductor with a critical temperature ($T_c$) exceeding 200 K. Using Nuclear-Electronic Orbital Density Functional Theory (NEO-DFT), we treat hydrogen nuclei quantum mechanically on the same footing as electrons within a first-principles framework. Our calculations reveal that nuclear quantum effects (NQEs) induce subtle modifications to the electronic band structure and density of states (DOS) near the Fermi energy, including features associated with van Hove singularities. However, the resulting changes in the DOS would increase $T_c$ by only a few percent. On the other hand, calculations of the phonon dispersion with the NEO-DFT method show large changes in the hydrogen-dominated phonons that arise from a stiffening of the S-H bonds due to NQEs. These findings imply that the experimentally observed reduction in $T_c$ upon deuteration arises predominantly from changes in the phonon properties, while NQEs-induced modifications to the electronic structure itself are minimal.