Anharmonic theory of superconductivity in the high-pressure materials

TL;DR

This paper presents a minimal theoretical model explaining how pressure-induced anharmonic phonon effects influence superconductivity, revealing a non-monotonic relationship between critical temperature and phonon damping, with implications for high-pressure superconductors.

Contribution

It introduces a simplified model that captures the impact of phonon anharmonicity and decoherence on superconductivity under pressure, providing insights into experimental observations.

Findings

Optimal $T_c$ occurs at a critical phonon damping ratio $rac{ extGamma}{ extomega_0}$.

$T_c$ exhibits non-monotonic behavior as a function of pressure-related parameters.

The model explains recent experimental data on TlInTe$_2$ under high pressure.

Abstract

Electron-phonon superconductors at high pressures have displayed the highest values of critical superconducting temperature $T_c$ on record, now rapidly approaching room temperature. Despite the importance of high-$P$ superconductivity in the quest for room-temperature superconductors, a mechanistic understanding of the effect of pressure and its complex interplay with phonon anharmonicity and superconductivity is missing, as numerical simulations can only bring system-specific details clouding out key players controlling the physics. Here we develop a minimal model of electron-phonon superconductivity under an applied pressure which takes into account the anharmonic decoherence of the optical phonons. We find that $T_c$ behaves non-monotonically as a function of the ratio $\Gamma/\omega_0$, where $\Gamma$ is the optical phonon damping and $\omega_0$ the optical phonon energy at zero pressure and momentum. Optimal pairing occurs for a critical ratio $\Gamma/\omega_0$ when the phonons are on the verge of decoherence ("diffuson-like" limit). Our framework gives insights into recent experimental observations of $T_c$ as a function of pressure in the complex BCS material TlInTe$_2$.