Anharmonic theory of superconductivity in the high-pressure materials

Abstract

Electron-phonon superconductors at high pressures have displayed the highest values of critical superconducting temperature Tc 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 bring only 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 Tc behaves nonmonotonically as a function of the ratio Γ/ω0, where Γ is the optical phonon damping and ω0 is the optical phonon energy at zero pressure and momentum. Optimal pairing occurs for a critical ratio Γ/ω0 when the phonons are on the verge of decoherence ("diffusonlike"limit). Our framework gives insights into recent experimental observations of Tc as a function of pressure in the complex BCS material TlInTe2