Anharmonic theory of superconductivity in the high-pressure materials
Chandan Setty, Matteo Baggioli, Alessio Zaccone
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 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 ${T}_{c}$ behaves nonmonotonically as a function of the ratio $\mathrm{\ensuremath{\Gamma}}/{\ensuremath{\omega}}_{0}$, where $\mathrm{\ensuremath{\Gamma}}$ is the optical phonon damping and ${\ensuremath{\omega}}_{0}$ is the optical phonon energy at zero pressure and momentum. Optimal pairing occurs for a critical ratio $\mathrm{\ensuremath{\Gamma}}/{\ensuremath{\omega}}_{0}$ when the phonons are on the verge of decoherence (``diffusonlike'' limit). Our framework gives insights into recent experimental observations of ${T}_{c}$ as a function of pressure in the complex BCS material ${\mathrm{TlInTe}}_{2}$.