Anharmonic theory of superconductivity and its applications to emerging quantum materials

Abstract

The role of anharmonicity on superconductivity has often been disregarded in the past. Recently, it has been recognized that anharmonic decoherence could play a fundamental role in determining the superconducting properties (electron-phonon coupling, critical temperature, etc) of a large class of materials, including systems close to structural soft-mode instabilities, amorphous solids and metals under extreme high-pressure conditions. Here, we review recent theoretical progress on the role of anharmonic effects, and in particular certain universal properties of anharmonic damping, on superconductivity. Our focus regards the combination of microscopic-agnostic effective theories for bosonic mediators with the well-established BCS theory and Migdal-Eliashberg theory for superconductivity. We discuss in detail the theoretical frameworks, their possible implementation within first-principles methods, and the experimental probes for anharmonic decoherence. Finally, we present several concrete applications to emerging quantum materials, including hydrides, ferroelectrics and systems with charge density wave instabilities.

matching the published version

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• Accurate Electron-phonon Interactions from Advanced Density Functional Theory
• Quantum confinement theory of ultra-thin films: electronic, thermal and superconducting properties
• Ab initio study on magnetism suppression, anharmonicity, rattling mode and superconductivity in Sc${}_{6}M$Te${}_2$ ($M$=Fe, Co, Ni)
• Polarons with arbitrary nonlinear electron-phonon interaction
• Constrains on s and d components of electron boson coupling constants in one band d wave Eliashberg theory for high Tc superconductors
• Correlation between optical phonon softening and superconducting $T_c$ in YBa${}_2$Cu${}_3$O${}_x$ within $d$-wave Eliashberg theory
• Pressure-induced concurrent amorphization and superconductivity in topological material NbNiTe5