Competition of electron-phonon mediated superconductivity and Stoner magnetism on a flat band

TL;DR

This paper extends Eliashberg theory to flat band systems, analyzing the competition between electron-phonon mediated superconductivity and Stoner magnetism, and provides a phase diagram relevant for quantum materials.

Contribution

It generalizes strong-coupling superconductivity theory to flat bands and relates critical temperature to microscopic interactions, including magnetic phases.

Findings

Derived a relation between critical temperature and microscopic parameters.

Constructed a phase diagram showing superconducting and magnetic phases.

Analyzed strong-coupling corrections to BCS theory.

Abstract

The effective attractive interaction between electrons, mediated by electron-phonon coupling, is a well-established mechanism of conventional superconductivity. In metals exhibiting a Fermi surface, the critical temperature of superconductivity is exponentially smaller than the characteristic phonon energy. Therefore such superconductors are found only at temperatures below a few Kelvin. Systems with flat energy bands have been suggested to cure the problem and provide a route to room-temperature superconductivity, but previous studies are limited to only BCS models with an effective attractive interaction. Here we generalize Eliashberg's theory of strong-coupling superconductivity to systems with flat bands and relate the mean-field critical temperature to the microscopic parameters describing electron-phonon and electron-electron interaction. We also analyze the strong-coupling corrections to the BCS results, and construct the phase diagram exhibiting superconductivity and magnetic phases on an equal footing. Our results are especially relevant for novel quantum materials where electronic dispersion and interaction strength are controllable.