Mean-field theory for superconductivity in twisted bilayer graphene

TL;DR

This paper develops a mean-field theory for s-wave superconductivity in twisted bilayer graphene near the magic angle, exploring how the superconducting state varies with twist angle and doping, and highlighting the role of flat bands and electron-phonon interactions.

Contribution

It introduces a mean-field model for superconductivity in twisted bilayer graphene, emphasizing the effects of flat bands and inhomogeneous order parameters, and connects findings to experimental observations.

Findings

Superconductivity is influenced by flat-band localization.

The order parameter becomes highly inhomogeneous.

Electron-phonon interactions may mediate pairing.

Abstract

Recent experiments show how a bilayer graphene twisted around a certain magic angle becomes superconducting as it is doped into a region with approximate flat bands. We investigate the mean-field $s$-wave superconducting state in such a system and show how the state evolves as the twist angle is tuned, and as a function of the doping level. We argue that part of the experimental findings could well be understood to result from an attractive electron--electron interaction mediated by electron--phonon coupling, but the flat-band nature of the excitation spectrum makes also superconductivity quite unusual. For example, as the flat-band states are highly localized around certain spots in the structure, also the superconducting order parameter becomes strongly inhomogeneous.