Theory of phonon-mediated superconductivity in twisted bilayer graphene

TL;DR

This paper develops a microscopic theory explaining phonon-mediated superconductivity in twisted bilayer graphene near the magic angle, highlighting the roles of $s$ and $d$ wave pairing channels and Coulomb repulsion effects.

Contribution

It introduces a detailed phonon-electron coupling model for twisted bilayer graphene, predicting the conditions favoring $s$ or $d$ wave pairing and their spatial characteristics.

Findings

Phonons induce attractive interactions in $s$ and $d$ wave channels.

Coulomb repulsion suppresses $s$-wave pairing, favoring $d$-wave.

Superconducting pair amplitude varies with moiré pattern and differs between pairing symmetries.

Abstract

We present a theory of phonon-mediated superconductivity in near magic angle twisted bilayer graphene. Using a microscopic model for phonon coupling to moir\'e band electrons, we find that phonons generate attractive interactions in both $s$ and $d$ wave pairing channels and that the attraction is strong enough to explain the experimental superconducting transition temperatures. Before including Coulomb repulsion, the $s$-wave channel is more favorable; however, on-site Coulomb repulsion can suppress $s$-wave pairing relative to $d$-wave. The pair amplitude varies spatially with the moir\'e period, and is identical in the two layers in the $s$-wave channel but phase shifted by $\pi$ in the $d$-wave channel. We discuss experiments that can distinguish the two pairing states.