Jahn-Teller coupling to moir\`e phonons in the continuum model formalism for small angle twisted bilayer graphene

TL;DR

This paper extends the continuum model of small-angle twisted bilayer graphene to include Jahn-Teller phonon coupling, revealing potential for gap opening and superconductivity phenomena.

Contribution

It introduces a method to incorporate Jahn-Teller phonons into the continuum model, enabling analysis of their effects on electronic properties.

Findings

Jahn-Teller phonons can open gaps at integer fillings.

Derived quantum mechanical electron-phonon Hamiltonian.

Potential implications for phonon-mediated superconductivity.

Abstract

We show how to include the Jahn-Teller coupling of \mo phonons to the electrons in the continuum model formalism which describes small-angle twisted bilayer graphene. These phonons, which strongly couple to the valley degree of freedom, are able to open gaps at most integer fillings of the four flat bands around the charge neutrality point. Moreover, we derive the full quantum mechanical expression of the electron-phonon Hamiltonian, which may allow accessing phenomena such as the phonon-mediated superconductivity and the dynamical Jahn-Teller effect.