Electron-phonon bound states in graphene in a perpendicular magnetic field

TL;DR

This paper investigates electron-phonon complexes in graphene under a magnetic field, revealing bound states near phonon emission thresholds that are governed by non-perturbative effects.

Contribution

It introduces a non-perturbative analysis of electron-phonon bound states in graphene in a magnetic field, highlighting new spectral branches near phonon emission thresholds.

Findings

Bound states of electrons and phonons exist near emission thresholds.

These states have a binding energy proportional to the electron-phonon coupling.

Perturbation theory fails near the phonon emission threshold.

Abstract

The spectrum of electron-phonon complexes in a monolayer graphene is investigated in the presence of a perpendicular quantizing magnetic field. Despite the small electron-phonon coupling, usual perturbation theory is inapplicable for calculation of the scattering amplitude near the threshold of the optical phonon emission. Our findings beyond perturbation theory show that the true spectrum near the phonon emission threshold is completely governed by new branches, corresponding to bound states of an electron and an optical phonon with a binding energy of the order of $\alpha \omega_{0}$ where $\alpha$ is the electron-phonon coupling and $\omega_{0}$ the phonon energy.