Effects of electron-phonon coupling on Landau levels in graphene

TL;DR

This paper investigates how electron-phonon interactions affect Landau levels in graphene, revealing the emergence of new peaks and potential splitting of Landau levels depending on the phonon coupling and energy gaps.

Contribution

It provides a detailed analysis of the effects of phonon coupling on Landau levels, including the formation of new peaks and level splitting, which was not previously characterized.

Findings

Coupling to an Einstein phonon mode shifts and broadens Landau levels.

New peaks appear at energies offset by the phonon frequency, causing level splitting.

Extended phonon spectra do not qualitatively change the main effects.

Abstract

We calculate the density of states (DOS) in graphene for electrons coupled to a phonon in an external magnetic field. We find that coupling to an Einstein mode of frequency $\omega_E$ not only shifts and broadens the Landau levels (LLs), but radically alters the DOS by introducing a new set of peaks at energies $E_n\pm\omega_E$, where $E_n$ is the energy of the $n$th LL. If one of these new peaks lies sufficiently close to a LL, it causes the LL to split in two; if the system contains an energy gap, a LL may be split in three. The new peaks occur outside the interval $(-\omega_E,\omega_E)$, leaving the LLs in that interval largely unaffected. If the chemical potential is greater than the phonon frequency, the zeroth LL lies outside the interval and can be split, eliminating its association with a single Dirac point. We find that coupling to an extended phonon distribution such as a Lorentzian or Debye spectrum does not qualitatively alter these results.