Magneto-optical conductivity in graphene including electron-phonon coupling

TL;DR

This paper investigates how electron-phonon coupling influences the magneto-optical conductivity of graphene, revealing shifted absorption peaks, new phonon-assisted features, and asymmetries in spectral weight distribution.

Contribution

It provides a detailed analysis of phonon-induced modifications to graphene's optical spectra, including selection rules and the impact on Landau level transitions under magnetic fields.

Findings

Coupling causes shifts and broadening of absorption peaks.

Additional peaks arise from phonon sidebands and Landau level splitting.

Asymmetry in spectral weight affects polarization-dependent transitions.

Abstract

We show how coupling to an Einstein phonon $\omega_E$ affects the absorption peaks seen in the optical conductivity of graphene under a magnetic field $B$. The energies and widths of the various lines are shifted, and additional peaks arise in the spectrum. Some of these peaks are Holstein sidebands, resulting from the transfer of spectral weight in each Landau level (LL) into phonon-assisted peaks in the spectral function. Other additional absorption peaks result from transitions involving split LLs, which occur when a LL falls sufficiently close to a peak in the self-energy. We establish the selection rules for the additional transitions and characterize the additional absorption peaks. For finite chemical potential, spectral weight is asymmetrically distributed about the Dirac point; we discuss how this causes an asymmetry in the transitions due to left- and right-handed circularly polarized light and therefore oscillatory behavior in the imaginary part of the off-diagonal Hall conductivity. We also find that the semiclassical cyclotron resonance region is renormalized by an effective-mass factor but is not directly affected by the additional transitions. Last, we discuss how the additional transitions can manifest in broadened, rather than split, absorption peaks due to large scattering rates seen in experiment.