Impact of Many-Body Effects on Landau Levels in Graphene

TL;DR

This study uses magneto-Raman spectroscopy on suspended graphene to explore how many-body electron-electron interactions influence Landau level energies and Fermi velocity, revealing a density-dependent linear scaling due to magnetic field effects.

Contribution

It provides the first experimental observation of a piecewise linear Fermi velocity scaling in graphene under magnetic fields, supported by tight-binding Hartree-Fock calculations.

Findings

Fermi velocity scales linearly with charge density in magnetic fields

Long-range Coulomb interactions are suppressed by magnetic fields

Estimated excitonic binding energy is approximately 6 meV

Abstract

We present magneto-Raman spectroscopy measurements on suspended graphene to investigate the charge carrier density-dependent electron-electron interaction in the presence of Landau levels. Utilizing gate-tunable magneto-phonon resonances, we extract the charge carrier density dependence of the Landau level transition energies and the associated effective Fermi velocity $v_\mathrm{F}$. In contrast to the logarithmic divergence of $v_\mathrm{F}$ at zero magnetic field, we find a piecewise linear scaling of $v_\mathrm{F}$ as a function of charge carrier density, due to a magnetic field-induced suppression of the long-range Coulomb interaction. We quantitatively confirm our experimental findings by performing tight-binding calculations on the level of the Hartree-Fock approximation, which also allow us to estimate an excitonic binding energy of $\approx$ 6 meV contained in the experimentally extracted Landau level transitions energies.