Theoretical analysis of the density of states of graphene at high magnetic field using Haldane pseudopotentials

TL;DR

This paper provides a theoretical analysis of the density of states in graphene under high magnetic fields, revealing additional spectral peaks influenced by Haldane pseudopotentials, which can help measure electron interactions.

Contribution

It introduces a theoretical framework linking spectral peaks in graphene's density of states to Haldane pseudopotentials, highlighting complex peak dependencies unlike in standard 2D gases.

Findings

Additional spectral peaks ('sashes') appear in the density of states.

Peak energies depend on combinations of multiple pseudopotentials.

Measuring these peaks can determine interaction strengths in graphene.

Abstract

We study the density of states in graphene at high magnetic field, when the physics is dominated by strong correlations between electrons. In particular we use the method of Haldane pseudopotentials to focus on almost empty or almost filled Landau levels. We find that, besides the usual Landau level peaks, additional peaks ("sashes") appear in the spectrum. The energies of these peaks are determined by the strength of Haldane's pseudopotentials, but as opposed to the usual two-dimensional gas, when there is a one-to-one correspondence between a Haldane pseudopotential and a peak in the spectrum, the energy of each peak is determined in general by a combination of more than one pseudopotential values. An eventual measure of these peak in the density of states spectrum of graphene would allow one to determine the value of the pseudopotentials in graphene, and thus test the strength of the interactions in this system.