Local density of states of electron-crystal phases in graphene in the quantum Hall regime

TL;DR

This study calculates the local density of states for electron-crystal phases in graphene under strong magnetic fields, revealing scaling properties and potential for experimental measurement via spectroscopy.

Contribution

It provides the first detailed analysis of local density of states in electron-crystal phases in graphene, highlighting scaling relations and experimental observability.

Findings

Total density of states shows peaks corresponding to electrons per lattice site.

Local density of states at peak energies exhibits specific scaling properties.

Lowest peaks' local density of states are identical across different electron counts.

Abstract

We calculate, within a self-consistent Hartree-Fock approximation, the local density of states for different electron crystals in graphene subject to a strong magnetic field. We investigate both the Wigner crystal and bubble crystals with M_e electrons per lattice site. The total density of states consists of several pronounced peaks, the number of which in the negative energy range coincides with the number of electrons M_e per lattice site, as for the case of electron-solid phases in the conventional two-dimensional electron gas. Analyzing the local density of states at the peak energies, we find particular scaling properties of the density patterns if one fixes the ratio nu_N/M_e between the filling factor nu_N of the last partially filled Landau level and the number of electrons per bubble. Although the total density profile depends explicitly on M_e, the local density of states of the lowest peaks turns out to be identical regardless the number of electrons M_e. Whereas these electron-solid phases are reminiscent to those expected in the conventional two-dimensional electron gas in GaAs heterostructures in the quantum Hall regime, the local density of states and the scaling relations we highlight in this paper may be, in graphene, directly measured by spectroscopic means, such as e.g. scanning tunneling microscopy.