Wigner crystal and bubble phases in graphene in the quantum Hall regime

TL;DR

This paper investigates the ground states of graphene under strong magnetic fields, revealing conditions for Wigner crystal formation and predicting anisotropic transport phenomena in high Landau levels.

Contribution

It provides the first mean-field analysis of broken translational symmetry states in graphene's quantum Hall regime, including phase diagrams and conditions for Wigner crystal states.

Findings

Wigner crystal states are favored at non-integer fillings.

The phase diagram resembles that of semiconductor quantum Hall systems.

Predicted anisotropic transport in high Landau levels due to non-uniform states.

Abstract

Graphene, a single free-standing sheet of graphite with honeycomb lattice structure, is a semimetal with carriers that have linear dispersion. A consequence of this dispersion is the absence of Wigner crystallization in graphene, since the kinetic and potential energies both scale identically with the density of carriers. We study the ground state of graphene in the presence of a strong magnetic field focusing on states with broken translational symmetry. Our mean-field calculations show that at integer fillings a uniform state is preferred, whereas at non-integer filling factors Wigner crystal states (with broken translational symmetry) have lower energy. We obtain the phase diagram of the system. We find that it is qualitatively similar to that of quantum Hall systems in semiconductor heterostructures. Our analysis predicts that non-uniform states, including Wigner crystal state, will occur in graphene in the presence of a magnetic field and will lead to anisotropic transport in high Landau levels.