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

Abstract

Graphene, a single freestanding 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 density of carriers. We study the ground state of graphene in the presence of 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 noninteger fillings, 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 nonuniform 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.