Fractional Quantum Hall Effects in Graphene and Its Bilayer

TL;DR

This paper investigates fractional quantum Hall effects in single-layer and bilayer graphene, revealing valley polarization and excitations, with bilayer graphene showing the largest excitation gap at 1/3 filling, suggesting experimental observability.

Contribution

It provides the first detailed analysis of fractional quantum Hall states in graphene systems using DMRG, highlighting valley polarization and excitation gaps.

Findings

Valley polarization at specific filling factors in graphene.

Largest excitation gap at 1/3 filling in bilayer graphene.

Potential for experimental observation of fractional quantum Hall effect.

Abstract

Single-layer and Bilayer of graphene are new classes of two-dimensional electron systems with unconventional band structures and valley degrees of freedom. The ground states and excitations in the integer and fractional quantum Hall regimes are investigated on torus and spherical geometries with the use of the density matrix renormalization group (DMRG) method. At nonzero Landau level indices, the ground states at effective filling factors 1, 1/3, 2/3 and 2/5 are valley polarized both in single-layer and bilayer graphenes. We examine the elementary charge excitations which could couple with the valley degrees of freedom (so called valley skyrmions). The excitation gaps are calculated and extrapolated to the thermodynamic limit. The largest excitation gap at effective filling 1/3 is obtained in bilayer graphene, which is a good candidate for experimental observation of fractional quantum Hall effect.