Fractional quantum Hall effects in graphene on a h-BN substrate

TL;DR

This study investigates how the mass term induced by an h-BN substrate affects fractional quantum Hall states in graphene, revealing that it lifts valley degeneracy and alters the nature of excitations, aligning with experimental observations.

Contribution

It provides a detailed analysis of the impact of the mass term on FQH states in graphene using exact diagonalization, highlighting the transition from valley unpolarized to polarized states.

Findings

Mass term lifts valley degeneracy in FQH states.

Valley unpolarized excitations are suppressed with increasing mass.

Results agree with recent experimental observations.

Abstract

Fractional quantum Hall (FQH) effects in graphene are studied because of their relativistic characteristics and the valley degree of freedom. Recently FQH effects have been observed at various filling factors with graphene on a hexagonal boron nitride (h-BN) substrate. However, it is known that h-BN creates the mass term in the Dirac Hamiltonian that acts as the effective model of graphene. To understand recent experiments, we shall investigate many-body effects in the massive Dirac electron system. In this paper, we study the mass-term effects on the FQH states of Dirac electrons by exact diagonalization. We examine the ground state at filling factor 1/3 in the $n=\pm 1$ Landau level. Without the mass term, the ground state in the Laughlin state featuring valley degeneracy and the lowest excitation is characterized by the valley unpolarized state (known as the valley skyrmion state). Conversely, we find that the mass-term lifts the valley degeneracy due to the breaking of the inversion symmetry. We also demonstrate that the valley unpolarized excitation is suppressed and that the fully or partially polarized state appears in the lowest excitation by increasing the mass term. Finally, we discuss the stability of FQH states in the massive Dirac Hamiltonian in experimental situations. We find that our numerical results are in agreement with previous experimental results.