Zero-energy modes and valley asymmetry in the Hofstadter spectrum of bilayer graphene van der Waals heterostructures with hBN

TL;DR

This paper explores the effects of moire potential-induced inversion symmetry breaking on the magnetic minibands and valley symmetry in bilayer graphene/hBN heterostructures, revealing zero-energy Landau level persistence and secondary Dirac points.

Contribution

It introduces effective models for magnetic minibands and demonstrates the emergence of secondary Dirac points and their impact on the fractal energy spectrum in BLG/hBN heterostructures.

Findings

Zero-energy Landau level persists with reduced degeneracy.

Secondary Dirac points appear in the valence band.

Single-particle gaps lead to observable incompressible states.

Abstract

We investigate the magnetic minibands of a heterostructure consisting of bilayer graphene (BLG) and hexagonal boron nitride (hBN) by numerically diagonalizing a two-band Hamiltonian that describes electrons in BLG in the presence of a moire potential. Due to inversion-symmetry breaking characteristic for the moire potential, the valley symmetry of the spectrum is broken, but despite this, the zero-energy Landau level in BLG survives, albeit with reduced degeneracy. In addition, we derive effective models for the low-energy features in the magnetic minibands and demonstrate the appearance of secondary Dirac points in the valence band, which we confirm by numerical simulations. Then, we analyze how single-particle gaps in the fractal energy spectrum produce a sequence of incompressible states observable under a variation of carrier density and magnetic field.