Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure

TL;DR

This paper demonstrates how stacking graphene on hexagonal boron nitride creates a tunable band structure with massive Dirac fermions and Hofstadter butterfly patterns, revealing new quantum phenomena in van der Waals heterostructures.

Contribution

It introduces a method to engineer band structures in graphene/hBN heterostructures, showing tunable gaps and observing fractional quantum Hall states and Hofstadter butterfly effects.

Findings

Observation of a large, tunable band gap at charge neutrality.

Detection of fractional quantum Hall states indicating massive Dirac fermions.

Emergence of Hofstadter butterfly patterns at high magnetic fields.

Abstract

Van der Waals heterostructures comprise a new class of artificial materials formed by stacking atomically-thin planar crystals. Here, we demonstrate band structure engineering of a van der Waals heterostructure composed of a monolayer graphene flake coupled to a rotationally-aligned hexagonal boron nitride substrate. The spatially-varying interlayer atomic registry results both in a local breaking of the carbon sublattice symmetry and a long-range moir\'e superlattice potential in the graphene. This interplay between short- and long-wavelength effects results in a band structure described by isolated superlattice minibands and an unexpectedly large band gap at charge neutrality, both of which can be tuned by varying the interlayer alignment. Magnetocapacitance measurements reveal previously unobserved fractional quantum Hall states reflecting the massive Dirac dispersion that results from broken sublattice symmetry. At ultra-high fields, integer conductance plateaus are observed at non-integer filling factors due to the emergence of the Hofstadter butterfly in a symmetry-broken Landau level.