Landau Levels as a Probe for Band Topology in Graphene Moiré Superlattices

Abstract

We propose Landau levels as a probe for the topological character of electronic bands in two-dimensional moiré superlattices. We consider two configurations of twisted double bilayer graphene (TDBG) that have very similar band structures, but show different valley Chern numbers of the flat bands. These differences between the AB-AB and AB-BA configurations of TDBG clearly manifest as different Landau level sequences in the Hofstadter butterfly spectra calculated using the tight-binding model. The Landau level sequences are explained from the point of view of the distribution of orbital magnetization in momentum space that is governed by the rotational $C_2$ and time-reversal $\mathcal{T}$ symmetries. Our results can be readily extended to other twisted graphene multilayers and $h$-BN/graphene heterostructures thus establishing the Hofstadter butterfly spectra as a powerful tool for detecting the non-trivial valley band topology.

5 pages, 3 figures

References in corpus (9)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
• Flat Bands in Slightly Twisted Bilayer Graphene
• Flatbands in twisted double bilayer graphene
• Band structure and topological property of twisted double bilayer graphenes
• Landau levels in twisted bilayer graphene and semiclassical orbits
• Hofstadter butterflies of bilayer graphene
• Band-unfolding approach to Moirè-induced band-gap opening and Fermi-level-velocity reduction in twisted bilayer graphene
• Tunable bandwidths and gaps in twisted double bilayer graphene system on the verge of correlations

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• Tunable moire spinons in magnetically encapsulated twisted van der Waals quantum spin-liquids
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• An effective curved space-time geometric theory of generic twist angle graphene with application to a rotating bilayer configuration
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• Hofstadter Butterfly in Graphene