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arXiv · 2105.04948

Fractal energy gaps and topological invariants in hBN/Graphene/hBN double moir\'{e} systems

Hiroki Oka·Mikito Koshino
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Abstract

We calculate the electronic structure in quasiperiodic double-moir\'e systems of graphene sandwiched by hexagonal boron nitride, and identify the topological invariants of energy gaps. We find that the electronic spectrum contains a number of minigaps, and they exhibit a recursive fractal structure similar to the Hofstadter butterfly when plotted against the twist angle. Each of the energy gaps can be characterized by a set of integers, which are associated with an area in the momentum space. The corresponding area is geometrically interpreted as a quasi Brillouin zone, which is a polygon enclosed by multiple Bragg planes of the composite periods and can be uniquely specified by the plain wave projection in the weak potential limit.

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Hiroki Oka, Mikito Koshino. 2021-05-11. Fractal energy gaps and topological invariants in hBN/Graphene/hBN double moir\'{e} systems. https://doi.org/10.1103/physrevb.104.035306

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