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arXiv · 2311.16967

Hofstadter quasicrystals, hidden symmetries and irrational quantum oscillations

Kirill Kozlov·Grigor Adamyan·Mariia Kryvoruchko·Yelizaveta Kulynych·Leonid Levitov
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Abstract

Landau levels perturbed by a periodic potential is a prime setting to design quantum systems with exotic fractal spectra. Motivated by recent advances in twistronics, we introduce `Hofstadter quasicrystal' problem describing Landau levels perturbed by a set of incommensurate cosine waves. We illustrate the underlying physics for moir\'{e} quasicrystals with octagonal and dodecagonal symmetries, finding spectra that are vastly more complex than the Hofstadter spectrum. Surprisingly, due to the high spatial symmetry, the quasicrystal problem exhibits hidden `inner' symmetry arising at special `magic' values of the magnetic field. The $1/B$-periodic pattern of magic field values explains striking wide-range oscillations in the observed spectra that have irrational periodicity incommensurate with the Aharonov-Bohm and Brown-Zak periodicities. The prominent character of these oscillations makes them readily accessible in state-of-the-art moir\'{e} graphene systems.

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Kirill Kozlov, Grigor Adamyan, Mariia Kryvoruchko, Yelizaveta Kulynych, Leonid Levitov. 2023-11-28. Hofstadter quasicrystals, hidden symmetries and irrational quantum oscillations. https://arxiv.org/abs/2311.16967

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