English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

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

Hofstadter quasicrystals, hidden symmetries and irrational quantum oscillations