Extended critical phase in quasiperiodic quantum Hall systems

Jonas F. Karcher, Romain Vasseur, Sarang Gopalakrishnan

Research output: Contribution to journalArticlepeer-review


We consider the effects of quasiperiodic spatial modulation on the quantum Hall plateau transition by analyzing the Chalker-Coddington network model with quasiperiodically modulated link phases. In the conventional case (uncorrelated random phases), there is a critical point separating topologically distinct integer quantum Hall insulators. Surprisingly, the quasiperiodic version of the model supports an extended critical phase for some angles of modulation. We characterize this critical phase and the transitions between critical and insulating phases. For quasiperiodic potentials with two incommensurate wavelengths, the transitions we find are in a different universality class from the random transition. With the addition of more wavelengths they undergo a crossover to the uncorrelated random case. We expect our results to be relevant to the quantum Hall phases of twisted bilayer graphene or other moiré systems with large unit cells.

Original languageEnglish (US)
Article number064208
JournalPhysical Review B
Issue number6
StatePublished - Feb 1 2024
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


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