Bosonic Hofstadter butterflies in synthetic antiferromagnetic patterns

Yury S. Krivosenko*, Ivan V. Iorsh, Ivan A. Shelykh

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The emergence of Hofstadter butterflies for bosons in synthetic-gauge-field antiferromagnetic (AFM) patterns is theoretically studied. We report on a specific tight-binding model of artificial AFM structures incorporating both nearest and next-to-nearest neighbour tunnelings and allowing for the formation of the fractal spectra even with the vanishing gauge field flux through the lattice. The model is applied to square and honeycomb lattices. Possible experimental realization is suggested for the lattices of microring resonators connected by waveguides. Finally, the structure of the butterflies is analyzed for different points in the magnetic Brillouin zone for both the ferromagnetic and AFM patterns.

Original languageEnglish
Article number135802
JournalJournal of Physics Condensed Matter
Issue number13
Publication statusPublished - 31 Mar 2021

Bibliographical note

Funding Information:
The authors acknowledge support from Russian Science Foundation (project No. 18-72-10110). The work of IAS was also supported by Icelandic Science Foundation (Project ‘Hybrid Polaritonics’). YSK is grateful to Dr A Nalitov for the useful discussion.

Publisher Copyright:
© 2021 IOP Publishing Ltd Printed in the UK

Other keywords

  • Antiferromagnetic patterns
  • Artificial gauge fields
  • Tight-binding approximation


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