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Non-Hermitian Landau levels

Anton Montag1,2,3,* and Tomoki Ozawa1,4,†

  • *Contact author: anton.montag@mpl.mpg.de
  • †Contact author: tomoki.ozawa.d8@tohoku.ac.jp
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Phys. Rev. B 114, 245128 – Published 20 October, 2026

DOI: https://doi.org/10.1103/sklt-tzlx

Abstract

We formulate non-Hermitian Landau levels in two-dimensional systems under a complex perpendicular magnetic field. In the symmetric gauge, we derive their discretely spaced, highly degenerate complex spectra and biorthogonal eigenstates. In addition we derive analogous results in the Landau gauge and clarify the role of nonunitary gauge transformations. We find that while normalizable eigenstates exist for both gauges for Re(B)>0, they are not always related by such a gauge transformation. A non-Hermitian Harper-Hofstadter lattice model confirms the continuum theory and reveals Gaussian wave packet dynamics governed by semiclassical equations with a complex Lorentz force, pointing to possible experimental realizations of complex magnetic fields in mechanical metamaterials or ultracold atom gases.

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Phys. Rev. B 114, 245128– Published 20 October, 2026
  • Received 22 May 2026
  • Accepted 8 October 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by Max Planck Society.

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