The study of charged particles in magnetic field has been a fundamental topic in condensed matter physics, underlying phenomena such as Landau levels and the quantum Hall effect. In the traditional Hermitian system Landau levels arise from the interaction between a charged particle and a real-valued magnetic field which induces cyclotron motion and discrete Landau levels. Recently, these ideas have been extended into non-Hermitian systems, in which certain phenomena is emerge such as non-Hermitian skin effect (NHSE), where eigenstates accumulate at system boundaries [2]. Additionally, a recent study [1] introduced a two-dimensional non-Hermitian lattice model subjected to an imaginary magnetic field revealing unique topological and spectral properties of non-Hermitian systems. Here we analyze the effect of imaginary vector potential on Landau problem and explore how non-Hermitian nature of the system modifies energy spectrum. In particular, we investigate how the non-Hermitian nature of the system and imaginary magnetic field alters Landau levels, leading to complex energy spectrum, altering the conventional understanding of Landau quantization. This sets a stage for further investigation into non-Hermitian physics.
IMAGINARY SYNTHETIC MAGNETIC FIELD
Saulius Alminas1, Domantas Burba1, Gediminas Juzeliūnas1, Tomas Babelis1, Ian B. Spielman2
1 Institute of Theoretical Physics and Astronomy, Vilnius University, Lithuania
2 National Institute of Standards and Technology, Gaithersburg, USA
[1] Ozawa, T., Hayata, T. Two-dimensional lattice with an imaginary magnetic field. Phys. Rev. B 109, 085113 (2024).
[2] Zhao, E., Wang, Z., He, C. et al. Two-dimensional non-Hermitian skin effect in an ultracold Fermi gas. Nature 637, 565–573 (2025).