Tunable Landau quantization via imaginary electric fields

When charged particles are subjected to a magnetic field, their continuous energy spectrum splits into discrete Landau levels. Landau quantization is a cornerstone of quantum Hall effects. In classical wave systems, artificial gauge fields have been developed to reproduce similar Landau levels in photonic, acoustic, and mechanical structures. However, previous studies have mainly focused on real-valued artificial gauge fields in Hermitian systems. How complex-valued gauge fields affect Landau quantization has remained largely unexplored.

Recently, a collaborative team from Beijing Institute of Technology, The Hong Kong University of Science and Technology, University of Exeter, and The University of Hong Kong have proposed a mechanism for tunable Landau quantization in a two-dimensional Dirac system by constructing a real pseudo-magnetic field and an imaginary pseudo-electric field simultaneously. Their interplay enlarges Landau-level spacing and enhances mode localization.

 Experimentally, the researchers constructed an acoustic metamaterial. The real pseudo-magnetic field was generated by gradually increasing the widths of the connecting tubes, while the imaginary pseudo-electric field was realized by varying the insertion depths of absorptive sponges in the acoustic cavities to create a loss gradient. The researchers measured the frequency-response spectra and acoustic-field distributions. The results showed that imaginary pseudo-electric field can enlarge Landau-level spacing and enhance localization of Landau modes.

The mechanism extends the interplay between electric and magnetic fields into the complex domain and provides a flexible route for controlling the spectral and spatial properties of Landau levels and modes. These findings also open new avenues for exploring quantum-Hall-like phenomena through engineered loss landscapes, with potential relevance to both fundamental research and practical applications.

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