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Related Experiment Video

Updated: Sep 11, 2025

Using Microwave and Macroscopic Samples of Dielectric Solids to Study the Photonic Properties of Disordered Photonic Bandgap Materials
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Phase-Space Generalized Brillouin Zone For Spatially Inhomogeneous Non-Hermitian Systems.

Qingya Li1, Hui Jiang2,1, Ching Hua Lee1

  • 1Department of Physics, National University of Singapore, Singapore, 117551, Singapore.

Advanced Science (Weinheim, Baden-Wurttemberg, Germany)
|August 11, 2025
PubMed
Summary

A new phase-space formalism extends the generalized Brillouin zone (GBZ) to inhomogeneous non-Hermitian systems. This framework reveals GBZ bifurcation, protecting topological zero modes and real spectra in novel metamaterials.

Keywords:
generalized impurity Generalized Brillouin Zone (GBZ) treatmentnon‐Hermitian skin effect in phase spacenovel Generalized Brillouin Zone bifurcationsspatially inhomogeneous systemsunconventional Generalized Brillouin Zone in phase spaceunconventional topological transitions

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Area of Science:

  • Condensed Matter Physics
  • Topological Physics
  • Quantum Mechanics

Background:

  • The generalized Brillouin zone (GBZ) is crucial for understanding non-Hermitian systems.
  • GBZ faces challenges in spatially inhomogeneous systems due to competing localization and interference effects.

Purpose of the Study:

  • Develop a generalized phase-space GBZ formalism for spatially inhomogeneous non-Hermitian systems.
  • Investigate novel phenomena arising from this new formalism, including spectral and topological properties.

Main Methods:

  • Developed a general phase-space GBZ formalism encoding non-Bloch deformations in position and momentum space.
  • Analyzed the phenomenon of GBZ branch bifurcation and its impact on eigenstates.
  • Identified emergent degrees of freedom protecting spectral stability and topological zero modes.

Main Results:

  • Introduced a phase-space GBZ formalism accurately representing inhomogeneous non-Hermitian pumping.
  • Discovered GBZ branch bifurcation, enabling abrupt eigenstate jumps and accommodating inhomogeneity.
  • Demonstrated the protection of real spectra and the robustness of unique topological zero modes.
  • Showcased potential experimental realization in photonic crystals and circuit arrays.

Conclusions:

  • The phase-space GBZ formalism overcomes limitations in characterizing inhomogeneous non-Hermitian systems.
  • GBZ bifurcation offers a new mechanism for topological protection and spectral stability.
  • The framework provides a versatile platform for exploring unconventional spectral and topological transitions in complex non-Hermitian settings.