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Chiral edge modes in quantum Hall insulators are not always tied to Chern numbers due to the non-Hermitian skin effect. New non-Bloch Chern numbers accurately predict edge modes, offering a revised topological framework.

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Area of Science:

  • Condensed Matter Physics
  • Topological Materials
  • Quantum Hall Effect

Background:

  • The bulk-boundary correspondence links topological invariants in the bulk to the presence of protected states at the boundary.
  • Quantum Hall insulators exhibit chiral edge modes governed by bulk Chern numbers, a key example of this principle.
  • Conventional theories rely on Bloch's theorem, which may fail for non-Hermitian systems.

Purpose of the Study:

  • To investigate the breakdown of the conventional bulk-boundary correspondence in non-Hermitian systems.
  • To introduce a new topological invariant that accurately predicts chiral edge modes in the presence of non-Hermitian effects.
  • To establish a non-Bloch framework for characterizing the topology of non-Hermitian bands.

Main Methods:

  • Analysis of chiral edge modes and bulk Chern numbers in quantum Hall insulators.
  • Investigation of non-Bloch-wave behavior and the non-Hermitian skin effect.
  • Development and application of non-Bloch Chern numbers.
  • Validation using open-boundary energy spectra, dynamics, and phase diagrams of lattice models.

Main Results:

  • Chiral edge modes are not strictly determined by Chern numbers from non-Hermitian Bloch Hamiltonians.
  • The non-Hermitian skin effect causes eigenstates to deviate from Bloch-wave behavior, altering phase diagrams.
  • Non-Bloch Chern numbers are introduced and shown to faithfully predict the number of chiral edge modes.
  • Theoretical predictions are confirmed by numerical simulations of lattice models.

Conclusions:

  • The conventional bulk-boundary correspondence breaks down in non-Hermitian systems due to the non-Hermitian skin effect.
  • A generalized topological framework using non-Bloch Chern numbers is necessary for non-Hermitian band theory.
  • This work reveals unique topological properties of non-Hermitian bands and proposes a new characterization method.