Two-dimensional Asymptotic Generalized Brillouin Zone Theory
- URL: http://arxiv.org/abs/2311.16868v2
- Date: Tue, 16 Jan 2024 03:24:35 GMT
- Title: Two-dimensional Asymptotic Generalized Brillouin Zone Theory
- Authors: Zeqi Xu, Bo Pang, Kai Zhang, and Zhesen Yang
- Abstract summary: We show that for any given non-Hermitian Hamiltonian, the corresponding region should be independent of the open boundary geometry.
A corollary of our theory is that most symmetry-protected exceptional semimetals should be robust to variations in OBC geometry.
- Score: 10.66748920431153
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In this work, we propose a theory on the two-dimensional non-Hermitian skin
effect by resolving two representative minimal models. Specifically, we show
that for any given non-Hermitian Hamiltonian, (i) the corresponding region
covered by its open boundary spectrum on the complex energy plane should be
independent of the open boundary geometry; and (ii) for any given open boundary
eigenvalue $E_0$ , its corresponding two-dimensional asymptotic generalized
Brillouin zone is determined by a series of geometry-independent
Bloch/non-Bloch Fermi points and geometry-dependent non-Bloch equal frequency
contours that connect them. A corollary of our theory is that most
symmetry-protected exceptional semimetals should be robust to variations in OBC
geometry. Our theory paves the way to the discussion on the higher dimensional
non-Bloch band theory and the corresponding non-Hermitian bulk-boundary
correspondence.
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