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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