Non-Bloch band theory and bulk–edge correspondence in non-Hermitian systems

2020/09/14 by Kazuki Yokomizo, Shuichi Murakami · 1 citation
Physics and Astronomy · #Bloch wave #Brillouin zone #Electronic band structure #Enhanced Data Rates for GSM Evolution #Hermitian matrix #Invariant (physics) #Mathematical physics #Nonlinear Photonic Systems #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum mechanics #Simple (philosophy) #Theoretical physics #Topological Materials and Phenomena #cond-mat.mes-hall

paper · pdf · doi:10.1093/ptep/ptaa140

12 pages, 6 figures

openalex created_date 2020/09/14 · openalex publication_date 2020/09/14 · arxiv created 2020/11/25 · arxiv updated 2020/11/26 · openalex updated_date 2026/08/05

Abstract

Abstract In this paper, we review our non-Bloch band theory in 1D non-Hermitian tight-binding systems. In our theory, it is shown that in non-Hermitian systems, the Brillouin zone is determined so as to reproduce continuum energy bands in a large open chain. By using simple models, we explain the concept of the non-Bloch band theory and the method to calculate the Brillouin zone. In particular, for the non-Hermitian Su–Schrieffer–Heeger model, the bulk–edge correspondence can be established between the topological invariant defined from our theory and existence of the topological edge states.

Citations

• Non-Hermitian Topological Theory of Finite-Lifetime Quasiparticles: Prediction of Bulk Fermi Arc Due to Exceptional Point
• Topological exceptional surfaces in non-Hermitian systems with parity-time and parity-particle-hole symmetries
• Non-Hermitian systems and topology: A transfer-matrix perspective
• Non-Hermitian Boundary Modes
• Observation of bulk boundary correspondence breakdown in topolectrical circuits
• Observation of non-Hermitian bulk-boundary correspondence in quantum dynamics
• Exceptional topology of non-Hermitian systems
• Topological Origin of Non-Hermitian Skin Effects

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