Bulk-boundary correspondence in non-Hermitian topological systems and generalization of Bloch band theory

2023 Fiscal Year Final Research Report

• Project/Area Number: 21K03405
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
• Research Institution: Hiroshima University
• Principal Investigator: TAKANE Yositake 広島大学, 先進理工系科学研究科(先), 教授 (40254388)
• Project Period (FY): 2021-04-01 – 2024-03-31
• Keywords: 非エルミート系 / トポロジカル物質 / バルク境界対応

Outline of Final Research Achievements

To describe bulk boundary correspondence in non-Hermitian topological systems, we propose a new framework that enables us to relate a topological invariant defined in a bulk geometry under a modified periodic boundary condition to the presence or absence of topological boundary states in a boundary geometry under an open boundary condition. The modified periodic boundary condition is an extension of the conventional periodic boundary condition, in terms of which we can take account of an exponential increase or decrease in wave functions. We applied this framework to three non-Hermitian topological systems (i.e., Chern insulator and quantum spin-Hall insulator with a pure imaginary potential, and a Kitaev chain model containing three types of non Hermitian terms), and showed that the bulk boundary correspondence holds precisely.

Free Research Field

物性理論

Academic Significance and Societal Importance of the Research Achievements

トポロジカル系では，境界に局在するトポロジカル状態の有無は境界のないバルク形状において計算したトポロジカル不変量と関係付けられる．この関係（バルク境界対応）はエルミートなトポロジカル系において広く成立するが，非エルミート系ではしばしば破れてしまう．また，非エルミート系に関する議論は1次元トポロジカル系に集中しており，2次元系においてバルク境界対応を精密に立証した前例は見当たらない．本研究では非エルミート系におけるバルク境界対応を記述する新しい枠組みを提案し，その有効性を立証した．特に，2次元系においてバルク境界対応が精密に成り立つことを示した結果は，先駆的な成果と言える．