Robustness of irrational charges in two-dimensional topological systems

2021 Fiscal Year Final Research Report

• Project/Area Number: 19K03660
• 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: Toho University
• Principal Investigator: KAWARABAYASHI Tohru 東邦大学, 理学部, 教授 (90251488)
• Project Period (FY): 2019-04-01 – 2022-03-31
• Keywords: トポロジカル欠陥 / カイラル対称性 / 非整数電荷

Outline of Final Research Achievements

Irrational charges associated with topological defects (vortex) in two dimensional systems are investigated numerically by the kernel polynomial method. A lattice model with a non-abelian gauge field which hosts vertical/tilted Dirac fermions and respects the chiral symmetry is adopted. A precise numerical analysis reveals that the charges associated with the topological defects are not sensitive to disorder nor tilting the Dirac dispersion, as long as the chiral symmetry is respected. It is further demonstrated that even for the cases where the chiral symmetry is broken by the staggered potential, rational/irrational charges of topological defects are again insensitive to perturbations respecting the chiral symmetry.

Free Research Field

物性理論

Academic Significance and Societal Importance of the Research Achievements

本研究のテーマであるトポロジカル欠陥に伴う非整数電荷の研究は、１次元のポリアセチレンにおけるソリトンに付随する非整数電荷の研究に端を発し、グラフェンの発見により、２次元系での渦構造へと研究が進められてきたものである。こうした歴史的な問題に対し、近年の進展が目覚ましい冷却原子系などの新しい実験系への応用を念頭に、非整数電荷の普遍性について、ランダムネスに対する安定性などを具体的に示せたことは、実験での観測に向けた新たな知見として有用であると考えられる。