Modified Dirac equation approach to topological systems

2020 Fiscal Year Final Research Report

• Project/Area Number: 18K03460
• 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): 2018-04-01 – 2021-03-31
• Keywords: ワイル半金属

Outline of Final Research Achievements

We show that quasiparticle states in a Weyl semimetal, including two-dimensional chiral surface states as well as one-dimensional chiral states along a screw dislocation, can be described by combining the Weyl equation with a supplemental equation that is derived in this study. By using the resulting quasiparticle states, we obtain an analytical expression of a persistent current, which is qualitatively consistent with the result of numerical simulations. We elucidate characteristic features of the chiral states in a Weyl semimetal.
As an unexpected by-product, we give a theoretical framework to describe bulk-boundary correspondence in non-Hermitian Dirac systems. In additions, we formulate a theoretical method to describe the electromagnetic response of a Weyl semimetal and a numerical method to determine the wavefunction of corner states in a second-order topological insulator.

Free Research Field

物性理論

Academic Significance and Societal Importance of the Research Achievements

ワイル半金属のバルクな電子状態はワイル方程式（質量ゼロのディラック方程式）によって記述され，波数空間において円錐状のエネルギー分散を示す．しかしこの物質の顕著な特徴と見なされる，表面に局在した2次元的カイラル状態や螺旋転位に沿って現れる1次元的カイラル状態はワイル方程式によって記述できない．本研究では，ワイル方程式から零れ落ちた情報を補助方程式によって補えば，これらのカイラル状態を適切に記述できることを示し，ワイル方程式だけでは不充分な理由を明らかにした．
ワイル半金属はワイル方程式によって記述できると理解されている．本研究はこの広く定着した理解が孕む本質的な問題を明らかにしたものと言える．