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Modified Dirac equation approach to topological systems

Research Project

Project/Area Number 18K03460
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
Research InstitutionHiroshima 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
Project Status Completed (Fiscal Year 2020)
Budget Amount *help
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywordsワイル半金属 / 非エルミート系 / ディラック方程式
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.

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.

Report

(4 results)
  • 2020 Annual Research Report   Final Research Report ( PDF )
  • 2019 Research-status Report
  • 2018 Research-status Report
  • Research Products

    (17 results)

All 2021 2020 2019 2018

All Journal Article (10 results) (of which Peer Reviewed: 10 results,  Open Access: 1 results) Presentation (7 results) (of which Int'l Joint Research: 1 results)

  • [Journal Article] Bulk-Boundary Correspondence in a Non-Hermitian Chern Insulator2021

    • Author(s)
      Takane Yositake
    • Journal Title

      Journal of the Physical Society of Japan

      Volume: 90 Issue: 3 Pages: 033704-033704

    • DOI

      10.7566/jpsj.90.033704

    • NAID

      40022509736

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Unified Formula for Stationary Josephson Current in Planar Graphene Junctions2020

    • Author(s)
      Takane Yositake
    • Journal Title

      Journal of the Physical Society of Japan

      Volume: 89 Issue: 9 Pages: 094702-094702

    • DOI

      10.7566/jpsj.89.094702

    • NAID

      40022344824

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Generalized Bloch band theory for non-Hermitian bulk-boundary correspondence2020

    • Author(s)
      Ken-Ichiro Imura, Yositake Takane
    • Journal Title

      Prog. Theor. Exp. Phys.

      Volume: 2020 Issue: 12

    • DOI

      10.1093/ptep/ptaa100

    • Related Report
      2020 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Persistent Current due to a Screw Dislocation in Weyl Semimetals: Role of One-Dimensional Chiral States2019

    • Author(s)
      Kentaro Kodama, and Yositake Takane
    • Journal Title

      J. Phys. Soc. Jpn.

      Volume: 88 Issue: 5 Pages: 054715-054715

    • DOI

      10.7566/jpsj.88.054715

    • NAID

      40021885934

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Zero-Energy State Localized near an Arbitrary Edge in Quadrupole Topological Insulators2019

    • Author(s)
      Yositake Takane
    • Journal Title

      J. Phys. Soc. Jpn.

      Volume: 88 Issue: 9 Pages: 094712-094712

    • DOI

      10.7566/jpsj.88.094712

    • NAID

      40022008810

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Generalized bulk-edge correspondence for non-Hermitian topological systems2019

    • Author(s)
      Ken-Ichiro Imura, and Yositake Takane
    • Journal Title

      Phys. Rev. B

      Volume: 100 Issue: 16

    • DOI

      10.1103/physrevb.100.165430

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] 螺旋転位が引き起こす永久電流―ワイル半金属のカイラル性とその発現―2019

    • Author(s)
      高根美武
    • Journal Title

      固体物理

      Volume: 54 Pages: 767-774

    • NAID

      40022104670

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Regularized continuum model of a Weyl semimetal for describing anomalous electromagnetic response2019

    • Author(s)
      Y. Takane
    • Journal Title

      J. Phys. Soc. Jpn.

      Volume: 88 Issue: 1 Pages: 014703-014703

    • DOI

      10.7566/jpsj.88.014703

    • NAID

      40021772176

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Gauge-invariant cutoff for Dirac electron systems with a vector potential2019

    • Author(s)
      Y. Takane
    • Journal Title

      J. Phys. Soc. Jpn.

      Volume: 88 Issue: 3 Pages: 034702-034702

    • DOI

      10.7566/jpsj.88.034702

    • NAID

      210000135129

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Spontaneous charge current in a doped Weyl semimetal2018

    • Author(s)
      Y. Takane
    • Journal Title

      J. Phys. Soc. Jpn.

      Volume: 87 Issue: 7 Pages: 074706-074706

    • DOI

      10.7566/jpsj.87.074706

    • NAID

      210000134902

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Presentation] 非エルミートなチャーン絶縁体におけるバルク-境界対応2021

    • Author(s)
      高根美武
    • Organizer
      日本物理学会第76回年次大会(2021年)
    • Related Report
      2020 Annual Research Report
  • [Presentation] グラフェン平面接合におけるジョセフソン電流2020

    • Author(s)
      高根美武
    • Organizer
      日本物理学会2020年秋季大会
    • Related Report
      2020 Annual Research Report
  • [Presentation] 螺旋転位を含むワイル半金属における永久電流2020

    • Author(s)
      高根美武
    • Organizer
      日本物理学会第75回年次大会
    • Related Report
      2019 Research-status Report
  • [Presentation] 入り組んだ端構造をもつ四極子トポロジカル絶縁体のゼロ・エネルギー状態2019

    • Author(s)
      高根美武
    • Organizer
      日本物理学会2019年秋季大会
    • Related Report
      2019 Research-status Report
  • [Presentation] Persistent current due to a screw dislocation in Weyl semimetals2019

    • Author(s)
      Yositake Takane
    • Organizer
      International Conference on Topological Materials Science 2019
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] ディラック電子系に対するゲージ不変なエネルギー切断2019

    • Author(s)
      高根美武
    • Organizer
      日本物理学会 第74回年次大会
    • Related Report
      2018 Research-status Report
  • [Presentation] ワイル半金属の風変わりな電気磁気応答と連続極限モデル2018

    • Author(s)
      高根美武
    • Organizer
      日本物理学会 2018年秋季大会
    • Related Report
      2018 Research-status Report

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Published: 2018-04-23   Modified: 2022-01-27  

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