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Chiral symmetry in quantum transport phenomena of Dirac particles in two dimensions

Research Project

Project/Area Number 15K05218
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Mathematical physics/Fundamental condensed matter physics
Research InstitutionToho University

Principal Investigator

KAWARABAYASHI Tohru  東邦大学, 理学部, 教授 (90251488)

Project Period (FY) 2015-10-21 – 2019-03-31
Project Status Completed (Fiscal Year 2018)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Keywordsカイラル対称性 / ディラック粒子 / 格子模型 / 傾いたディラック粒子系 / 電荷の分数化 / ゼロモード / ディラック電子 / トポロジカル欠陥
Outline of Final Research Achievements

We have shown that the generalized chiral symmetry, which we propose for characterizing generic tilted Dirac particles, can be defined not only for low-energy effective hamiltonians but also for lattice models exactly. We have developed a general theoretical framework for such systems in which we show that lattice models respecting the generalized chiral symmetry can be systematically generated by an algebraic deformation of a lattice model with the conventional chiral symmetry. With this general framework for the generalized chiral symmetry, we have discussed an exact extension of the zero modes of the tilted fermion-vortex systems in two dimensions as well as the topological protection of the doubling of the tilted Dirac fermions on lattice models.

Academic Significance and Societal Importance of the Research Achievements

有機導体などで見られる2次元ディラック粒子系では、多くの場合傾いたディラック・コーンが観測され、通常のカイラル対称性が破れている。このため、傾いたディラック電子系一般の特徴付けは自明ではなかったが、我々は、傾いたディラック・コーンが「一般化されたカイラル対称性」によって特徴付けられること、また、こうした対称性が格子模型レベルで厳密に定義できることを示した。これにより、フェルミオン・ダブリング(フェルミオンが同じエネルギーに偶数個縮退して現れること)の問題などが議論できるようになり、傾いたディラック粒子系一般に対して、新たな概念、視点を提供することができた。

Report

(5 results)
  • 2018 Annual Research Report   Final Research Report ( PDF )
  • 2017 Research-status Report
  • 2016 Research-status Report
  • 2015 Research-status Report
  • Research Products

    (23 results)

All 2019 2018 2017 2016

All Journal Article (3 results) (of which Peer Reviewed: 3 results,  Acknowledgement Compliant: 1 results) Presentation (20 results) (of which Int'l Joint Research: 12 results,  Invited: 3 results)

  • [Journal Article] Fractionally Quantized Berry's Phase in an Anisotropic Magnet on the Kagome Lattice2019

    • Author(s)
      Tohru Kawarabayashi, Kota Ishii, and Yasuhiro Hatsugai
    • Journal Title

      J. Phys. Soc. Jpn.

      Volume: 88 Issue: 4 Pages: 45001-45001

    • DOI

      10.7566/jpsj.88.045001

    • NAID

      210000155583

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Topologically Protected Doubling of Tilted Dirac Fermions in Two Dimensions2019

    • Author(s)
      Tohru Kawarabayashi, Hideo Aoki, and Yasuhiro Hatsugai
    • Journal Title

      Phys. Status Solidi B

      Volume: - Issue: 6

    • DOI

      10.1002/pssb.201800524

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Lattice realization of the generalized chiral symmetry in two dimensions2016

    • Author(s)
      T. Kawarabayashi, H. Aoki and Y. Hatsugai
    • Journal Title

      Phys. Rev. B

      Volume: 94 Issue: 23 Pages: 235307-235307

    • DOI

      10.1103/physrevb.94.235307

    • NAID

      120007135174

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] 非可換ゲージ場中のディラック粒子系におけるn=0ランダウ準位のランダムネスに対する安定性2019

    • Author(s)
      藤澤周平, 初貝安弘, 河原林透
    • Organizer
      日本物理学会第74回年次大会
    • Related Report
      2018 Annual Research Report
  • [Presentation] 格子上の傾いたディラック電子のダブリングと一般化されたカイラル対称性2018

    • Author(s)
      河原林透, 青木秀夫, 初貝安弘
    • Organizer
      日本物理学会2018年秋季大会
    • Related Report
      2018 Annual Research Report
  • [Presentation] Topological order in quantum phases in anisotropic Kagome magnets2018

    • Author(s)
      Tohru Kawarabayashi, Kota Ishii, Yasuhiro Hatsugai
    • Organizer
      The 23rd international conference on High Magnetic Fields in Semiconductor Physics
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Topologically Protected Doubling of Tilted Dirac Fermions in Two Dimensions2018

    • Author(s)
      Tohru Kawarabayashi, Hideo Aoki, Yasuhiro Hatsugai
    • Organizer
      The 34th international conference on the Physics of Semiconductors
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Topological zero-energy states in deformed fermion-vortex systems2018

    • Author(s)
      Tohru Kawarabayashi
    • Organizer
      International workshop “Variety and universality of bulk-edge correspondence in topological phases: from solid state physics to transdisciplinary concepts” (BEC2018X)
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Robust n=0 Landau levels of Dirac particles in non-abelian gauge fields,2018

    • Author(s)
      Shuhei Fujisawa, Yasuhiro Hatsugai, Tohru Kawarabayashi
    • Organizer
      International workshop “Variety and universality of bulk-edge correspondence in topological phases: from solid state physics to transdisciplinary concepts” (BEC2018X)
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Tilted Dirac fermions in lattice models with generalized chiral symmetry2018

    • Author(s)
      Tohru Kawarabayashi
    • Organizer
      the international workshop “Variety and universality of bulk-edge correspondence in topological phases: From solid state physics to transdisciplinary concepts”
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Topological properties of q-deformed Wilson-Dirac model2018

    • Author(s)
      S. Fujisawa, T. Kawarabayashi
    • Organizer
      the international workshop “Variety and universality of bulk-edge correspondence in topological phases: From solid state physics to transdisciplinary concepts”
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] Numerical study of irrational charges in fermion-vortex system2018

    • Author(s)
      M. Hirasaka, R. Itagaki, Y. Hatsugai, H. Aoki, T. Kawarabayashi
    • Organizer
      the international workshop “Variety and universality of bulk-edge correspondence in topological phases: From solid state physics to transdisciplinary concepts”
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] Topological characterization of quantum phases in an anisotropic Kagome magnet2018

    • Author(s)
      K. Ishii, Y. Hatsugai, T. Kawarabayashi
    • Organizer
      the international workshop “Variety and universality of bulk-edge correspondence in topological phases: From solid state physics to transdisciplinary concepts”
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] カゴメ格子上の異方的XXZスピン系における量子相とベリー位相2018

    • Author(s)
      河原林透、石井航太、初貝安弘
    • Organizer
      日本物理学会第73回年次大会
    • Related Report
      2017 Research-status Report
  • [Presentation] 格子模型の擬ゼロモードのトポロジカル安定性2017

    • Author(s)
      河原林透、青木秀夫、初貝安弘
    • Organizer
      日本物理学会第72回年次大会
    • Place of Presentation
      大阪大学(大阪府豊中市)
    • Year and Date
      2017-03-17
    • Related Report
      2016 Research-status Report
  • [Presentation] Topological Description of Tilted Dirac Fermions with/without Mass2017

    • Author(s)
      Tohru Kawarabayashi, Hideo Aoki, Yasuhiro Hatsugai
    • Organizer
      the 22nd international conference on Electronic Properties of Two-Dimensional Systems
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research
  • [Presentation] フラットバンド格子模型におけるディラック電子系の代数的変形2017

    • Author(s)
      河原林透、青木秀夫、初貝安弘
    • Organizer
      日本物理学会2017年秋季大会
    • Related Report
      2017 Research-status Report
  • [Presentation] Deformation of Dirac fermions with invariant zero modes2016

    • Author(s)
      T. Kawarabayashi
    • Organizer
      the Yukawa Institute for Theoretical Physics (YITP) international workshop "Physics of bulk-edge correspondence and its universality: From solid state physics to cold atoms”
    • Place of Presentation
      京都大学基礎物理学研究所(京都府京都市)
    • Year and Date
      2016-09-27
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Irrational charges of fermion-vortex systems: robustness against disorder2016

    • Author(s)
      R. Itagaki, H. Aoki, Y. Hatsugar, T. Kawarabayashi
    • Organizer
      the Yukawa Institute for Theoretical Physics (YITP) international workshop "Physics of bulk-edge correspondence and its universality: From solid state physics to cold atoms”
    • Place of Presentation
      京都大学基礎物理学研究所(京都府京都市)
    • Year and Date
      2016-09-27
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] 二次元ディラック電子系のvortexに伴う非分数電荷のランダムネスに対する安定性2016

    • Author(s)
      板垣諒、初貝安弘、青木秀夫、河原林透
    • Organizer
      日本物理学会2016年次秋季大会
    • Place of Presentation
      金沢大学(石川県金沢市)
    • Year and Date
      2016-09-16
    • Related Report
      2016 Research-status Report
  • [Presentation] 傾いたディラック電子を持つ格子模型の連続変形2016

    • Author(s)
      河原林透、青木秀夫、初貝安弘
    • Organizer
      日本物理学会2016年次秋季大会
    • Place of Presentation
      金沢大学(石川県金沢市)
    • Year and Date
      2016-09-14
    • Related Report
      2016 Research-status Report
  • [Presentation] Zero modes of two-dimensional tilted Dirac fermions with vortices2016

    • Author(s)
      T. Kawarabayashi, H. Aoki, Y. Hatsugai
    • Organizer
      the international conference “Graphene week 2016”
    • Place of Presentation
      Warsaw(Poland)
    • Year and Date
      2016-06-14
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research
  • [Presentation] 一般化されたカイラル対称性を持つ格子模型2016

    • Author(s)
      河原林透、初貝安弘、青木秀夫
    • Organizer
      日本物理学会第71回年次大会
    • Place of Presentation
      東北学院大学(宮城県仙台市)
    • Year and Date
      2016-03-22
    • Related Report
      2015 Research-status Report

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Published: 2015-10-21   Modified: 2020-03-30  

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