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Geometrical phases by Majorana representation and topological order parameters

Research Project

Project/Area Number 25610101
Research Category

Grant-in-Aid for Challenging Exploratory Research

Allocation TypeMulti-year Fund
Research Field Mathematical physics/Fundamental condensed matter physics
Research InstitutionUniversity of Tsukuba

Principal Investigator

HATSUGAI Yasuhiro  筑波大学, 数理物質系, 教授 (80218495)

Project Period (FY) 2013-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Keywords幾何学的位相 / ベリー接続 / トポロジカル秩序 / エンタングルメントチャーン数 / マヨラナ表示 / トポロジカル相 / BdG方程式 / 量子エンタングルメント / ベリー位相 / ボゴリューボフ・ドジャンハミルトニアン
Outline of Final Research Achievements

Topological material is a class of novel phases of matter where any of symmetry breaking is not crucially important for the classification. As for such topological phases, we have constructed series of topological order parameters using geometrical phases such as the Chern numbers and Berry phases. Here in this project, we have investigated a Majorana representation of fermions in relation to the Berry connection to define novel topological order parameters. Then we have developed a theoretical framework for the Bogoliubov-de Gennes equation.
Through the theoretical trials, we have noticed and found an advantage of the quantum entanglement for the characterization. Then we have defined an entanglement Chern number and entanglement Berry phases associated with an extensive partition using a purification of the entanglement Hamiltonian.

Report

(3 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • Research Products

    (42 results)

All 2015 2014 2013 Other

All Journal Article (15 results) (of which Peer Reviewed: 15 results,  Open Access: 4 results,  Acknowledgement Compliant: 6 results) Presentation (23 results) (of which Invited: 8 results) Book (2 results) Remarks (2 results)

  • [Journal Article] Disentangled topological numbers by a purification of entangled mixed states for non-interacting2015

    • Author(s)
      T. Fukui and Y. Hatsugai
    • Journal Title

      J. Phys. Soc. Jpn.

      Volume: 84 Issue: 4 Pages: 0437031-6

    • DOI

      10.7566/jpsj.84.043703

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Survival of sharp n = 0 Landau levels in massive tilted Dirac fermions: Role of the generalized chiral operator2015

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

      Phys. Rev. B

      Volume: 91 Issue: 8 Pages: 0851121-6

    • DOI

      10.1103/physrevb.91.085112

    • NAID

      120007130351

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Flat bands in the Weaire-Thorpe model and silicene2015

    • Author(s)
      Y. Hatsugai, K. Shiraishi and H. Aoki
    • Journal Title

      New J. Phys.

      Volume: 17 Issue: 2 Pages: 0250091-8

    • DOI

      10.1088/1367-2630/17/2/025009

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Characterizing the weak topological properties: Berry phase point of view2014

    • Author(s)
      Y. Yoshimura, K.-I. Imura, T. Fukui, and Y. Hatsugai
    • Journal Title

      Phys. Rev. B

      Volume: 90 Issue: 15

    • DOI

      10.1103/physrevb.90.155443

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Entanglement Chern number for an extensive partition of a topological ground state2014

    • Author(s)
      T. Fukui and Y. Hatsugai
    • Journal Title

      J. Phys. Soc. Jpn.

      Volume: 83 Issue: 11 Pages: 1137051-7

    • DOI

      10.7566/jpsj.83.113705

    • NAID

      40020264793

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Polarization as a topological quantum number in graphene2014

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

      Phys. Rev. B

      Volume: 90 Issue: 8

    • DOI

      10.1103/physrevb.90.085132

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Emergence of Topologically Stable Dirac Dispersions in a Fermionic Shastry-Sutherland Model2014

    • Author(s)
      Toshikaze Kariyado and Yasuhiro Hatsugai
    • Journal Title

      JPS Conf. Proc.

      Volume: 1

    • DOI

      10.7566/jpscp.1.012001

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Characterization of Dimers in Graphene Flakes2014

    • Author(s)
      Daichi, Seki, Yuji, Hamamoto and Yasuhiro Hatsugai
    • Journal Title

      JPS Conf. Proc.

      Volume: 1

    • DOI

      10.7566/jpscp.1.012068

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Sharp zero-energy Landau levels in multilayer graphene2014

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

      JPS Conf. Proc.

      Volume: 1 Pages: 12069-12069

    • DOI

      10.7566/jpscp.1.012069

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Sharp zero-energy Landau levels in multilayer graphene2014

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

      JPS Conf. Proc.

      Volume: 1 Pages: 12069-12069

    • DOI

      10.1088/1742-6596/456/1/012020

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Chiral Symmetry and Fermion Doubling in the Zero-mode Landau Levels of Massless Dirac Fermions with Disorder2013

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

      AIP Conference Proceedings

      Volume: 1566 Pages: 283-284

    • DOI

      10.1063/1.4848396

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Symmetry Protected Quantization and Bulk-Edge Correspondence of Massless Dirac Fermions : Application to Fermionic Shastry-Sutherland Model2013

    • Author(s)
      T. Kariyado and Y. Hatsugai
    • Journal Title

      Phys. Rev. B

      Volume: 88 Issue: 24

    • DOI

      10.1103/physrevb.88.245126

    • NAID

      120007135879

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Chiral Symmetry and Many-Body Effect in Multilayer Graphene2013

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

      Journal of Physics : Conference series

      Volume: 456 Pages: 12013-12013

    • DOI

      10.1088/1742-6596/456/1/012013

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] T. Fukui, K.-I. Imura and Y. Hatsugai2013

    • Author(s)
      T. Fukui, K.-I. Imura and Y. Hatsugai
    • Journal Title

      Journal of the Physical Society of Japan

      Volume: 82 Issue: 7 Pages: 073708-073708

    • DOI

      10.7566/jpsj.82.073708

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Spin-resolved chiral condensate as a spin unpolarizedν=0 quantum Hall state in graphene2013

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

      Physical Review

      Volume: B88 Issue: 19 Pages: 195141-195141

    • DOI

      10.1103/physrevb.88.195141

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] エンタングルメント・チャーン数の提案と応用2015

    • Author(s)
      福井隆裕,初貝安弘
    • Organizer
      日本物理学会 第70回年次大会
    • Place of Presentation
      早稲田大学早稲田キャンパス,東京都
    • Year and Date
      2015-03-21 – 2015-03-24
    • Related Report
      2014 Annual Research Report
  • [Presentation] Symmetry in topological phases: Quantization and entanglement Chern numbers2014

    • Author(s)
      Y. Hatsugai
    • Organizer
      Trends in Theory of Correlated Materials (TTCM2014)
    • Place of Presentation
      青山大学、渋谷区、東京
    • Year and Date
      2014-10-05 – 2014-10-08
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 傾いたディラック電子系におけるn=0ランダウ準位の異常性とstaggered ポテンシャル2014

    • Author(s)
      河原林透、初貝安弘、青木秀夫
    • Organizer
      日本物理学会2014年秋季大会
    • Place of Presentation
      中部大学春日井キャンパス,愛知県
    • Year and Date
      2014-09-09
    • Related Report
      2014 Annual Research Report
  • [Presentation] 必ずしもカイラルでない系におけるベリー位相の量子化2014

    • Author(s)
      福井隆裕,初貝安弘
    • Organizer
      日本物理学会2014年秋季大会
    • Place of Presentation
      中部大学春日井キャンパス,愛知県
    • Year and Date
      2014-09-07 – 2014-09-10
    • Related Report
      2014 Annual Research Report
  • [Presentation] Symmetry protection and Berry connections in condensed matter systems2014

    • Author(s)
      Y. Hatsugai
    • Organizer
      Geometric Aspects of Quantum States in Condensed Matter
    • Place of Presentation
      Natal, Brazil
    • Year and Date
      2014-08-27
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Geometric aspects of graphene: chiral symmetry and polarization2014

    • Author(s)
      Y. Hatsugai
    • Organizer
      Geometric Aspects of Quantum States in Condensed Matter
    • Place of Presentation
      Natal, Brazil
    • Year and Date
      2014-08-26
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Local density of states at topological defects in a Kekue bond order in graphene2014

    • Author(s)
      T. Kawarabayashi, Y. Inoue, Y. Hatsugai, and H.Aoki
    • Organizer
      the 21st international conference on “High Magnetic Fields in Semiconductor Physics”
    • Place of Presentation
      Panama City Beach, U.S.A.
    • Year and Date
      2014-08-04 – 2014-08-08
    • Related Report
      2014 Annual Research Report
  • [Presentation] Local density of states at topological defects in a Kekue bond order in graphene2014

    • Author(s)
      T. Kawarabayashi, Y. Inoue, Y. Hatsugai, and H.Aoki
    • Organizer
      Graphene week 2014
    • Place of Presentation
      Gothenburg, Sweden
    • Year and Date
      2014-06-23 – 2014-06-27
    • Related Report
      2014 Annual Research Report
  • [Presentation] Bulk-Edge Correspondence: Variety and Universality2014

    • Author(s)
      Y. Hatsugai
    • Organizer
      “Topology in the New Frontiers of Materials Science”
    • Place of Presentation
      NIMS, Namik, Tsukuba, JAPAN
    • Year and Date
      2014-04-01 – 2014-04-02
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Universality & variety of edge states in graphene & silicene2014

    • Author(s)
      Y. Hatsugai
    • Organizer
      CENIDE-CNMM-TIMS Joint Symposium on Interdisciplinary Nano-Science and Technology
    • Place of Presentation
      Hsinchu, Taiwan
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] ベリー位相の分数量子化とディラック電子系のエッジ状態2014

    • Author(s)
      苅宿俊風, 初貝安弘
    • Organizer
      日本物理学会第69回年会
    • Place of Presentation
      東海大学、神奈川
    • Related Report
      2013 Research-status Report
  • [Presentation] 超格子系の弱トポロジカル相とエッジ状態2014

    • Author(s)
      吉村幸徳,井村健一郎,福井隆裕A,初貝安弘
    • Organizer
      日本物理学会第69回年会
    • Place of Presentation
      東海大学、神奈川
    • Related Report
      2013 Research-status Report
  • [Presentation] グラフェンのディラックコーンとゼロエネルギー局在状態2013

    • Author(s)
      初貝安弘
    • Organizer
      グラフェンナノデバイスの新しい展開
    • Place of Presentation
      AIST, Tsukuba, Japan
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Symmetry protection and strong correlation in graphene with bulk-edge correspondence2013

    • Author(s)
      Y. Hatsugai
    • Organizer
      Trends in theory of Correlated Materials 2013
    • Place of Presentation
      Lausanne, Switzerland
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Symmetry, Berry connection and Bulk-edge correspondence2013

    • Author(s)
      Y. Hatsugai
    • Organizer
      Emergent Quantum Phases in Condensed Matter
    • Place of Presentation
      ISSP, Kashiwa, Japan
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] 時間反転対称性を破る格子ディラック模型の離散対称性と量子化2013

    • Author(s)
      初貝安弘, 福井隆裕, 井村健一郎
    • Organizer
      日本物理学会 2013年秋季大会
    • Place of Presentation
      徳島大学、徳島
    • Related Report
      2013 Research-status Report
  • [Presentation] Symmetry protected Z2 Berry phase in massless Dirac fermion systems2013

    • Author(s)
      苅宿 俊風, 初貝安弘
    • Organizer
      FIRST-QS2C WS on "Emergent Phenomena of Correlated Materials"
    • Place of Presentation
      Shinagawa Intercity Hall, Tokyo
    • Related Report
      2013 Research-status Report
  • [Presentation] フェルミオンShastry-Sutherland模型におけるディラックコーンとエッジ状態2013

    • Author(s)
      苅宿俊風, 初貝安弘
    • Organizer
      日本物理学会 2013年秋季大会
    • Place of Presentation
      徳島大学、徳島
    • Related Report
      2013 Research-status Report
  • [Presentation] Z2 Berry phase as a local dimer order parameter of grapheme flakes2013

    • Author(s)
      Daichi Sek, Yuji Hamamoto, Yasuhiro Hatsugai
    • Organizer
      Statphys25
    • Place of Presentation
      Seoul, Korea
    • Related Report
      2013 Research-status Report
  • [Presentation] Emergence of Topologically Stable Dirac Dispersions in a Fermionic Shastry Sutherland Model2013

    • Author(s)
      Toshikaze Kariyado, Yasuhiro Hatsugai
    • Organizer
      The 12th Asia Pacific Physics Conference
    • Place of Presentation
      Makuhari, Chiba
    • Related Report
      2013 Research-status Report
  • [Presentation] Fermionic Shastry-Sutherland model: Emergence of Dirac dispersions, edge modes, and topological properties2013

    • Author(s)
      T. Kariyado, Y. Hatsugai
    • Organizer
      Emergent Quantum Phases in Condensed Matter
    • Place of Presentation
      ISSP, Kashiba Chiba
    • Related Report
      2013 Research-status Report
  • [Presentation] Landau levels of disordered massless Dirac fermions when the Dirac cones are both shifted and tilted2013

    • Author(s)
      T. Honda, Y. Hatsugai, H. Aok, T. Kawarabayashi
    • Organizer
      20th International Conference on Electronic Properties of Two-Dimensional Systems (EP2DS-20)
    • Place of Presentation
      Wroclaw, Poland
    • Related Report
      2013 Research-status Report
  • [Presentation] Doubly-Degenerate Chiral Condensate as a Spin-Unpolarized ν = 0 Quantum Hall State in Graphene2013

    • Author(s)
      Y., Hamamoto; T., Kawarabayashi; H., Aoki; Y., Hatsugai
    • Organizer
      The 7th International Conference on the Fundamental Science of Graphene and Applications of Graphene-Based Devices (Graphene Week 2013)
    • Place of Presentation
      Chemnitz, Germany
    • Related Report
      2013 Research-status Report
  • [Book] Graphene: Topological Properties, Chiral Symmetry and Their Manipulation in Physics of Graphene2014

    • Author(s)
      Y. Hatsugai and H. Aoki
    • Total Pages
      350
    • Publisher
      Springer
    • Related Report
      2013 Research-status Report
  • [Book] パリティー2013年11月号:原子崩壊がグラフェンで現実に(翻訳)2013

    • Author(s)
      初貝安弘
    • Total Pages
      80
    • Publisher
      丸善
    • Related Report
      2013 Research-status Report
  • [Remarks] 筑波大学・数理物質系・物理学域・初貝研究室

    • URL

      http://rhodia.ph.tsukuba.ac.jp/

    • Related Report
      2014 Annual Research Report
  • [Remarks] 初貝研究室

    • URL

      http://rhodia.ph.tsukuba.ac.jp

    • Related Report
      2013 Research-status Report

URL: 

Published: 2014-07-25   Modified: 2019-07-29  

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