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Dirac Electron System in Solid State Physics

Massless Dirac Electron in Organic Conductor

Our group has found a massless particle in the quasi-two-dimensional organic conductor α-(BEDT-TTF)2I3. Since this particle behaves like a s=1/2 fermion described by the Dirac equation in the relativistic quantum mechanics, it is called “Dirac electron”. As shown in the right figure, the relationship between energy E and momentums px and py is conical, so it is called "Dirac cone". Only the lower cone is filled with electrons, resulting in a “zero gap” state. Such material shows anomalous transport phenomena. The electrical resistance hardly changes as temperature decreases, even though the carrier density decreases dramatically.

  1. A. Kobayashi, B. Zhou, R. Takagi, K. Miyagawa, S. Ishibashi, A. Kobayashi, T. Kawamura, E. Nishibori, and K. Kanoda,
    "Single-Component Molecular Conductors - Multi-Orbital Correlated π-d Electron Systems"
    Bull. Chem. Soc. Jpn. 94, 2540 (2021).
  2. T. Kawamura, D. Ohki, B. Zhou, A. Kobayashi, and A. Kobayashi,
    "Tight-Binding Model and Electronic Property of Dirac Nodal Line in Single-Component Molecular Conductor [Pt(dmdt)2]"
    J. Phys. Soc. Jpn. 89, 074704 (2020).
  3. K. Kajita, Y. Nishio, N. Tajima, Y. Suzumura, and A. Kobayashi
    "Molecular Dirac Fermion Systems -Theoretical and Experimental Approaches"
    J. Phys. Soc. Jpn. 83, 072002 (2014). [Invited review paper]
  4. A. Kobayashi, S. Katayama, Y. Suzumura, and H. Fukuyama
    “Massless Fermions in Organic Conductor”
    J. Phys. Soc. Jpn. 76, 034711 (2007).
  5. S. Katayama, A. Kobayashi, and Y. Suzumura
    Pressure-Induced Zero-Gap Semiconducting State in the Organic Conductor alpha-(BEDT-TTF)2I3 Salt"
    J. Phys. Soc. Jpn. 75, 054705 (2006). [Editor' choice]
    第14回日本物理学会論文賞(2009年3月)、科学新聞(2006年5月26日)
  6. A. Kobayashi, S. Katayama, K. Noguchi, and Y. Suzumura
    "Superconductivity in Charge Ordered Organic Conductor - alpha-(ET)2I3 Salt"
    J. Phys. Soc. Jpn. 73, 3135-3148 (2004)    .

Inter-Band Effect of Magnetic Field

Dirac electrons in solids exhibit unique properties different from conventional metals, such as the strong diamagnetism induced by the inter-band effect of magnetic field, which is due to orbital motion of electrons and holes. We have found the inter-band effect of magnetic field strongly affect the Hall coefficient and orbital diamagnetism in α-(BEDT-TTF)2I3.

  1. A. Kobayashi, Y. Suzumura, and H. Fukuyama
    "Hall Effect and Orbital Diamagnetism in Zerogap State of Molecular Conductor alpha-(BEDT-TTF)2I3"
    J. Phys. Soc. Jpn. 77 064718 (2008).

Dirac Electron under Strong Magnetic Field

There are two Dirac cones in the organic conductor. The axes of the Dirac cones are tilted in opposite directions. We have theoretically shown that the tilting of the Dirac cones drastically changes the electronic state under strong magnetic field. The tilting breaks the symmetry of the long-range Coulomb interaction in the valley pseudo-spin space, for the N=0 Landau states. We have shown that the XY ferromagnetism occurs in which the valley pseudo-spins are aligned in the two-dimensional conducting plane. This situation is actually observed by the nuclear magnetoresistance (NMR) measurement.

  1. T. Tani and A. Kobayashi,
    "Spin-Lattice Relaxation Rate in Organic Dirac Electron System α-(BEDT-TTF)2I3 under Strong Magnetic Field"
    J. Phys. Soc. Jpn. 88, 054713 (2019).
  2. T. Tani, N. Tajima, and A. Kobayashi,
    "Field-Angle Dependence of Interlayer Magnetoresistance in Organic Dirac Electron System α-(BEDT-TTF)2I3"
    Crystals 9, 212 (2019).
  3. A. Kobayashi, Y. Suzumura, H. Fukuyama, and M.O. Goerbig
    "Tilted-Cone-induced easy-plane pseudo-spin ferromagnet and Kosterlitz-Thouless transition in massless Dirac fermions"
    J. Phys. Soc. Jpn. 78 114711 (2009). [Editor's choice]

Effects of Long-Range Coulomb Interaction between Dirac electrons

In the absence of Coulomb interaction, the Knight shift (the magnetic susceptibility) of the two-dimensional massless Dirac electron is proportional to temperature T. However, in the nuclear magnetoresistance (NMR) measurement, the Knight shift is strongly suppressed comparing to T-linear behavior. We have shown that the self-energy of the long-range Coulomb interaction between Dirac electrons suppresses the Knight shift. Furthermore, we have found the anomalous spin fluctuation being a precursory fluctuation of the excitonic transition, which is one of the spontaneous mass generation mechanisms.

  1. T. Kawamura and A. Kobayashi,
    "Fragment-orbital-dependent spin fluctuations in the single-component molecular conductor [Ni(dmdt)2]"
    Phys. Rev. B 105, 205145 (2022).
  2. D. Ohki, K. Yoshimi, and A. Kobayashi,
    "Interaction-induced quantum spin Hall insulator in the organic Dirac electron system α-(BEDT-TSeF)2I3"
    Phys. Rev. B 105, 205123 (2022).
  3. T. Kawamura, B. Zhou, A. Kobayashi, and A. Kobayashi
    "Possible Spin-Density Wave on Fermi Arc of Edge State in Single-Component Molecular Conductors [Pt(dmdt)2] and [Ni(dmdt)2]"
    J. Phys. Soc. Jpn. 90, 064710 (2021)
  4. M. Hirata, A. Kobayashi, C. Berthier, and K. Kanoda
    "Interacting chiral electrons at the 2D Dirac points: a review"
    Rep. Prog. Phys. 84, 036502 (2021).
  5. D. Ohki, K. Yoshimi, and A. Kobayashi
    "Transport properties of the organic Dirac electron system α-(BEDT-TSeF)2I3"
    Phys. Rev. B 102, 235116 (2020).
  6. D. Ohki, M. Hirata, T. Tani, K. Kanoda, and A. Kobayashi
    "Chiral excitonic instability of two-dimensional tilted Dirac cones"
    Phys. Rev. Research 2, 033479 (2020).
  7. D. Ohki, Y. Omori, and A. Kobayashi
    "Effect of Coulomb interactions on the Seebeck coefficient of the organic Dirac electron system α-(BEDT-TTF)2I3"
    Phys. Rev. B 101, 245201 (2020).
  8. 小林晃人、平田倫啓、鹿野田一司
    "有機導体のディラック電子系における電子相関効果"
    固体物理 Vol. 54 No. 10 p. 495-504 (2019)　解説
  9. G. Matsuno and A. Kobayashi
    "Coexistence of Velocity Renormalization and Ferrimagnetic Fluctuation in the Organic Dirac Electron System alpha-(BEDT-TTF)2I3"
    J. Phys. Soc. Jpn. 87, 054706 (2018).
  10. 平田倫啓、鹿野田一司、松野元樹、小林晃人
    "有機物質のディラックコーンにおける強相関効果"
    日本物理学会誌　『最近の研究から』　Vol. 73, No. 4, p. 214-220, (2018)
  11. 平田倫啓、鹿野田一司、小林晃人、石川恭平、松野元樹、宮川和也、田村雅史、Claude Berthier
    相互作用する2次元ワイルフェルミオンの異常なスピン相関とエキシトン不安定性
    Science日本事務局「サイエンス誌に載った日本人研究者」2018年号 p. 61
  12. M. Hirata, K. Ishikawa, G. Matsuno, A. Kobayashi, K. Miyagawa, M. Tamura, C. Berthier, and K. Kanoda
    "Anomalous spin correlations and excitonic instability of interacting 2D Weyl fermions"
    Science 358, 1403 (2017).
  13. 平田倫啓、石川恭平、松野元樹、小林晃人、宮川和也、田村雅史、Claude Berthier、鹿野田一司
    "質量がゼロの電子がしめす新規なスピンのゆらぎを発見 ― 電子が自発的に質量を獲得する新現象の解明に期待 ―"
    プレスリリース（東大、東北大、東京理科大、名大）2017年12月15日.
  14. M. Hirata, K. Ishikawa, K. Miyagawa, M. Tamura, C. Berthier, D. Basko, A. Kobayashi, G. Matsuno, and K. Kanoda
    "Observation of an anisotropic Dirac cone reshaping and ferrimagnetic spin polarization in an organic conductor"
    Nat. Commun. 7, 12666 (2016).
  15. 平田倫啓、石川恭平、宮川和也、田村雅史、Claude Berthier、Denis Basko、小林晃人、松野元樹、鹿野田一司
    "せめぎ合うゼロ質量電子～ 相互作用が織り成す多彩な競合現象の解明"
    プレスリリース（東大、東北大、東京理科大、名大）2016年8月31日.
  16. Genki Matsuno and Akito Kobayashi
    "Effect of Interband Fluctuation on Spin Susceptibility in Molecular Dirac Fermion System alpha-(BEDT-TTF)2I3"
    J. Phys. Soc. Jpn. 86, 014705 (2017).

Edge States and Domain Walls in Dirac Electron System

The organic Dirac electron system α-(BEDT-TTF)2I3 exhibits the transition from the charge-ordered phase to the massless Dirac electron phase under hydrostatic pressure. In recent years, it has been observed that the conduction gap obtained from the in-plane resistance is almost zero, although the optical gap obtained from the optical conductivity is large. This suggests that some conduction channels exist in the charge ordered phase. We have shown that the finite-mass Dirac electrons in the charge ordered phase have the metallic edge states. Furthermore, we have investigated the electronic states around the domain walls of the charge order and found that the bound states of the Dirac electrons exhibit high electrical conductivity. These results can qualitatively explain the experimental results.

  1. D. Ohki, Y. Omori, and A. Kobayashi
    "Domain wall conductivity with strong Coulomb interaction of two-dimensional massive Dirac electrons in the organic conductorα-(BEDT-TTF)2I3"
    Phys. Rev. B 100, 075206 (2019).
  2. D. Ohki, G. Matsuno, Y. Omori, and A. Kobayashi
    "Melting of Domain Wall in Charge Ordered Dirac Electron of Organic Conductor alpha-(BEDT-TTF)2I3"
    J. Phys. Soc. Jpn. 87, 054703 (2018).
  3. D. Ohki, G. Matsuno, Y. Omori and A. Kobayashi
    "Optical Conductivity in a Two-Dimensional Extended Hubbard Model for an Organic Dirac Electron System α-(BEDT-TTF)2I3"
    Crystals 8(3), 137 (2018).
  4. Y. Omori, G. Matsuno, and A. Kobayashi
    "Longitudinal conductivity on edge and domain wall of molecular Dirac electron system α-(BEDT-TTF)2I3"
    J. Phys. Soc. Jpn. 86, 074708 (2017).
  5. G. Matsuno, Y. Omori, T. Eguchi, and A. Kobayashi
    "Topological Domain Wall and Valley Hall Effect in Charge Ordered Phase of Molecular Dirac Fermion System alpha-(BEDT-TTF)2I3"
    J. Phys. Soc. Jpn. 85, 094710 (2016).
  6. Y. Omori, G. Matsuno, and A. Kobayashi
    "Edge States in Molecular Solid alpha-(BEDT-TTF)2I3: Effects of Electron Correlations"
    JPS Conf. Proc. 1, 012119 (2014).
  7. A. Kobayashi, Y. Suzumura, F. Piechon, and G. Montambaux
    “Emergence of Dirac electron pair in the charge-ordered state of the organic conductor alpha-(BEDT-TTF)2I3”
    Phys. Rev. B 84, 075450 (2011)    .