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Emergence of Dirac electron pair in the charge-ordered state of the organic conductor α-(BEDT-TTF)2I3

A. Kobayashi, Y. Suzumura, F. Piéchon, and G. Montambaux
Phys. Rev. B 84, 075450 – Published 10 August 2011
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  • INTRODUCTION
  • TIGHT-BINDING MODEL FOR α-(BEDT-TTF)2I3
  • PHASE DIAGRAM
  • TOPOLOGICAL TRANSITION AROUND THE M POIN…
  • BERRY CURVATURE ASSOCIATED WITH THE…
  • SUMMARY AND DISCUSSION
  • ACKNOWLEDGEMENTS
  • APPENDICES
    • References

    Abstract

    We reexamine the band structure of the stripe charge ordered state of α-(BEDT-TTF)2I3 under pressure by using an extended Hubbard model within the Hartree mean-field theory. By increasing pressure, we find a topological transition from a conventional insulator with a single-minimum in the dispersion relation at the M point in the Brillouin zone, toward a new phase which exhibits a double minimum. This transition is characterized by the appearance of a pair of Dirac electrons with a finite mass. Using the Luttinger-Kohn representation at the M point, it is shown that such a variation of the band structure can be described by an effective 2×2 low-energy Hamiltonian with a single driving parameter. The topological nature of this transition is confirmed by the calculation of the Berry curvature which vanishes in the conventional phase and has a double peak structure with opposite signs in the new phase. We compare the structure of this transition with a simpler situation which occurs in two-component systems, like boron-nitride.

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    • Received 28 April 2011

    DOI:https://doi.org/10.1103/PhysRevB.84.075450

    ©2011 American Physical Society

    Authors & Affiliations

    A. Kobayashi1, Y. Suzumura1, F. Piéchon2, and G. Montambaux2

    • 1Department of Physics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8602 Japan
    • 2Laboratoire de Physique des Solides, CNRS UMR 8502, Universite Paris-Sud, F-91405 Orsay Cedex, France

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    Vol. 84, Iss. 7 — 15 August 2011

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    Images

    • Figure 1
      Figure 1
      The model describing the electronic system of α-(BEDT-TTF)2I3 (Refs. 13, 25, and 26). The unit cell consists of four BEDT-TTF molecules A, A′, B, and C with seven transfer energies. The nearest-neighbor repulsive interactions are given by Va and Vb. The a and b axis in the conventional notation correspond to the y and x axis in the present paper.Reuse & Permissions
    • Figure 2
      Figure 2
      The phase diagram on the uniaxial pressure along the a axis (Pa [kbar]) and the repulsive interaction between nearest-neighbor sites along the a axis (Va [eV]), where U = 0.4 eV and Vb = 0.05 eV. The CO and COM denote insulating and metallic states, respectively. In addition to the phase (I) of the previous work,[9] there exists a new phase (II), which is characterized by a double minimum in the up-spin band.Reuse & Permissions
    • Figure 3
      Figure 3
      Schematic behavior of the energy spectrum close to the Fermi energy (horizontal line) in the different subphases of the CO phase: (a) CO(I), (b) CO(II), (c) COM(I), (d) COM(II). The red and blue bands correspond, respectively, to ↑ and ↓ spins. The center of the horizontal line corresponds to the M point [kM=(π,±π)].Reuse & Permissions
    • Figure 4
      Figure 4
      The q dependence of the conduction and valence bands for ↑ spin where q=k−kM, and the center denotes the M point [kM=(π,±π)]. (a) Spectrum of the CO(I) phase with a single minimum at the M point. (b) Spectrum of the CO(II) phase with a double minimum around the M point. Here the parameters are Va=0.18 eV and Vb=0.05 eV, and the pressures are, respectively, Pa=4.5 kbar and Pa=5.4 kbar, for the CO(I) and CO(II) phases.Reuse & Permissions
    • Figure 5
      Figure 5
      (a) Contours of the gap function Δk=[ξ+(k)−ξ−(k)]/2 for Pa=5.4 kbar in CO (II) phase, where 0<ky<2π and 0<kx<2π. The two Dirac points emerge from the M point kM=(π,±π). Points O, X, and Y denote (0,0), (π,0), and (0,π), respectively. (b) The same contour Δq in the vicinity of the M point, which is taken as the origin (q=k−kM). The red curve represents the energy contour Δq=Δ. The two red lines denote the angles θmin and θmax defined in the text (29). Note that on Fig. (b), the scales are different along the two axes.Reuse & Permissions
    • Figure 6
      Figure 6
      Pressure dependence of (a) Δ, (b) vj, (c) w3ij, (d) w¯3ij, (e) detSM, and (f) θmax, θmin for Va=0.18 eV and Vb=0.05 eV. The pressure Pa is in kbar.Reuse & Permissions
    • Figure 7
      Figure 7
      Contours of Δ(q) for the BN model. Here we have taken the same parameters as for the CO(I)-CO(II) transition in α(BEDT-TTF)2I3, Δ, w1=w1yy, w3=w3yy, vx, other w1ij, w3ij, vy being zero. In this simple case, since the parameter w¯3xy=0, the Dirac points stay along the y axis. The red curve corresponds to Δ(q)=Δ. The two lines indicate the directions θmax and θmin.Reuse & Permissions
    • Figure 8
      Figure 8
      (a) Berry curvature B1↑(k) in CO(I) with Pa=4.4 kbar; (b) Berry curvature B1↑(k) in CO(II) with Pa=5.4 kbar, where Va=0.18 eV and Vb=0.05 eV. The center denotes the M point.Reuse & Permissions
    • Figure 9
      Figure 9
      Pa dependence of the Berry phase |Γ(k±)| defined in Eq. (54) (solid line) compared with the expression Γ± given in Eq. (55) (dashed line). The inset denotes q+y, the y component of one Dirac point k+, where q=k−kM.Reuse & Permissions
    • Figure 10
      Figure 10
      The energy bands of ξ1σ and ξ2σ for ↑ spin band (a) and the ↓ spin band (b) in the CO(II) for Pa=5.4 kbar, Va=0.18 eV, and Vb=0.05 eV. The center denotes the M point.Reuse & Permissions
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