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Optical Conductivity in a Two-Dimensional Extended Hubbard Model for an Organic Dirac Electron System α-(BEDT-TTF)_{2}I_{3}

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## Abstract

**:**

## 1. Introduction

## 2. Formulation

## 3. Results

## 4. Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

DE | Dirac electron |

CO | charge order |

VHS | Van Hove singularity |

DOS | density of states |

TRIM | time reversal invariant momentum |

Mc-VHS | Van Hove singularity at the M-point in the conduction band |

Mv-VHS | Van Hove singularity at the M-point in the valence band |

Yv-VHS | Van Hove singularity at the Y-point in the valence band |

## References

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**Figure 1.**(

**a**) Schematic figure of two-dimensional conductive plane in $\alpha $-(BEDT-TTF)${}_{2}$I${}_{3}$. Some ellipses represent sublattices of the BEDT-TTF molecule. In the figure, signs of b1, b2, ..., a4${}^{\prime}$ correspond to transfer integrals ${t}_{b1},{t}_{b2},\dots ,{t}_{a4}^{\prime}$ between two molecules. Nearest-neighbor Coulomb repulsions ${V}_{a}$, ${V}_{b}$ are represented by the red dotted arrows. On-site Coulomb repulsion U also exists, although it is not shown in the figure. The unit cell is a region surrounded by a black dotted square in the figure. In the absence of the Coulomb interactions, the inversion symmetry points exist on B and C sublattices, and at the midpoint between A and A${}^{\prime}$ sublattices. (

**b**) The conduction band (purple) and valence band (green) in the massless DE phase for ${V}_{a}=0.18$, and (

**c**) a view of same two bands projected from the side along ${k}_{x}$ axis.

**Figure 2.**The optical conductivities divided by the universal conductivity ${\sigma}_{0}=\pi {e}^{2}/2h$ [38] for ${V}_{a}=0.180,0.190,0.198,0.199,0.205,0.212,0.220,0.230,0.240$

**(a)**. ${\omega}_{\mathrm{CO}}$ and ${\omega}_{\mathrm{peak}}$ for ${V}_{a}={V}_{a}^{c2}=0.212$ are shown in (

**a**). ${V}_{a}$-dependences of ${\omega}_{\mathrm{CO}}$ and ${\omega}_{\mathrm{peak}}$ are shown in (

**b**). A characteristic peak structure is found near the CO transition in the extended Hubbard model describing the organic Dirac electron system $\alpha $-(BEDT-TTF)${}_{2}$I${}_{3}$.

**Figure 3.**The density of states $\rho \left(\omega \right)$ for ${V}_{a}=0.198,0.205,0.212,0.220,0.230$. The origin of the peak structure in the optical conductivity is identified.

**Figure 4.**The contour plots of the conduction band for ${V}_{a}=0.205$ (

**a**), ${V}_{a}={V}_{a}^{c2}=0.212$ (

**b**), and ${V}_{a}=0.220$ (

**c**). The band structures as a function of ${k}_{x}$ for ${V}_{a}=0.205$ (

**d**), ${V}_{a}={V}_{a}^{c2}=0.212$ (

**e**), and ${V}_{a}=0.220$ (

**f**), where the CO gaps open between the conduction bands (the purple bands) and the valence bands (the green bands). Tilting of the Dirac cones causes electron-hole asymmetric behavior as the CO gap increases.

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**MDPI and ACS Style**

Ohki, D.; Matsuno, G.; Omori, Y.; Kobayashi, A.
Optical Conductivity in a Two-Dimensional Extended Hubbard Model for an Organic Dirac Electron System *α*-(BEDT-TTF)_{2}I_{3}. *Crystals* **2018**, *8*, 137.
https://doi.org/10.3390/cryst8030137

**AMA Style**

Ohki D, Matsuno G, Omori Y, Kobayashi A.
Optical Conductivity in a Two-Dimensional Extended Hubbard Model for an Organic Dirac Electron System *α*-(BEDT-TTF)_{2}I_{3}. *Crystals*. 2018; 8(3):137.
https://doi.org/10.3390/cryst8030137

**Chicago/Turabian Style**

Ohki, Daigo, Genki Matsuno, Yukiko Omori, and Akito Kobayashi.
2018. "Optical Conductivity in a Two-Dimensional Extended Hubbard Model for an Organic Dirac Electron System *α*-(BEDT-TTF)_{2}I_{3}" *Crystals* 8, no. 3: 137.
https://doi.org/10.3390/cryst8030137