# Optical Conductivity Spectra of Charge-Crystal and Charge-Glass States in a Series of θ-Type BEDT-TTF Compounds

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

## 3. Results

#### 3.1. Electrical Resistivity in ${\theta}_{o}$-CsZn, ${\theta}_{o}$-RbZn, and ${\theta}_{m}$-TlZn

#### 3.2. Optical Conductivity Spectra in ${\theta}_{o}$-CsZn, ${\theta}_{o}$-RbZn, and ${\theta}_{m}$-TlZn

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Crystal structure and phase diagram of $\theta $–type (BEDT–TTF) salts. (

**a**) Crystal structure of the ${\theta}_{\mathrm{o}}$-type salts viewed along the c-axis direction. The rectangle indicates the unit cell. (

**b**) 2D conducting BEDT-TTF layers within the a-c plane for the ${\theta}_{\mathrm{o}}$-type salts. (

**c**) Crystal structure of the ${\theta}_{\mathrm{m}}$-type system viewed along the b-axis direction. The parallelogram indicates the unit cell. (

**d**) 2D conducting BEDT-TTF layers within the b-c plane for the ${\theta}_{\mathrm{m}}$-type system. (

**e**) Phase diagram of the ${\theta}_{\mathrm{o}}$-type system a function of the anisotropy parameter, ${V}_{2}/{V}_{1}$. (

**f**) Critical cooling rate for charge-glass formation for various $\theta $-type salts as a function of ${V}_{2}/{V}_{1}$.

**Figure 2.**Resistivity and Arrhenius plot in the $\theta $–type salts. (

**a**) $\rho \left(T\right)$ curve of ${\theta}_{\mathrm{o}}$-CsZn measured during cooling. (

**b**) Arrhenius plot of the same data in (

**a**). (

**c**) $\rho \left(T\right)$ curve of ${\theta}_{\mathrm{o}}$-RbZn measured during rapid cooling of 30 K/min (blue) and slow cooling of 0.1 K/min (red). (

**d**) Arrhenius plot of the same data in (

**c**). (

**e**) $\rho \left(T\right)$ curve of ${\theta}_{\mathrm{m}}$-TlZn measured during rapid cooling of 100 K/min (blue) and slow heating after slow cooling of 0.1 K/min (red). (

**f**) Arrhenius plot of the same data in (

**e**). The black lines in (

**b**,

**d**,

**f**) represent the fits to $\rho \propto exp(\Delta /\left({k}_{\mathrm{B}}T\right))$.

**Figure 3.**Optical conductivity spectra in the $\theta $–type salts. (

**a**) Optical conductivity spectra ${\sigma}_{1}\left(\omega \right)$ in ${\theta}_{\mathrm{o}}$-CsZn measured at several temperatures during slow cooling of 1 K/min. (

**b**) Optical conductivity spectra ${\sigma}_{1}\left(\omega \right)$ in ${\theta}_{\mathrm{o}}$-RbZn measured at several temperatures during slow cooling of 1 K/min (solid line) and slow heating after rapid cooling of more than 50 K/min when passing through ${T}_{\mathrm{CO}}$ (dashed line). (

**c**) Optical conductivity spectra ${\sigma}_{1}\left(\omega \right)$ in ${\theta}_{\mathrm{m}}$-TlZn measured at several temperatures during slow cooling of 1 K/min (solid line) and slow heating after rapid cooling of more than 50 K/min when passing through ${T}_{\mathrm{CO}}$ (dashed line). For clarity, the data are shifted vertically. Note that the sharp peak at approximately 2100 cm${}^{-1}$ is the CN stretching mode of SCN in the anion layer.

**Figure 4.**Comparison of optical conductivity spectra of the charge–glass states in the $\theta $–type salts. Optical conductivity spectra of the charge-glass states in ${\theta}_{\mathrm{o}}$-CsZn (red), ${\theta}_{\mathrm{o}}$-RbZn (blue), and ${\theta}_{\mathrm{m}}$-TlZn (green) measured at 4 K, 50 K, and 50 K, respectively.

**Figure 5.**Polarization dependence of optical conductivity spectra in the charge–glass/crystal states of the $\theta $–type salts. (

**a**–

**c**) Optical conductivity spectra of (

**a**) the charge-glass state in ${\theta}_{\mathrm{o}}$-CsZn for $\mathit{E}\Vert \mathit{a}$ (blue) and $\mathit{E}\Vert \mathit{c}$ (red) measured at 4 K, (

**b**) the charge-crystal state in ${\theta}_{\mathrm{o}}$-RbZn for $\mathit{E}\Vert \mathit{a}$ (blue) and $\mathit{E}\Vert \mathit{c}$ (red) measured at 50 K, and (

**c**) the charge-crystal state in ${\theta}_{\mathrm{m}}$-TlZn for $\mathit{E}\Vert \mathit{c}$ (blue) and $\mathit{E}\Vert \mathit{b}$ (red) measured at 50 K.

**Figure 6.**Schematic charge configurations on triangular lattices. (

**a**) Charge configurations on the isosceles triangular lattice. Vertical, horizontal, diagonal, and three-sublattice COs are described. In the three-sublattice structure, the sublattice A is filled by one hole (pin), the sublattice B is empty, and the sublattice C is randomly occupied by the remaining holes (ball). The green hexagon stands for the unit cell. (

**b**) Chain striped CO patterns on the isosceles triangular lattice, such as horizontal and diagonal COs. ${V}_{1}$ and ${V}_{2}$ (${V}_{1}>{V}_{2}$) are the nearest-neighbor Coulomb interactions. Since all these states are degenerate in the classical limit of the t-V model, the classical ground state can be described by the superposition of these states. The magenta and white circles represent the charge-rich and charge-poor sites, respectively.

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**MDPI and ACS Style**

Hashimoto, K.; Kobayashi, R.; Ohkura, S.; Sasaki, S.; Yoneyama, N.; Suda, M.; Yamamoto, H.M.; Sasaki, T. Optical Conductivity Spectra of Charge-Crystal and Charge-Glass States in a Series of *θ*-Type BEDT-TTF Compounds. *Crystals* **2022**, *12*, 831.
https://doi.org/10.3390/cryst12060831

**AMA Style**

Hashimoto K, Kobayashi R, Ohkura S, Sasaki S, Yoneyama N, Suda M, Yamamoto HM, Sasaki T. Optical Conductivity Spectra of Charge-Crystal and Charge-Glass States in a Series of *θ*-Type BEDT-TTF Compounds. *Crystals*. 2022; 12(6):831.
https://doi.org/10.3390/cryst12060831

**Chicago/Turabian Style**

Hashimoto, Kenichiro, Ryota Kobayashi, Satoshi Ohkura, Satoru Sasaki, Naoki Yoneyama, Masayuki Suda, Hiroshi M. Yamamoto, and Takahiko Sasaki. 2022. "Optical Conductivity Spectra of Charge-Crystal and Charge-Glass States in a Series of *θ*-Type BEDT-TTF Compounds" *Crystals* 12, no. 6: 831.
https://doi.org/10.3390/cryst12060831