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

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 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

- Takahashi, T.; Nogami, Y.; Yakushi, K. Charge ordering in organic conductors. J. Phys. Soc. Jpn.
**2006**, 75, 051008. [Google Scholar] [CrossRef] - Seo, H.; Merino, J.; Yoshioka, H.; Ogata, M. Theoretical aspects of charge ordering in molecular conductors. J. Phys. Soc. Jpn.
**2006**, 75, 051009. [Google Scholar] [CrossRef] - Chiba, R.; Hiraki, K.; Takahashi, T.; Yamamoto, H.M.; Nakamura, T. Charge disproportionation and dynamics in θ-(BEDT-TTF)
_{2}CsZn(SCN)_{4}. Phys. Rev. B**2008**, 77, 115113. [Google Scholar] [CrossRef] - Kagawa, F.; Sato, T.; Miyagawa, K.; Kanoda, K.; Tokura, Y.; Kobayashi, K.; Kumai, R.; Murakami, Y. Charge-cluster glass in an organic conductor. Nat. Phys.
**2013**, 9, 419–422. [Google Scholar] [CrossRef] - Sato, T.; Kagawa, F.; Kobayashi, K.; Miyagawa, K.; Kanoda, K.; Kumai, R.; Murakami, Y.; Tokura, Y. Emergence of nonequilibrium charge dynamics in a charge-cluster glass. Phys. Rev. B
**2014**, 89, 121102(R). [Google Scholar] [CrossRef] - Sato, T.; Kagawa, F.; Kobayashi, K.; Ueda, A.; Mori, H.; Miyagawa, K.; Kanoda, K.; Kumai, R.; Murakami, Y.; Tokura, Y. Systematic variations in the charge-glass-forming ability of geometrically frustrated θ-(BEDT-TTF)
_{2}X organic conductors. J. Phys. Soc. Jpn.**2014**, 83, 083602. [Google Scholar] [CrossRef] - Hashimoto, K.; Zhan, S.C.; Kobayashi, R.; Iguchi, S.; Yoneyama, N.; Moriwaki, T.; Ikemoto, Y.; Sasaki, T. Collective excitation of a short-range charge ordering in θ-(BEDT-TTF)
_{2}CsZn(SCN)_{4}. Phys. Rev. B**2014**, 89, 085107. [Google Scholar] [CrossRef] - Oike, H.; Kagawa, F.; Ogawa, N.; Ueda, A.; Mori, H.; Kawasaki, M.; Tokura, Y. Phase-change memory function of correlated electrons in organic conductors. Phys. Rev. B
**2015**, 91, 041101. [Google Scholar] [CrossRef] - Sato, T.; Miyagawa, K.; Kanoda, K. Electronic crystal growth. Science
**2017**, 357, 1378–1381. [Google Scholar] [CrossRef] - Sasaki, S.; Hashimoto, K.; Kobayashi, R.; Itoh, K.; Iguchi, S.; Nishio, Y.; Ikemoto, Y.; Moriwaki, T.; Yoneyama, N.; Watanabe, M.; et al. Crystallization and vitrification of electrons in a glass-forming charge liquid. Science
**2017**, 357, 1381–1385. [Google Scholar] [CrossRef] - Mahmoudian, S.; Rademaker, L.; Ralko, A.; Fratini, S.; Dobrosavljević, V. Glassy dynamics in geometrically frustrated Coulomb liquids without disorder. Phys. Rev. Lett.
**2015**, 115, 025701. [Google Scholar] [CrossRef] [PubMed] - Mori, H.; Tanaka, S.; Mori, T.; Kobayashi, A.; Kobayashi, H. Crystal structure and physical properties of M = Rb and Tl salts of (BEDT-TTF)
_{2}MM^{′}(SCN)_{4}[M^{′}= Co, Zn]. Bull. Chem. Soc. Jpn.**1998**, 71, 797–806. [Google Scholar] [CrossRef] - Watanabe, M.; Nogami, Y.; Oshima, K.; Mori, H.; Tanaka, S. Novel pressure-induced 2k
_{F}CDW state in organic low-dimensional compound θ-(BEDT-TTF)_{2}CsCo(SCN)_{4}. J. Phys. Soc. Jpn.**1999**, 68, 2654–2663. [Google Scholar] [CrossRef] - Nogami, Y.; Pouget, J.P.; Watanabe, M.; Oshima, K.; Mori, H.; Tanaka, S.; Mori, T. Structural modulation in θ-(BEDT-TTF)
_{2}CsM^{′}(SCN)_{4}[M^{′}= Co, Zn]. Synth. Met.**1999**, 103, 1911. [Google Scholar] [CrossRef] - Watanabe, M.; Noda, Y.; Nogami, Y.; Mori, H. Investigation of X-ray diffuse scattering in θ-(BEDT-TTF)
_{2}RbM^{′}SCN_{4}. Synth. Met.**2003**, 135–136, 665–666. [Google Scholar] [CrossRef] - Watanabe, M.; Noda, Y.; Nogami, Y.; Mori, H. Transfer integrals and the spatial pattern of charge ordering in θ-(BEDT-TTF)
_{2}RbZn(SCN)_{4}at 90 K. J. Phys. Soc. Jpn.**2004**, 73, 116–122. [Google Scholar] [CrossRef] - Mori, H.; Tanaka, S.; Mori, T. Systematic study of the electronic state in θ-type BEDT-TTF organic conductors by changing the electronic correlation. Phys. Rev. B
**1998**, 57, 12023–12029. [Google Scholar] [CrossRef] - Tajima, H.; Kyoden, S.; Mori, H.; Tanaka, S. Estimation of charge-ordering patterns in θ-ET
_{2}MM^{′}(SCN)_{4}(MM^{′}= RbCo, RbZn, CsZn) by reflection spectroscopy. Phys. Rev. B**2000**, 62, 9378–9385. [Google Scholar] [CrossRef] - Miyagawa, K.; Kawamoto, A.; Kanoda, K. Charge ordering in a quasi-two-dimensional organic conductor. Phys. Rev. B
**2000**, 62, R7679–R7682. [Google Scholar] [CrossRef] - Suzuki, K.; Yamamoto, K.; Yakushi, K. Charge-ordering transition in orthorhombic and monoclinic single-crystals of θ-(BEDT-TTF)
_{2}TlZn(SCN)_{4}studied by vibrational spectroscopy. Phys. Rev. B**2004**, 69, 085114. [Google Scholar] [CrossRef] - Sawano, F.; Terasaki, I.; Mori, H.; Mori, T.; Watanabe, M.; Ikeda, N.; Nogami, Y.; Noda, Y. An organic thyristor. Nature
**2005**, 437, 522. [Google Scholar] [CrossRef] [PubMed] - Takahide, Y.; Konoike, T.; Enomoto, K.; Nishimura, M.; Terashima, T.; Uji, S.; Yamamoto, H.M. Current-voltage characteristics of charge-ordered organic crystals. Phys. Rev. Lett.
**2006**, 96, 136602. [Google Scholar] [CrossRef] [PubMed] - Nad, F.; Monceau, P.; Yamamoto, H.M. Effect of cooling rate on charge ordering in θ-(BEDT-TTF)
_{2}RbZn(SCN)_{4}. Phys. Rev. B**2007**, 76, 205101. [Google Scholar] [CrossRef] - Nogami, Y.; Hanasaki, N.; Watanabe, M.; Yamamoto, K.; Ito, T.; Ikeda, N.; Ohsumi, H.; Toyokawa, H.; Noda, Y.; Terasaki, I.; et al. Charge order competition leading to nonlinearity in organic thyristor family. J. Phys. Soc. Jpn.
**2010**, 79, 044606. [Google Scholar] [CrossRef] - Mori, T. Non-stripe charge order in the θ-phase organic conductors. J. Phys. Soc. Jpn.
**2003**, 72, 1469–1475. [Google Scholar] [CrossRef] - Merino, J.; Seo, H.; Ogata, M. Quantum melting of charge order due to frustration in two-dimensional quarter-filled systems. Phys. Rev. B
**2005**, 71, 125111. [Google Scholar] [CrossRef] - Kaneko, M.; Ogata, M. Mean-field study of charge order with long periodicity in θ-(BEDT-TTF)
_{2}X. J. Phys. Soc. Jpn.**2006**, 75, 014710. [Google Scholar] [CrossRef] - Watanabe, H.; Ogata, M. Novel charge order and superconductivity in two-dimensional frustrated lattice at quarter filling. J. Phys. Soc. Jpn.
**2006**, 75, 063702. [Google Scholar] [CrossRef] - Hotta, C.; Furukawa, N. Strong coupling theory of the spinless charges on triangular lattices: Possible formation of a gapless charge-ordered liquid. Phys. Rev. B
**2006**, 74, 193107. [Google Scholar] [CrossRef] - Kuroki, K. The origin of the charge ordering and its relevance to superconductivity in θ-(BEDT-TTF)
_{2}X: The effect of the Fermi surface nesting and the distant electron-electron interactions. J. Phys. Soc. Jpn.**2006**, 75, 114716. [Google Scholar] [CrossRef] - Nishimoto, S.; Shingai, M.; Ohta, Y. Coexistence of distinct charge fluctuations in θ-(BEDT-TTF)
_{2}X. Phys. Rev. B**2008**, 78, 035113. [Google Scholar] [CrossRef] - Dressel, M.; Drichko, N.; Schlueter, J.; Merino, J. Proximity of the layered organic conductors α-(BEDT-TTF)
_{2}MHg(SCN)_{4}(M = K, NH_{4}) to a charge-ordering transition. Phys. Rev. Lett.**2003**, 90, 167002. [Google Scholar] [CrossRef] [PubMed] - Drichko, N.; Dressel, M.; Kuntscher, C.A.; Pashkin, A.; Greco, A.; Merino, J.; Schlueter, J. Electronic properties of correlated metals in the vicinity of a charge-order transition: Optical spectroscopy of α-(BEDT-TTF)
_{2}MHg(SCN)_{4}(M= NH_{4}, Rb, Tl). Phys. Rev. B**2006**, 74, 235121. [Google Scholar] [CrossRef] - Kaiser, S.; Dressel, M.; Sun, Y.; Greco, A.; Schlueter, J.A.; Gard, G.L.; Drichko, N. Bandwidth tuning triggers interplay of charge order and superconductivity in two-dimensional organic materials. Phys. Rev. Lett.
**2010**, 105, 206402. [Google Scholar] [CrossRef] - Clay, R.T.; Mazumdar, S.; Campbell, D.K. Charge ordering in θ-(BEDT-TTF)
_{2}X materials. J. Phys. Soc. Jpn.**2002**, 71, 1816–1819. [Google Scholar] [CrossRef] - Udagawa, M.; Motome, Y. Charge ordering and coexistence of charge fluctuations in quasi-two-dimensional organic conductors θ-(BEDT-TTF)
_{2}X. Phys. Rev. Lett.**2007**, 98, 206405. [Google Scholar] [CrossRef] - Yoshimi, K.; Maebashi, H. Coulomb frustrated phase separation in quasi-two-dimensional organic conductors on the verge of charge ordering. J. Phys. Soc. Jpn.
**2012**, 81, 063003. [Google Scholar] [CrossRef] - Naka, M.; Seo, H. Long-period charge correlations in charge-frustrated molecular θ-(BEDT-TTF)
_{2}X. J. Phys. Soc. Jpn.**2014**, 83, 053706. [Google Scholar] [CrossRef] - Pustogow, A.; Treptow, K.; Rohwer, A.; Saito, Y.; Alonso, M.S.; Lo¨hle, A.; Schlueter, J.A.; Dressel, M. Charge order in β
^{′′}-phase BEDT-TTF salts. Phys. Rev. B**2019**, 99, 155144. [Google Scholar] [CrossRef] - Wannier, H. Antiferromagnetism. The triangular Ising net. Phys. Rev.
**1950**, 79, 357–364. [Google Scholar] [CrossRef] - Houtappel, R.M.F. Order-disorder in hexagonal lattices. Physica
**1950**, 16, 425–455. [Google Scholar] [CrossRef] - Thomas, T.; Saito, Y.; Agarmani, Y.; Thyzel, T.; Hashimoto, K.; Sasaki, T.; Lang, M.; Müller, J. Involvement of structural dynamics in the charge-glass formation in molecular metals. Phys. Rev. B
**2022**, 105, L041114. [Google Scholar] [CrossRef] - Thomas, T.; Thyzel, T.; Sun, H.; Müller, J.; Hashimoto, K.; Sasaki, T.; Yamamoto, H.M. Comparison of the charge-crystal and charge-glass state in geometrically frustrated organic conductors studied by fluctuation spectroscopy. Phys. Rev. B
**2022**, 105, 205111. [Google Scholar] [CrossRef]

**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.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**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