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Crystallization and vitrification of electrons in a glass-forming charge liquid

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Science  29 Sep 2017:
Vol. 357, Issue 6358, pp. 1381-1385
DOI: 10.1126/science.aal3120
  • Fig. 1 Charge crystallization and vitrification in θm-(BEDT-TTF)2TlZn(SCN)4.

    (A) Generic entropy-temperature diagram of a glass-forming liquid. Tm is the melting temperature, Tg is the glass transition temperature, and TX is the crystallization temperature. A supercooled liquid state emerges when the liquid is cooled quickly enough to avoid crystallization. Slower and faster heating processes (1 and 2) lead to lower and higher crystallization temperatures (TX1 and TX2). (B) Temperature dependence of the resistivity for θm-TlZn measured in the rapid or slow heating process (after rapid or slow cooling) and in the rapid cooling process. Curves are color-coded. Charge crystallization occurs at TX, which is lower than Tg, in the slow heating process after rapid cooling. Inset: Hysteresis loop of the resistivity during the heating/cooling process at a sweeping rate of 100 K/min. (C to E) Illustrations of the charge-liquid state (C), the charge-crystal state (D), and the charge-glass state (E) in θm-TlZn. The orange lines in (C) and (D) denote the unit cell. At the CO transition, the monoclinic unit cell is reduced to a triclinic cell (16). V1 and V2 are the nearest-neighbor Coulomb interactions, where V2/V1 ~ 0.8 (see also fig. S1D). The A and B sites in (C) are crystallographically equivalent, owing to the screw axis along the b axis. In the charge-crystal state (D), a diagonal CO pattern is formed, where the charge-rich (+0.85) sites, A and A′, and the charge-poor (+0.15) sites, B and B′, are not crystallographically equivalent. The difference in the charge density between A and A′ (and between B and B′) is too small to be detected experimentally (16).

  • Fig. 2 Noise spectroscopy, optical conductivity, and x-ray diffuse scattering measurements in the charge-crystal, charge-liquid, and charge-glass states.

    (A) Typical normalized resistance noise power spectral density at 185 K. The red line indicates a fit to a background SR/R2 ∝ 1/fα with α = 0.9. (B) Power spectral density multiplied by fα at various temperatures above Tm. The black solid curves represent fits to the distributed Lorentzian model (11, 12) with a characteristic center frequency fc = Embedded Image, where fc1 and fc2 are the high- and low-frequency cutoffs, respectively. The dashed lines are guides to the eye. (C) Temperature dependence of the cutoff frequencies fc1 and fc2. The dashed lines are guides to the eye. (D) Arrhenius plot of the relaxation time τc = 1/(2πfc) derived from the power spectral density. The diagonal dashed line is a fit to the Arrhenius law, τ0 exp(Δ/kBT), where τ0 = 10–14 s and Δ/kB = 5200 K. The gap size Δ corresponds to the energy scale of barriers in an energy landscape (Fig. 3B). The charge crystallization process prevents measurements in the supercooled charge-liquid state (gray shaded area). (E) Sketch of the infrared active vibrational mode v27 of the BEDT-TTF molecule. The center frequency can be expressed as v27c) = 1398 cm−1 + 140(1 – ρc) cm−1 (21). The components coming from charge-rich (v27I) and charge-poor (v27N) sites are observed at 1420 cm−1 and 1515 cm−1, respectively (25). (F) Temperature dependence of the v27I mode measured during slow cooling (solid lines) and slow heating after rapid cooling (dashed lines). (G) Temperature dependence of the v27I mode intensity. An upturn observed above ~120 K during slow heating after rapid cooling is attributed to charge crystallization. (H and I) Oscillation photographs of the b*-c* plane measured at 100 K after slow cooling (H) and rapid cooling (I). In the charge-crystal state (H), clear satellite peaks appear at q0 = Embedded Image. By contrast, in the charge-glass state (I), diffuse lines of qd = Embedded Image are observed. (J and K) Oscillation photographs of the b*-c* plane measured at 171 K and 290 K, respectively. At room temperature, only Bragg reflections exist. In contrast, diffuse lines at qd = Embedded Image are observed above Tm. The blue arrows in (I) and (J) indicate the diffuse lines.

  • Fig. 3 Semimacroscopic degeneracy of striped CO patterns and energy landscape.

    (A) Schematics of various striped CO patterns. The magenta circles represent the charge-rich sites. V1 and V2 (V1 > V2) are the nearest-neighbor Coulomb interactions. Because 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, which has a degeneracy of Embedded Image, where Lc is the system length in the c direction. (B) Illustration of an energy landscape with multiple local minima separated by barriers having an energy scale of the hopping integral thopping and/or the long-range Coulomb interaction V, which are on the order of ~1 eV.

  • Fig. 4 Derivation of the time-temperature-transformation (TTT) diagram of θm-(BEDT-TTF)2TlZn(SCN)4.

    (A) Time-dependent resistivity change during the charge crystallization process, measured at various temperatures. (B and C) Time evolution of the CO volume fraction ϕ(t) calculated from the data in (A) using the effective medium percolation theory. Shown are the evolutions above (B) and below (C) the nose temperature. (D to F) ϕ(t) at 165 K, 157 K, and 130 K, respectively. Also shown in (D) to (F) are fits by the JMAK formula, ϕ(t) = 1 – exp(–ktn), where k and n are the JMAK parameters, and the Ostwald ripening process, ϕ(t) = 1 – (1 + kt)–1/3, where k′ is a constant. (G) TTT diagram derived from ϕ(t) in (B) and (C). The dotted curve connects the data points where ϕ(t) = 0.95.

Supplementary Materials

  • Crystallization and vitrification of electrons in a glass-forming charge liquid

    S. Sasaki, K. Hashimoto, R. Kobayashi, K. Itoh, S. Iguchi, Y. Nishio, Y. Ikemoto, T. Moriwaki, N. Yoneyama, M. Watanabe, A. Ueda, H. Mori, K. Kobayashi, R. Kumai, Y. Murakami, J. MuÌ^ller, T. Sasaki

    Materials/Methods, Supplementary Text, Tables, Figures, and/or References

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    • Materials and Methods
    • Supplementary Text
    • Figs. S1 to S7
    • References

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