Mott metal-insulator transition induced by utilizing a glasslike structural ordering in low-dimensional molecular conductors

We utilize a glasslike structural transition in order to induce a Mott metal-insulator transition in the quasi-two-dimensional organic charge-transfer salt $\kappa -{\text{(BEDT-TTF)}}_2\mathrm{Cu}\left[\mathrm{N}{\text{(CN)}}_2\mathrm{Br}\right]$. In this material, the terminal ethylene groups of the BEDT-TTF molecules can adopt two different structural orientations within the crystal structure, namely eclipsed (E) and staggered (S) with the relative orientation of the outer C–C bonds being parallel and canted, respectively. These two conformations are thermally disordered at room temperature and undergo a glasslike ordering transition at $T_g\sim 75$ K. When cooling through $T_g$, a small fraction that depends on the cooling rate remains frozen in the S configuration, which is of slightly higher energy, corresponding to a controllable degree of structural disorder. We demonstrate that, when thermally coupled to a low-temperature heat bath, a pulsed heating current through the sample causes a very fast relaxation with cooling rates at $T_g$ of the order of several $1000 \mathrm{K}/\min$. The freezing of the structural degrees of freedom causes a decrease of the electronic bandwidth $W$ with increasing cooling rate, and hence a Mott metal-insulator transition as the system crosses the critical ratio ${(W/U)}_c$ of bandwidth to on-site Coulomb repulsion $U$. Due to the glassy character of the transition, the effect is persistent below $T_g$ and can be reversibly repeated by melting the frozen configuration upon warming above $T_g$. Both by exploiting the characteristics of slowly changing relaxation times close to this temperature and by controlling the heating power, the materials can be fine-tuned across the Mott transition. A simple model allows for an estimate of the energy difference between the E and S state as well as the accompanying degree of frozen disorder in the population of the two orientations.

Figure 1

(a) Phase diagram of $\kappa$-(ET)${}_{2}X$. The horizontal axis represents the substitution ratio $x$ for $\kappa -[(h-\mathrm{ET}{)}_{1-x}$($d$-ET)${}_x{\mathrm{]}}_2\mathrm{Cu}\left[\mathrm{N}{\text{(CN)}}_2\mathrm{Br}\right]$, and the corresponding hydrostatic pressure for $\kappa -{\text{(ET)}}_2\mathrm{Cu}\left[\mathrm{N}{\text{(CN)}}_2\right]\mathrm{Cl}$. Open circles indicate values taken from the literature of the second-order critical endpoint of the first-order Mott MIT (thick solid curve) in $\kappa -{\text{(ET)}}_2\mathrm{Cu}\left[\mathrm{N}{\text{(CN)}}_2\right]\mathrm{Cl}$, see [7] and references therein. The horizontal position also changes with the cooling rate employed at $T_g\simeq 75$–80 K. Colors indicate positions after different preparation conditions in this work. Yellow marks the pristine (slowly cooled) state. (b) Temperature dependence of the resistivity, $\rho$ vs $T$, of $\kappa -[(h-\mathrm{ET}{)}_{0.2}$($d-\mathrm{ET}{)}_{0.8}{\mathrm{]}}_2\mathrm{Cu}\left[\mathrm{N}{\text{(CN)}}_2\mathrm{Br}\right]$ for cooling rates ranging from 5-h annealing at 75 K (yellow) to $q=1$, 2, 5, 10, and 32 $\mathrm{K}/\min$ (red). Vertical arrows indicate the possibility of reaching an insulating state (thick green line) after applying a voltage pulse $V$ at different temperatures. Intermediate states have been realized by relaxing the system at 75 K for $\sim 10$ min and subsequent cooling (green to blue). Inset shows a discrete ${\rho }_n$ vs $V$ measurement (sketched voltage-pulse sequence with $t=2$ s and $t_{\mathrm{w}}=20$ s is explained in the text) at $T=20$ K (compare violet arrow).

Figure 2

Resistance (two-wire) vs temperature (black circles) and resistance vs heating power (orange squares) measurements (see sketch and text) of $\kappa -{\text{(ET)}}_2\mathrm{Cu}\left[\mathrm{N}{\text{(CN)}}_2\mathrm{Br}\right]$. The power can be linked to the temperature axis by the sketched simple model of heat conduction with $T=P/\lambda +T_{\mathrm{bath}}$. The inset shows the sample temperature vs time after switching of a voltage pulse (5 V applied for 10 s), which was extracted using the sample resistance as a reference (see text). Red curve is a fit to the sketched model with $T=T_{0}exp(-\lambda /C·t)+T_{\mathrm{bath}}$.

Figure 3

Temperature-dependent occupation probability $p_{\mathrm{E}}\left(T\right)$, resulting from the general model of Eq. (5), for the favored eclipsed (E) conformation of the ET molecules' EEG for different cooling rates. “Pulse rate” refers to cooling after a heat pulse is applied as shown in Fig. 2 (inset). Faster cooling rates cause the system to fall out of thermal equilibrium at higher temperatures and the relaxation times (${\tau }_1$ and ${\tau }_2$ in the double-well potential) become too large to be observed for temperatures $T<T_g$ resulting in a frozen-in distribution of EEG conformations.