Electrically induced phase transition in $\alpha \text{−}{\left(\text{BEDT-TTF}\right)}_2{\mathrm{I}}_3$: Indications for Dirac-like hot charge carriers

The two-dimensional organic conductor $\alpha \text{−}{\left(\text{BEDT-TTF}\right)}_2{\mathrm{I}}_3$ undergoes a metal-insulator transition at $T_{\mathrm{CO}}=135\mathrm{K}$ due to electronic charge ordering. We have conducted time-resolved investigations of its electronic properties in order to explore the field- and temperature-dependent dynamics. At a certain threshold field, the system switches from a low-conducting to a high-conducting state, accompanied by a negative differential resistance. Our time-dependent infrared investigations indicate that close to $T_{\mathrm{CO}}$, the strong electric field pushes the crystal into a metallic state with optical properties similar to the one for $T>T_{\mathrm{CO}}$. Well into the insulating state, however, at $T=80\mathrm{K}$, the spectral response evidences a completely different electronically induced high-conducting state. Applying a two-state model of hot electrons explains the observations by excitation of charge carriers with a high mobility. They resemble the Dirac-like charge carriers with a linear dispersion of the electronic bands found in $\alpha \text{−}{\left(\text{BEDT-TTF}\right)}_2{\mathrm{I}}_3$ at high pressure. Extensive numerical simulations quantitatively reproduce our experimental findings in all details.

Figure 1

(a) Sketch of the bis-(ethylenedithio)tetrathiafulvalene molecule, called BEDT-TTF. (b) Drawing of the $\alpha \text{−}{\left(\text{BEDT-TTF}\right)}_2{\mathrm{I}}_3$ unit cell with orientation along the $c^{\prime }$ direction. The unit cell contains four BEDT-TTF and two ${\mathrm{I}}_3$ molecules. The cations are arranged in a herringbone-like structure within the $ab$ plane separated from each other along the $c^{\prime }$ direction by the anions. (c) Illustration of the development of the charge disproportionation and crystal symmetry in $\alpha \text{−}{\left(\text{BEDT-TTF}\right)}_2{\mathrm{I}}_3$ when cooling from room temperature to 0 K. The $ab$ plane is displayed with the four BEDT-TTF molecules labeled by A, B, and C; the anions are not included for clarity reasons. The A molecules are related to each other by a point inversion on their connecting line. The opacity of the green color represents the charge imbalance between the molecules. At $T=300\mathrm{K}$, there is an imbalance between molecules B and C. Below $T_{\mathrm{CO}}$, the point inversion is lost and the A molecules become inequivalent. A stripelike charge-order pattern develops along the $b$ direction.

Figure 2

(a) For time-dependent transport studies, a voltage pulse $U_S$ of some milliseconds duration is applied; the voltage drop $U_L$ across a load resistor measures the total current $I_{\mathrm{tot}}=U_L/R_L$. (b) Time dependence of the source voltage $U_S$ (blue lines) and drop $U_L$ across the load resistor (red curves) measured at $T=80\mathrm{K}$ along the $a$ direction of $\alpha \text{−}{\left(\text{BEDT-TTF}\right)}_2{\mathrm{I}}_3$. After a short switching pulse, a steady-state regime is reached for low voltages (dashed and dotted lines). Above a certain threshold field, however, the sample switches from a low-conducting, insulating state into a high-conducting state, which is marked by a steep increase of the current.

Figure 3

Contour plot of the time-dependent sample resistance of $\alpha \text{−}{\left(\text{BEDT-TTF}\right)}_2{\mathrm{I}}_3$ in a time frame of 10 ms for different electric fields $E_{\mathrm{sample}}$ recorded at (a) a temperature close to the charge-order transition, $T=125\mathrm{K}$, and (b) well below, $T=80\mathrm{K}$. The blue area corresponds to a metallic behavior (high conducting, HC), while the green to red areas indicate the insulating state (low conducting, LC). With increasing field, the delay time ${\tau }_d$ to enter the metallic state decreases. Note that in both frames different scales have been used for the applied field and for the observed resistance, respectively.

Figure 4

Current density $J$ as a function of the electric field $E_{\mathrm{sample}}$ recorded at a $\alpha \text{−}{\left(\text{BEDT-TTF}\right)}_2{\mathrm{I}}_3$ single crystal at different temperatures between $T=130$ and 80 K as indicated. At all temperatures, a negative differential regime is observed, where the threshold electric field increases with decreasing temperature.

Figure 5

(a) Temperature dependence of the threshold current density $J_{\mathrm{thresh}}$ (black, left axis) and threshold electric field $E_{\mathrm{thresh}}$ (red, right axis). (b) Power density $P_{\mathrm{thresh}}$ below the transition temperature $T_{\mathrm{CO}}$ of $\alpha \text{−}{\left(\text{BEDT-TTF}\right)}_2{\mathrm{I}}_3$. The green dotted lines are guides to the eye. The blue dashed vertical lines mark the metal-insulator transition temperature $T_{\mathrm{CO}}$.

Figure 6

Optical properties of $\alpha \text{−}{\left(\text{BEDT-TTF}\right)}_2{\mathrm{I}}_3$ for different temperatures as indicated. The upper panels (a) and (b) show the reflectivity for the polarization of the electric field $E\parallel a$ and $E\parallel b$. The corresponding optical conductivity is plotted in the lower panels (c) and (d); note the different vertical scales.

Figure 7

Difference of the optical reflectivity at $T=137\mathrm{K}$ (red), 130 K (orange), 120 K (blue), and 90 K (purple) with respect to the reflectivity at $T=80\mathrm{K}$. Panels (a) and (b) correspond to the polarizations $E\parallel a$ and $E\parallel b$, respectively.

Figure 8

Contour plot of the reflectivity change ${\mathrm{\Delta }}_{t}R(\nu ,t)$ along the (a) $a$ and (b) $b$ directions of $\alpha \text{−}{\left(\text{BEDT-TTF}\right)}_2{\mathrm{I}}_3$ at $T=125\mathrm{K}$ after applying an electric field of $E_{\mathrm{sample}}=216\mathrm{V}/\mathrm{cm}$ along the $a$ axis lasting for 10 ms. The dashed horizontal lines mark the onset and end of the voltage pulse, whereas the arrows mark the position where the spectra and the time slices were extracted from the frequency- and time-dependent spectrum, and they are displayed in Fig. 9. The vertical stripes in the spectrum are due to instabilities of the interferometer mirror during the step-scan run.

Figure 9

(a,b) Variation of the reflectivity ${\mathrm{\Delta }}_{t}R(\nu ,t)$ spectra of $\alpha \text{−}{\left(\text{BEDT-TTF}\right)}_2{\mathrm{I}}_3$ for different times at $T=125\mathrm{K}$. The data in the frequency range from $\nu =800$ to $3000{\mathrm{cm}}^{-1}$ are extracted from Fig. 8 for both polarizations (a) $E\parallel a$ and (b) $E\parallel b$. The lower panels display the time profile of the reflectivity $R(\nu ,t)$ taken at selected frequencies (c) $\nu =1000{\mathrm{cm}}^{-1}$ and (d) $1354{\mathrm{cm}}^{-1}$ between 0 and 20 ms. When the electric field is applied, $R(\nu ,t)$ increases only slightly and then remains constant in the high-conducting state. With a delay of a few milliseconds, the signal rises linearly until it saturates after the voltage pulse is switched off; the reflectivity then decays linearly. The vertical dotted lines mark the start and end points of the voltage pulse.

Figure 10

Contour plot of the reflectivity change ${\mathrm{\Delta }}_{t}R(\nu ,t)$ of $\alpha \text{−}{\left(\text{BEDT-TTF}\right)}_2{\mathrm{I}}_3$ for both polarizations at $T=80\mathrm{K}$ after applying an electric field of $E_{\mathrm{sample}}=2900\mathrm{V}/\mathrm{cm}$ along the $a$ axis lasting for 10 ms. The same color code is used as in Fig. 8. The dashed horizontal lines mark the onset and end of the voltage pulse, whereas the arrows mark the position where the spectra and the time slices were extracted from the frequency- and time-dependent spectrum, and they are displayed in Fig. 11.

Figure 11

(a,b) Variation of the reflectivity ${\mathrm{\Delta }}_{t}R(\nu ,t)$ spectra of $\alpha \text{−}{\left(\text{BEDT-TTF}\right)}_2{\mathrm{I}}_3$ for different times at $T=80\mathrm{K}$. The data in the frequency range from $\nu =800$ to $3000{\mathrm{cm}}^{-1}$ are extracted from Fig. 10 for both polarizations (a) $E\parallel a$ and (b) $E\parallel b$. The lower panels display the time profile of the reflectivity $R(\nu ,t)$ taken at selected frequencies (c) $\nu =1000{\mathrm{cm}}^{-1}$ and (d) $\nu =1354{\mathrm{cm}}^{-1}$ between 0 and 20 ms. When the electric field is applied, $R(\nu ,t)$ increases only slightly and then remains steady in the high-conducting state. With a delay of a few milliseconds, the signal rises linearly until it saturates after the voltage pulse is switched off; the reflectivity then decays linearly. The vertical dotted lines mark the start and end points of the voltage pulse.

Figure 12

Time evolution of the input power $P$ (red), the cooling power $K$ (blue), and the power absorbed by the electronic system (black) calculated for the temperature (a) $T=125\mathrm{K}$ and (b) $T=80\mathrm{K}$, where the applied electric field was $E_{\mathrm{sample}}=250$ and 3000 V/cm, respectively.

Figure 13

The electron temperature $T_e$ (solid lines) and the lattice temperature $T_L$ (dashed lines) plotted as a function of time for the two experimental temperatures $T=125\mathrm{K}$ (red) and $T=80\mathrm{K}$ (blue) by applying an external electric field of $E_{\mathrm{sample}}=250$ and 3000 V/cm, respectively.

Figure 14

Variation of the current density $J(E,t)$ with increasing electric field $E_{\mathrm{sample}}$ applied to the sample. Simulation for the temperature (a) $T=125\mathrm{K}$ and (b) $T=80\mathrm{K}$; note the different scales. The arrows indicate the delay time ${\tau }_d$. The low-conducting state (LC, blue area) is characterized by a small current density, while in the high-conducting part (HC, green-red) the current density is extremely high.

Figure 15

Simulated $J\text{−}E$ characteristic between 0 and 1900 V/cm from temperatures $T=130$ to 80 K. All curves exhibit a nonlinear regime with a negative differential resistance. Upon cooling, the threshold current decreases while the threshold electric field rises.

Figure 16

(a) Numerical simulations of the threshold electric field (red) and current density (black) as a function of temperature below $T_{\mathrm{CO}}$ using parameters for $\alpha \text{−}{\left(\text{BEDT-TTF}\right)}_2{\mathrm{I}}_3$. (b) Temperature dependence of the threshold power $P_{\mathrm{thesh}}$ determined from the product of $E_{\mathrm{thresh}}$ and $J_{\mathrm{thresh}}$. The vertical dotted line marks the phase-transition temperature of $T_{\mathrm{CO}}=135\mathrm{K}$.