Highly nonlinear current-voltage characteristics of the organic Mott insulator $\kappa$-(BEDT-TTF)${}_2$Cu[N(CN)${}_2$]Cl

The organic Mott insulator $\kappa$-(BEDT-TTF)${}_2$Cu[N(CN)${}_2$]Cl exhibits highly nonlinear current-voltage characteristics in a low current range at temperatures below $\approx$10 K. The nonlinear current-voltage characteristics are similar to those observed in the charge-ordered organic crystals $\theta$-(BEDT-TTF)${}_2$$M$Zn(SCN)${}_4$ ($M$ = Cs and Rb) and are accounted for in the same way in terms of exciton excitations: The electric field assists the thermal unbinding of pairs of a doublon and a holon that attract each other due to the two-dimensional long-range Coulomb interaction. Dielectric properties are understood within the context of the same model in terms of polarization of the bound pairs. $\kappa$-(BEDT-TTF)${}_2$Cu[N(CN)${}_2$]Cl has a smaller magnetoconductance than $\theta$-(BEDT-TTF)${}_2$$M$Zn(SCN)${}_4$ ($M$ = Cs and Rb), which probably reflects different spin states of the excitations for the Mott and charge-ordered states.

Figure 1

Temperature dependence of the in-plane low-bias conductance of $\kappa$-(BEDT-TTF)${}_2$Cu[N(CN)${}_2$]Cl. The electrode spacing $L\approx 5$ $\mu$m.

Figure 2

In-plane $I-V$ curves of $\kappa$-(BEDT-TTF)${}_2$Cu[N(CN)${}_2$]Cl. $T=$ 29.8, 19.9, 17.9, 15.9, 14.9, 13.9, 12.9, 11.9, 11.0, 10.0, 8.98, 7.99, 7.00, 6.01, 5.02, 4.02, 3.01, 2.00, 1.19, 0.61, 0.31 K from top left to bottom right. Data obtained for increasing and decreasing voltage are shown for each temperature. The electrode spacing $L\approx 5$ $\mu$m.

Figure 3

In-plane $I-V$ curves of the $\kappa$-(BEDT-TTF)${}_2$Cu[N(CN)${}_2$]Cl measured using two- and four-point configurations at $T=0.32$ K.

Figure 4

Calculated $I-V$ curves for $\kappa$-(BEDT-TTF)${}_2$Cu[N(CN)${}_2$]Cl (see text). $T=$ 29.8, 19.9, 17.9, 15.9, 14.9, 13.9, 12.9, 11.9, 11.0, 10.0, 8.98, 7.99, 7.00, 6.01, 5.02, 4.02 K from top left to bottom right.

Figure 5

Coulomb energy vs distance $r$. (a) Coulomb energy in vacuum, $e^2/\left(4\pi {\epsilon }_{0}r\right)$. (b) Coulomb energy in a metal, $e^2\exp [-r/r_s]/\left(4\pi {\epsilon }_{0}r\right)$; $r_s=0.055$ nm for Cu[18]. (c) Coulomb energy in a dielectric material, $e^2/\left(4\pi \epsilon r\right)$, $\epsilon =5{\epsilon }_0$. (d) Coulomb energy used to calculate the $I-V$ curves in Fig. 4 and the dielectric constant in Fig. 8.

Figure 6

Temperature dependence of the in-plane relative dielectric constant of $\kappa$-(BEDT-TTF)${}_2$Cu[N(CN)${}_2$]Cl at different frequencies. The curve indicated as CB was measured using the capacitance bridge, while the others were measured using the LCR meter. The ac excitation voltage was 100 mV${}_{\mathrm{rms}}$. The spacing and area of electrodes were 250 $\mu$m and $1.9\times {10}^4$ $\mu {\mathrm{m}}^2$.

Figure 7

Temperature dependence of the dissipation factor, tan($\delta$), of $\kappa$-(BEDT-TTF)${}_2$Cu[N(CN)${}_2$]Cl at different frequencies. The curve indicated as CB was measured using the capacitance bridge, while the others were measured using the LCR meter. The data were obtained at the same time as those in Fig. 6.

Figure 8

Temperature dependence of the in-plane relative dielectric constant calculated using Eq. (1). The parameter values of the logarithmic potential used for the calculation are the same as those that account for the nonlinear $I-V$ curves.

Figure 9

(a)–(c) Magnetic field dependence of current measured while voltage was kept constant in $\kappa$-(BEDT-TTF)${}_2$Cu[N(CN)${}_2$]Cl. The current is normalized to the value obtained in zero magnetic field at each temperature. The voltage was applied along an in-plane direction and the magnetic field was applied along the out-of-plane direction. (d) The temperature dependence of the current at $B=17.5$ T normalized to the value obtained at $B=0$.

Figure 10

Magnetic field dependence of current measured while voltage was kept constant in $\kappa$-(BEDT-TTF)${}_2$Cu[N(CN)${}_2$]Cl for the in-plane and out-of-plane magnetic fields at 1.4 K (a) and 10 K (b). The voltage was applied along an in-plane direction. The data for $B$//($a-c$ plane) are offset by $-$0.02 (a) and $-$0.01 (b) for clarity.