Energy exchange between phononic and electronic subsystems governing the nonlinear conduction in ${\mathrm{DCNQI}}_2\mathrm{Cu}$

We present a dynamical study on the nonlinear conduction behavior in the commensurate charge-density-wave phase of the quasi-one-dimensional conductor ${\mathrm{DCNQI}}_2\mathrm{Cu}$ below 75 K. We can accurately simulate magnitude and time dependence of the measured conductivity in response to large voltage pulses by accounting for the energy exchange between the phononic and electronic subsystems by means of an electrothermal model. Our simulations reveal a distinct nonequilibrium population of optical phonon states with an average energy of $\overline{E_{\text{ph}}}=19$ meV, being half the activation energy of about $\mathrm{\Delta }{E}_a=39$ meV observed in dc resistivity measurements. By inelastic scattering, this hot optical phonon bath generates additional charge-carrying excitations, thus providing a multiplication effect while energy transferred to the acoustic phonons is dissipated out of the system via heat conduction. Therefore, in high electric fields a preferred interaction of charge-carrying excitations with optical phonons compared to acoustic phonon modes is considered to be responsible for the nonlinear conduction effects observed in ${\mathrm{DCNQI}}_2\mathrm{Cu}$.

Figure 1

Illustration of the advanced electrothermal model based on Ref. [6]. Depending on the charge-carrier scattering rates, the electrical energy can be transferred to distinct microscopic subsystems of the material. An inefficient electron lattice scattering may lead to a direct excitation of charge carriers or hot electrons by the electric field. Due to their low contribution to the thermal conductivity, energy stored in the optical phonon system is available for excitation of additional charge carriers while energy in the acoustic phonon subsystem quickly dissipates out of the sample. Therefore, identification of the microscopic contributions to the effective specific heat, the latter governing the electrothermal model, allows for an understanding of the energy flow in the system in relation to the preferred charge-carrier scattering mechanism.

Figure 2

(a) Setup used for the transient resistance experiments. (b) Two-probe sample resistance during the cooling and the heating cycle plotted logarithmically against the inverse temperature. The linear fit yields an activation energy of $\mathrm{\Delta }E\approx$ 39 meV below the phase transition. The inset shows a microscope image of the sample. (c) Measured (dots) and simulated (solid lines) nonlinear current-voltage characteristics of (DCNQI-$d_6$)${}_2\mathrm{Cu}$ between 35 and 75 K in steps of 5 K. (d) Simulated temperature transients after applying a voltage pulse of 87 V to the crystal at $T_0=40$ K. The transient $P$ and $K$ terms [Eq. (3)] contributing to the temperature rise $dT/dt$ are illustrated separately.

Figure 3

(a) Measured (solid line) and simulated (dotted line) dynamic resistance response to voltage pulses of 56 and 97 V and sample temperature (dashed line) calculated from the measured resistance at $T_0=$ 40 K. At high voltages a kink is present in the measurement as well as in the simulations indicating when the phase transition temperature is reached. (b) Zoom-in on the initial temperature rise together with linear fits for different voltages. The slope $A_{\text{eff}}$ of the linear fit reveals a (c) $U^2$ dependence from which (d) the specific heat can be determined for each temperature measured. In addition to the literature data by Matsui et al. [13] and the expected acoustic phonon contribution, the fit of the effective Einstein model to our data is displayed.

Figure 4

Comparison of measured (solid lines) and simulated dynamic resistance response (a) to different voltage pulses at $T_0=40\text{K}$ and (b) at different temperatures utilizing a constant specific heat of $c_m=$ 55 J/(mol K) (dotted lines) and the effective Einstein model of the specific heat (dashed lines) as presented in Sec. 4b.