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Energy Exchange between Phononic and Electronic Subsystem Governing The Nonlinear Conduction in DCNQI$_2$Cu

We present a dynamical study on the nonlinear conduction behaviour in the commensurate charge-density-wave phase of the quasi-one-dimensional conductor DCNQI$_2$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 non-equilibrium population of optical phonon states with an average energy of E$_{ph}$ = 19 meV being half the activation energy of about $Δ$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 DCNQI$_2$Cu.