The time-dependent quantum transportation through a metal/polymer/metal system is theoretically investigated on the basis of a Su-Schrieffer-Heeger model combined with the hierarchical equations of motion formalism. Using a non-adiabatic dynamical method, the evolution of the electron subspace and lattice atoms with time can be obtained. It is found that the calculated transient currents vary with time and reach stable values after a response time under the bias voltages. However, the stable current as the system reaches its dynamical steady state exhibits a discrepancy between two sweep directions of the bias voltage, which results in pronounced electrical hysteresis loops in the current-voltage curve. By analyzing the evolution of instantaneous energy eigenstates, the occupation number of the instantaneous eigenstates, and the lattice of the polymer, we show that the formation of excitons and the delay of their annihilation are responsible for the hysteretic current-voltage characteristics, where electron-phonon interactions play the key factor. Furthermore, the hysteresis width and amplitude can also be modulated by the strength of the electron-phonon coupling, level-width broadening function, and temperature. We hope these results about past condition-dependent switching performance at a sweep voltage can provide further insight into some of the basic issues of interest in hysteresis processes in conducting polymers.
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