Time-dependent study of quantum transport and dissipation

Abstract

Dissipative time-dependent quantum transport theory with electron-phonon interaction in either weak or strong coupling regime is established. This theory goes beyond the conventional quantum master equation method and Kadanoff-Baym kinetic equations. It provides an efficient method for the simulation of transient quantum transport under arbitrary bias voltage with different electron-phonon coupling strength.

First, time-dependent quantum transport theory for non-interacting system and its combination with first-principles method is developed. Based on the Padé expansion to Fermi function, and wide-band limit approximation of lead self-energy, a set of equations of motion is developed for efficient evaluation of density matrix and related quantities. To demonstrate its applicability, this method is employed to study the transient transport through a carbon nanotube based electronic device.

Second, a dissipative time-dependent quantum transport theory is established in the weak electron-phonon coupling regime. In addition to the self-energy caused by leads, a new self-energy is introduced to characterize the dissipative effect induced by electron-phonon interaction. In the weak coupling regime, the lowest order expansion is employed for practical implementation. The corresponding closed set of equations of motion is derived, which provides an efficient and accurate treatment of transient quantum transport with electron-phonon interaction in the weak coupling regime. Numerical examples are demonstrated and its combination with first-principles method is also discussed.

Next, a dissipative quantum transport theory for strong electron-phonon interaction is established by employing small polaron transformation. The corresponding equation of motions are developed, which is used to study the quantum interference effect and phonon-induced decoherence dynamics. Numerical studies demonstrate the formation of quantum interference effect caused by the transport electrons through two quasi-degenerate states with different couplings to the leads. The quantum interference can be suppressed by phonon scattering, which indicates the importance of considering electron-phonon interaction in these systems with prominent quantum interference effect when the electron-phonon coupling is strong.

Last, the dissipative quantum transport theory for weak electron-phonon coupling regime is used to simulate the photovoltaic devices. Within the nonequilibrium Greens function formalism, a quantum mechanical method for nanostructured photovoltaic devices is presented. The method employs density-functional tight-binding theory for electronic structure, which make is possible to simulate the performance of photovoltaic devices without relying on empirical parameters. Numerical studies of silicon nanowirebased devices of realistic sizes with more than ten thousand atoms are performed and the results indicate that atomistic details and nonequilibrium conditions have clear impact on the photoresponse of the devices.