Application of hierarchical equations of motion to time dependent quantum transport

Abstract

Within the exact framework established recently, which is a successful marriage

between the time dependent density functional theory for open electronic system

and quantum dissipation theory formulated in the hierarchical equations of motion,

an entirely new scheme is proposed in this thesis to simulate the time-dependent

quantum transport in nano-devices at both zero and finite temperature equally

without relying on the pole structure of the Fermi distribution function. Neither

does it depend on any non-unique parametrization of the line-width matrix, hence,

this new practical approach can be integrated with the first principles simulations

seamlessly.

Beyond the exact framework, a reliable method which works under the Wide-

Band-Limit approximation at zero temperature is also developed. At the price of

loss of some non-Markovian memory effects on the dynamics, a set of equations

of motion which terminates at the first tier instead of the second tier is obtained.

Benefiting from the latest advancement of numerical analysis, a hybrid fourth-order

Runge-Kutta algorithm is proposed to solve this set of equations of motion which

comprises stiff ones. Based on this result, an alternative scheme is considered to

deal with the same approximation at finite temperature.

As an illustration of these new approaches, the transient current of the one

dimensional tight-binding periodical chain with and without a single impurity, driven

by some time alternating and/or static bias voltages, are investigated. The influence

of temperature and switch-on rate of bias voltage is exemplified. Particularly, in the

one dimensional tight-binding chain with a single impurity which breaks its perfect

periodicity, an asymmetry between the left and right transient current is found.

Comparison between the results under the Wide-Band-Limit approximation and

those with the exact description is carried out.