Quantum master equation scheme of time-dependent density functional theory to time-dependent transport in nano-electronic devices

TL;DR

This paper presents a first-principles quantum transport scheme combining master equations with time-dependent density functional theory, enabling accurate simulation of nano-electronic device behavior under dynamic conditions.

Contribution

It introduces a practical, partitioning-free approach using non-Markovian master equations and Kohn-Sham formalism for time-dependent quantum transport simulations.

Findings

Successfully models time-dependent transport currents in nano-electronic devices.

Incorporates non-Markovian effects and time-dependent biases.

Provides a framework for first-principles simulations of quantum transport.

Abstract

In this work a practical scheme is developed for the first-principles study of time-dependent quantum transport. The basic idea is to combine the transport master-equation with the well-known time-dependent density functional theory. The key ingredients of this paper include: (i) the partitioning-free initial condition and the consideration of the time-dependent bias voltages which base our treatment on the Runge-Gross existence theorem; (ii) the non-Markovian master equation for the reduced (many-body) central system (i.e. the device); and (iii) the construction of Kohn-Sham master equation for the reduced single-particle density matrix, where a number of auxiliary functions are introduced and their equations of motion (EOM) are established based on the technique of spectral decomposition. As a result, starting with a well-defined initial state, the time-dependent transport current can be calculated simultaneously along the propagation of the Kohn-Sham master equation and the EOM of the auxiliary functions.