Time-dependent quantum transport: an exact formulation based on TDDFT

TL;DR

This paper introduces an exact theoretical framework based on TDDFT for analyzing time-dependent quantum transport in fully interacting systems, capturing transient and steady-state phenomena with a focus on dephasing mechanisms.

Contribution

It presents a novel, exact formulation using TDDFT for time-dependent quantum transport, including interactions and a partition-free approach.

Findings

Steady-state current arises from a dephasing mechanism in macroscopic leads.

Derived a Landauer-like formula for steady-state current in the d.c. case.

Framework can handle transient phenomena and a.c. responses.

Abstract

An exact theoretical framework based on Time Dependent Density Functional Theory (TDDFT) is proposed in order to deal with the time-dependent quantum transport in fully interacting systems. We use a \textit{partition-free} approach by Cini in which the whole system is in equilibrium before an external electric field is switched on. Our theory includes the interactions between the leads and between the leads and the device. It is well suited for calculating measurable transient phenomena as well as a.c. and other time-dependent responses. We show that the steady-state current results from a \textit{dephasing mechanism} provided the leads are macroscopic and the device is finite. In the d.c. case, we obtain a Landauer-like formula when the effective potential of TDDFT is uniform deep inside the electrodes.