Kadanoff-Baym approach to time-dependent quantum transport in AC and DC fields

TL;DR

This paper develops a Kadanoff-Baym based method to study the real-time evolution of open, inhomogeneous quantum systems under AC and DC fields, capturing conservation laws and initial correlations, with applications to correlated chains and leads.

Contribution

The authors introduce a conserving Green's function approach using Kadanoff-Baym equations for time-dependent quantum transport, including initial correlations and embedding effects, applicable to arbitrary external fields.

Findings

Self-consistent 2B and GW approximations agree well over time.

HOMO-LUMO transition dominates transient oscillations in DC bias.

Harmonic generation depends on bias symmetry, with strong HOMO-LUMO mixing.

Abstract

We have developed a method based on the embedded Kadanoff-Baym equations to study the time evolution of open and inhomogeneous systems. The equation of motion for the Green's function on the Keldysh contour is solved using different conserving many-body approximations for the self-energy. Our formulation incorporates basic conservation laws, such as particle conservation, and includes both initial correlations and initial embedding effects, without restrictions on the time-dependence of the external driving field. We present results for the time-dependent density, current and dipole moment for a correlated tight binding chain connected to one-dimensional non-interacting leads exposed to DC and AC biases of various forms. We find that the self-consistent 2B and GW approximations are in extremely good agreement with each other at all times, for the long-range interactions that we consider. In the DC case we show that the oscillations in the transients can be understood from interchain and lead-chain transitions in the system and find that the dominant frequency corresponds to the HOMO-LUMO transition of the central wire. For AC biases with odd inversion symmetry odd harmonics to high harmonic order in the driving frequency are observed in the dipole moment, whereas for asymmetric applied bias also even harmonics have considerable intensity. In both cases we find that the HOMO-LUMO transition strongly mixes with the harmonics leading to harmonic peaks with enhanced intensity at the HOMO-LUMO transition energy.