Wavepacket basis for time-dependent processes and its application to relaxation in resonant electronic transport

TL;DR

This paper introduces a wavepacket basis tailored for time-dependent processes in extended systems and applies it to analyze relaxation dynamics in resonant electronic transport, revealing how energy structure influences transient behavior.

Contribution

It develops a formalism for a wavepacket basis in extended systems and demonstrates its application to time-dependent electronic transport phenomena.

Findings

Time scales in relaxation are linked to the energetic structure of the resonant barrier.

The generalized Landauer formula captures the temporal evolution of transport.

The basis facilitates semi-analytical analysis of transient electronic processes.

Abstract

Stroboscopic wavepacket basis sets [P. Bokes, F. Corsetti, R. W. Godby, Phys. Rev. Lett. 101, 046402 (2008)] are specifically tailored for a description of time-dependent processes in extended systems like non-periodic geometries of various contacts consisting of solids and molecules. The explanation of the construction of such a basis for two simple finite systems is followed by a review of the general theory for extended systems with continuous spectrum. The latter is further elaborated with the introduction of the interaction representation which takes the full advantage of the time-dynamics built into the basis. The formalism is applied to a semi-analytical example of electronic transport through resonant tunnelling barrier in 1D. Through the time-dependent generalisation of the Landauer formula given in terms of the Fourier expansion of the transmission amplitude we analyze the temporal character of the onset of the steady-state. Various time-scales in this process are shown to be directly related to the energetic structure of the resonant barrier.