Transient regime in non-linear transport through many-level quantum dots

TL;DR

This paper develops a numerical method to analyze nonstationary electronic transport in noninteracting quantum dot systems, revealing how transient currents evolve under various conditions without relying on common simplifying assumptions.

Contribution

It introduces a versatile approach using non-equilibrium Green-Keldysh formalism that handles strong lead coupling and arbitrary potentials, advancing the understanding of transient charge dynamics in quantum dots.

Findings

Transient current approaches steady state smoothly when higher energy levels are within the bias window.

Transient behavior exhibits step-like structures at moderate coupling, with step length increasing with system size.

Transient dynamics depend on the specific lead-system coupling configuration.

Abstract

We investigate the nonstationary electronic transport in noninteracting nanostructures driven by a finite bias and time-dependent signals applied at their contacts to the leads. The systems are modelled by a tight-binding Hamiltonian and the transient currents are computed from the non-equilibrium Green-Keldysh formalism. The numerical implementation is not restricted to weak coupling to the leads and does not imply the wide-band limit assumption for the spectral width of the leads. As an application of the method we study in detail the transient behavior and the charge dynamics in single and double quantum dots connected to leads by a step-like potential, but the method allows as well the consideration of non-periodic potentials or short pulses. We show that when the higher energy levels of the isolated system are located within the bias window of the leads the transient current approaches the steady state in a non-oscillatory smooth fashion. At moderate coupling to the leads and fixed bias the transient acquires a step-like structure, the length of the steps increasing with the system size. The number of levels inside a finite bias window can be tuned by a constant gate potential. We find also that the transient behavior depends on the specific way of coupling the leads to the mesoscopic system.