Geometrical effects and signal delay in time-dependent transport at the nanoscale

TL;DR

This paper studies how geometrical factors and signal delays influence time-dependent electron transport at the nanoscale, emphasizing non-Markovian effects and edge state propagation in magnetic fields.

Contribution

It introduces a comprehensive model incorporating non-Markovian dynamics and geometrical effects in nanoscale transport, using a generalized Master equation and tight-binding approach.

Findings

Transient currents are affected by the spectral structure of the sample.

Edge states dominate transport in strong magnetic fields.

Non-Markovian effects significantly influence transient dynamics.

Abstract

The nonstationary and steady-state transport through a mesoscopic sample connected to particle reservoirs via time-dependent barriers is investigated within the reduced density operator method. The generalized Master equation is solved via the Crank-Nicolson algorithm by taking into account the memory kernel which embodies the non-Markovian effects that are commonly disregarded. We propose a physically reasonable model for the lead-sample coupling which takes into account the match between the energy of the incident electrons and the levels of the isolated sample, as well as their overlap at the contacts. Using a tight-binding description of the system we investigate the effects induced in the transient current by the spectral structure of the sample and by the localization properties of its eigenfunctions. In strong magnetic fields the transient currents propagate along edge states. The behavior of populations and coherences is discussed, as well as their connection to the tunneling processes that are relevant for transport.