Non-equilibrium current and electron pumping in nanostructures

TL;DR

This paper introduces a numerical method for studying non-equilibrium electron transport in mesoscopic systems, enabling efficient simulation of large-scale devices with time-dependent conditions and revealing long-lived transient behaviors.

Contribution

The paper presents a novel operator equation of motion approach using Chebyshev time propagation, allowing scalable simulations of non-interacting electron transport in complex nanostructures.

Findings

Long-lived transient behaviors observed in electron pump and disordered systems

Method scales linearly with system size, enabling large-scale simulations

Transient effects may be experimentally accessible

Abstract

We discuss a numerical method to study electron transport in mesoscopic devices out of equilibrium. The method is based on the solution of operator equations of motion, using efficient Chebyshev time propagation techniques. Its peculiar feature is the propagation of operators backwards in time. In this way the resource consumption scales linearly with the number of states used to represent the system. This allows us to calculate the current for non-interacting electrons in large one-, two- and three-dimensional lead-device configurations with time-dependent voltages or potentials. We discuss the technical aspects of the method and present results for an electron pump device and a disordered system, where we find transient behaviour that exists for a very long time and may be accessible to experiments.