Controlling conductance statistics of quantum wires by driving ac fields

TL;DR

This paper investigates how time-dependent ac fields influence the conductance distribution of disordered quantum wires, revealing significant effects including a sharp cut-off at high frequencies and a log-normal distribution in strong localization.

Contribution

It introduces a combined Floquet and scaling approach to analyze conductance statistics under ac fields, extending understanding of quantum wire transport in dynamic conditions.

Findings

High-frequency ac fields cause a sharp cut-off in conductance distribution.

Conductance can be expressed as a product of frequency-dependent and disorder-dependent terms.

In strong localization, conductance distribution is log-normal.

Abstract

We calculate the entire distribution of the conductance P(G) of a one-dimensional disordered system --quantum wire-- subject to a time-dependent field. Our calculations are based on Floquet theory and a scaling approach to localization. Effects of the applied ac field on the conductance statistics can be strong and in some cases dramatic, as in the high-frequency regime where the conductance distribution shows a sharp cut-off. In this frequency regime, the conductance is written as a product of a frequency-dependent term and a field independent term, the latter containing the information on the disorder in the wire. We thus use the solution of the Mel'nikov equation for time-independent transport to calculate P(G) at any degree of disorder. At lower frequencies, it is found that the conductance distribution and the correlations of the transmission Floquet modes are described by a solution of the Dorokhov-Mello-Pereyra-Kumar equation with an effective number of channels. In the regime of strong localization, induced by the disorder or the ac field, P(G) is a log-normal distribution. Our theoretical results are verified numerically using a single-band Anderson Hamiltonian.