Nonlinear transport through a dynamic impurity in a strongly interacting one-dimensional electron gas

TL;DR

This paper investigates the nonlinear transport behavior of a strongly interacting one-dimensional electron system with a time-dependent impurity, providing exact and perturbative analytic solutions that reveal complex current-voltage characteristics and conductance enhancements.

Contribution

It offers the first full analytic solutions for a dynamic impurity in a Luttinger liquid, including special interaction cases, advancing understanding of nonlinear transport in such systems.

Findings

Nonlinear current-voltage characteristics are influenced by impurity oscillation frequency.

Analytic solutions are obtained for arbitrary interaction parameters and specific special cases.

Linear conductance can exceed the unitary limit of 2e^2/h due to impurity effects.

Abstract

We analyze the transport properties of a Luttinger liquid with an imbedded impurity of explicitly time-dependent strength. We employ a radiative boundary condition formalism to describe the coupling to the voltage sources. Assuming the impurity time dependence to be oscillatory we present a full analytic perturbative result in impurity strength for arbitrary interaction parameter calculated with help of Coulomb gas expansion (CGE). Moreover, a full analytic solution beyond the above restriction is possible for a special non-trivial interaction strength which has been achieved independently by full resummation of CGE series as well as via refermionization technique. The resulting nonlinear current-voltage characteristic turns out to be very rich due to the presence of the additional energy scale associated with the impurity oscillation frequency. In accordance with the previous studies we also find an enhancement of the linear conductance of the wire to values above the unitary limit G0 = 2e2/h.