Charge transport in a Tomonaga-Luttinger liquid: effects of pumping and bias

TL;DR

This paper investigates how bias and time-dependent impurities influence charge transport in a Tomonaga-Luttinger liquid, revealing power-law behaviors and interaction-dependent effects using bosonization.

Contribution

It provides a perturbative analysis of current in a Luttinger liquid under bias and oscillating impurities, including extended impurities and spin effects.

Findings

Current exhibits power-law dependence on bias and frequency with exponent 2K - 1.

For K < 1/2, the current is enhanced at specific bias values.

Results agree with Floquet scattering theory for non-interacting electrons (K=1).

Abstract

We study the current produced in a Tomonaga-Luttinger liquid by an applied bias and by weak, point-like impurity potentials which are oscillating in time. We use bosonization to perturbatively calculate the current up to second order in the impurity potentials. In the regime of small bias and low pumping frequency, both the DC and AC components of the current have power law dependences on the bias and pumping frequencies with an exponent 2K - 1 for spinless electrons, where K is the interaction parameter. For K < 1/2, the current becomes large for special values of the bias. For non-interacting electrons with K = 1, our results agree with those obtained using Floquet scattering theory for Dirac fermions. We also discuss the cases of extended impurities and of spin-1/2 electrons.