Transport in a Luttinger liquid with dissipation: two impurities

TL;DR

This paper theoretically analyzes how dissipation affects electron transport in a one-dimensional Luttinger liquid with two impurities, revealing a complex conductance behavior influenced by dissipation strength, voltage, temperature, and interaction parameters.

Contribution

It introduces a detailed theoretical model showing how dissipation prevents full electron transmission and alters conductance behavior in a two-impurity Luttinger liquid system.

Findings

Dissipation prevents complete electron transmission at resonance.

Conductance exhibits non-monotonic behavior for weak dissipation and 1/2<K<1.

Strong dissipation leads to exponentially small, monotonically increasing conductance.

Abstract

We consider theoretically the transport in a one-channel spinless Luttinger liquid with two strong impurities in the presence of dissipation. As a difference with respect to the dissipation free case, where the two impurities fully transmit electrons at resonance points, the dissipation prevents complete transmission in the present situation. A rich crossover diagram for the conductance as a function of applied voltage, temperature, dissipation strength, Luttinger liquid parameter K and the deviation from the resonance condition is obtained. For weak dissipation and 1/2<K<1, the conduction shows a non-monotonic increase as a function of temperature or voltage. For strong dissipation the conduction increases monotonically but is exponentially small.