Voltage profile and four terminal resistance of an interacting quantum wire

TL;DR

This paper studies how interactions in a quantum wire affect four-terminal resistance, revealing power-law behaviors and conditions for negative resistance values in different impurity and probe asymmetry scenarios.

Contribution

It provides a detailed analysis of four-terminal resistance in interacting quantum wires, highlighting the influence of impurities and probe asymmetries on resistance behavior.

Findings

Interactions cause power-law dependence of resistance on voltage and temperature.

Asymmetries introduced by probes are masked by interactions.

Negative resistance values can occur under certain conditions.

Abstract

We investigate the behavior of the four-terminal resistance $R_{4pt}$ in a quantum wire described by a Luttinger liquid in two relevant situations: (i) in the presence of a single impurity within the wire and (ii) under the effect of asymmetries introduced by dirty voltage probes. In the first case, interactions leave a signature in a power law behavior of $R_{4pt}$ as a function of the voltage $V$ and the temperature $T$. In the second case interactions tend to mask the effect of the asymmetries. In both scenarios the occurrence of negative values of $R_{4pt}$ is explained in simple terms.