Four-terminal resistance of an interacting quantum wire with weakly invasive contacts

TL;DR

This paper investigates how impurities, electron interactions, and invasive voltage probes influence the four-terminal resistance in an interacting quantum wire, revealing conditions for negative resistance phenomena.

Contribution

It introduces a perturbative analysis of invasive voltage probes in a Luttinger liquid model, highlighting their impact on resistance measurements in quantum wires.

Findings

Invasive probes can induce negative resistance effects.

Electron interactions significantly modify resistance behavior.

Impurities combined with invasiveness lead to complex resistance phenomena.

Abstract

We analyze the behavior of the four-terminal resistance, relative to the two-terminal resistance of an interacting quantum wire with an impurity, taking into account the invasiveness of the voltage probes. We consider a one-dimensional Luttinger model of spinless fermions for the wire. We treat the coupling to the voltage probes perturbatively, within the framework of non-equilibrium Green function techniques. Our investigation unveils the combined effect of impurities, electron-electron interactions and invasiveness of the probes on the possible occurrence of negative resistance.