Electron tunneling into a quantum wire in the Fabry-Perot regime

TL;DR

This paper investigates how a third terminal affects electron transport in a quantum wire in the Fabry-Perot regime, revealing complex behaviors influenced by interactions, asymmetry, and finite length, with implications for experimental studies of Luttinger liquids.

Contribution

It introduces a detailed analysis of a three-terminal quantum wire system, highlighting the impact of a tip on transport properties and the role of electron interactions in finite-length wires.

Findings

Tip as a voltage probe suppresses conductance and modulates oscillations.

Electron interactions cause observable oscillations in non-linear conductances.

Asymmetry in electron injection does not directly reveal charge fractionalization.

Abstract

We study a gated quantum wire contacted to source and drain electrodes in the Fabry-Perot regime. The wire is also coupled to a third terminal (tip), and we allow for an asymmetry of the tip tunneling amplitudes of right and left moving electrons. We analyze configurations where the tip acts as an electron injector or as a voltage-probe, and show that the transport properties of this three-terminal set-up exhibit very rich physical behavior. For a non-interacting wire we find that a tip in the voltage-probe configuration affects the source-drain transport in different ways, namely by suppressing the conductance, by modulating the Fabry-Perot oscillations, and by reducing their visibility. The combined effect of electron electron interaction and finite length of the wire, accounted for by the inhomogeneous Luttinger liquid model, leads to significantly modified predictions as compared to models based on infinite wires. We show that when the tip injects electrons asymmetrically the charge fractionalization induced by interaction cannot be inferred from the asymmetry of the currents flowing in source and drain. Nevertheless interaction effects are visible as oscillations in the non-linear tip-source and tip-drain conductances. Important differences with respect to a two-terminal set-up emerge, suggesting new strategies for the experimental investigation of Luttinger liquid behavior.