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

We study a gated quantum wire contacted to source and drain electrodes in the Fabry-Pérot regime. The wire is also coupled to a third terminal (tip), and we allow for an asymmetry of the tip tunneling amplitudes of right-moving 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 setup exhibit very rich physical behavior. For a noninteracting 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-Pérot 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 nonlinear tip-source and tip-drain conductances. Important differences with respect to a two-terminal setup emerge, suggesting new strategies for the experimental investigation of Luttinger liquid behavior.