Out-of-equilibrium transport in a typical multi-terminal setup

TL;DR

This paper develops a comprehensive out-of-equilibrium framework for a three-terminal setup involving an injector and an inhomogeneous wire, revealing how injector effects influence scattering, interactions, and the local density of states, with implications for multi-terminal geometries.

Contribution

It introduces a general out-of-equilibrium approach for multi-terminal systems, analyzing the impact of injector-induced effects and deriving new scaling laws for backscattering processes.

Findings

Injector voltage does not suppress relevant scattering processes.

Grounded or semi-infinite wires at low temperature reach strong coupling fixed points.

Cross-correlations are negative and dominated by two-terminal geometry values.

Abstract

We develop a general out-of-equilibrium framework for a typical three-terminal setup of common use: an injector, which can be interacting, coupled by both extended tunneling and Coulomb interactions to an inhomogeneous wire with any range of interactions and scattering processes. Some of the crucial results we obtain are of relevance to other muti-terminal geometries. We show that the voltage of the injector does not cut the flow of relevant scattering processes in the wire. Either a grounded or a semi-infinite wire at too low temperature is driven into the strong coupling regime. We show that the injector induce invasive effects. They are due to non-local backscattering processes generated both by virtual higher order tunneling processes and by Coulomb interactions with the injector. The latter induce in addition screening of interactions in the wire. For an STM, those effects can drastically mask the probed density of states (DOS). In the limit of zero temperature, a long and grounded wire is driven to its fixed point where it is disconnected at the tunneling point. Thus instead of the bulk expected DOS, the STM probes the end one. We analyze current auto- and cross-correlations. We show that the cross-correlations are dominated by their value in the two-terminal geometry. As these are opposite to the current auto-correlations, they are always negative for local scattering processes. We give novel scaling laws to all orders with respect to a local backscattering.