Tunneling of interacting fermions in 1D systems

TL;DR

This paper investigates how interacting spinless electrons tunnel through a delta barrier in a finite 1D wire, revealing universal power-law decay of conductance with wire length using a self-consistent Hartree-Fock approach.

Contribution

It demonstrates that the conductance decay in 1D interacting fermion systems follows a universal power law, connecting tunneling behavior to persistent current in a ring geometry.

Findings

Conductance decays as L^{-2α} with wire length.

Persistent current scales as L^{-1-α}.

Results align with correlated many-body models.

Abstract

Using the self-consistent Hartree-Fock approximation for spinless electrons at zero temperature, we study tunneling of the interacting electron gas through a single delta-barrier in a finite one-dimensional (1D) wire connected to contacts. Our results exhibit features known from correlated many-body models. In particular, the conductance decays with the wire length as $\propto L^{-2\alpha}$, where the power $\alpha$ is universal. We also show that a similar result for a wire conductance can be extracted from the persistent current (I) through the delta-barrier in a 1D ring, where it is known that I \propto L^{-1-\alpha}$.