Coherent transport of interacting electrons through a single scatterer

TL;DR

This paper investigates how electron interactions affect transport properties in a one-dimensional system, revealing power-law decay behaviors in persistent current and conductance using Hartree-Fock calculations.

Contribution

It demonstrates the emergence of power-law decay in transport properties within a Hartree-Fock framework, previously observed only in correlated models.

Findings

Persistent current decays as L^{-1-α}

Conductance decays as L^{-2α}

Power laws observed in Hartree-Fock model

Abstract

Using the self-consistent Hartree-Fock method, we calculate the persistent current of weakly-interacting spinless electrons in a one-dimensional ring containing a single delta-barrier. We find that the persistent current decays with the system length (L) asymptotically like $I \propto L^{-1-\alpha}$, where $\alpha > 0$ is the power depending only on the electron-electron interaction. We also simulate tunneling of the weakly-interacting one-dimensional electron gas through a single delta-barrier in a finite wire biased by contacts. We find that the Landauer conductance decays with the system length asymptotically like $L^{-2\alpha}$. The power laws $L^{-1-\alpha}$ and $L^{-2\alpha}$ have so far been observed only in correlated models. Their existence in the Hartree-Fock model is thus surprising.