Threshold features in transport through a 1D constriction

TL;DR

This paper investigates how Umklapp electron-electron interactions affect electron current suppression in a 1D channel, revealing nonmonotonous conductance behavior due to Hubbard gaps and density deviations.

Contribution

It introduces a detailed analysis of transport in 1D constrictions considering Umklapp interactions and Hubbard gaps, highlighting the conditions for divergent or vanishing conductance.

Findings

Conductance exhibits nonmonotonous dependence on voltage and temperature.

Hubbard gaps induce divergence in current suppression near certain conditions.

Behavior depends on the relation between system length, charge velocity, and density deviations.

Abstract

Suppression of electron current $ \Delta I$ through a 1D channel of length $L$ connecting two Fermi liquid reservoirs is studied taking into account the Umklapp electron-electron interaction induced by a periodic potential. This interaction causes Hubbard gaps $E_H$ for $L \to \infty$. In the perturbative regime where $E_H \ll v_c/L$ ($v_c:$ charge velocity), and for small deviations $\delta n$ of the electron density from its commensurate values $- \Delta I/V$ can diverge with some exponent as voltage or temperature $V,T$ decreases above $E_c=max(v_c/L,v_c \delta n)$, while it goes to zero below $E_c$. This results in a nonmonotonous behavior of the conductance.