Umklapp scattering in transport through a 1D wire of finite length

TL;DR

This paper investigates how Umklapp scattering affects electron transport in a finite 1D wire, revealing non-monotonous conductance behavior and conditions for transport suppression near band gaps and Mott-Hubbard gaps.

Contribution

It provides a detailed analysis of Umklapp interactions in finite 1D wires, highlighting their impact on conductance and the conditions for transport suppression at various fillings.

Findings

Conductance exhibits non-monotonous behavior near band gaps.

Transport is suppressed near half-filling when a large Mott-Hubbard gap exists.

Suppression of current occurs except in exponentially small regions at low temperature and voltage.

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 interaction induced by a periodic potential. This interaction opens band gaps at the integer fillings and Hubbard gaps $2m$ at some rational fillings in the infinite wire: $L \to \infty$. In the perturbative regime where $m \ll v_c/L$ ($v_c:$ 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 non-monotonous behavior of the conductance. In the case when the Umklapp interaction creates a large Mott-Hubbard gap $2m \gg T_L $ inside the wire, the transport is suppressed near half-filling everywhere inside the gap except for an exponentially small region of $V,T < T_L exp(-2m/T_L)$.