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

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 $V,T<T_{L}exp(-2m/T_L)$.

to appear in "Highlights in Condensed Matter Physics", proceedings of the APCTP/ICTP Joint International Conference, June 1998, Seoul, Y.M. Cho and M. Virasoro eds, World Scientific (Singapore); 10 twocolumn pages in RevTex, 4 figures included