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

Abstract

Suppression of electron current $ ΔI$ 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 $δn$ of the electron density from its commensurate values $- ΔI/V$ can diverge with some exponent as voltage or temperature $V,T$ decreases above $E_c=max(v_c/L,v_c δn)$, 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 $V,T < T_L exp(-2m/T_L)$.