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

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

1999-07-05

arxiv.org/abs/cond-mat/9907072v1

Physics

Condensed Matter

to appear in "Highlights in Condensed Matter Physics", proceedings of the APCTP/ICTP Joint International Conference, June 1998

Scientific paper

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 $V,T < T_L exp(-2m/T_L)$.

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