arXiv:cond-mat/0104558

Can backscattering off an impurity enhance the current?

Dima E. Feldman, Yuval Gefen

Published Apr 28, 2001• 0 citations

Abstract

It is well known that while forward scattering has no effect on the conductance of one-dimensional systems, backscattering off a static impurity suppresses the current. We study the effect of a time-dependent point impurity on the conductance of a one-channel quantum wire. At strong repulsive interaction (Luttinger liquid parameter g<1/2), backscattering renders the conductance greater than its value e^2/h in the absence of the impurity. A possible experimental realization of our model is a constricted Hall bar at fractional filling factors ν=1/(2n+1) with a time-dependent voltage at the constriction.

DOI: 10.48550/arxiv.cond-mat/0104558

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arXiv:cond-mat/0104558

Can backscattering off an impurity enhance the current?

Dima E. Feldman, Yuval Gefen

Published Apr 28, 2001• 0 citations

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.cond-mat/0104558

Related papers

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V

. The dc contribution of the backscattered current oscillates as a function of impurity frequency with the period depending on the Luttinger interaction strength. Furthermore, the oscillation of the dc contribution of the backscattered current is not a finite-length effect, which is different from that in the case of system with a static point impurity, and the oscillation characteristic is also connected with

V

. However, the final current-noise relation is similar to that in the case of a static point impurity.

(>1)

the switching process is relevant (irrelevant). Our results suggest the possibility of determining the value of the Luttinger parameter

K

through time measurements in transport experiments at fixed voltage.

(g=1)

by a rectangularlike barrier and find an exact solution for the backscattering current, as well as a perturbative solution for a weak static potential with an arbitrary shape. We then include electron-electron interactions and use the Keldysh formalism combined with the bosonization technique to study oscillating extended barriers. We show that the backscattering current off time-dependent impurities can be expressed in terms of the current for the corresponding static barrier. Then we determine the backscattering current for a static extended potential, which, in the limit of noninteracting electrons

(g=1)

, coincides with the result obtained using the B\"uttiker-Landauer formalism. In particular, we find that the conductance can be increased beyond its quantized value in the whole range of repulsive interactions

0<g<1

already in the case of a single oscillating extended impurity, in contrast to the case of a pointlike impurity, where this phenomenon occurs only for

0<g<1∕2

{v}_{F}∕gL

, where

{v}_{F}

is the Fermi velocity,

g

the Tomonaga-Luttinger interaction parameter, and

L

the length of the wire. The interplay of finite bias, finite temperature, and finite length yields rich structure in the noise spectrum which crucially depends on the electron-electron interaction. In particular, the excess noise, defined as the change of the noise due to the applied voltage, can become negative and is nonvanishing even for noise frequencies larger than the applied voltage, which are signatures of correlation effects.