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arXiv:cond-mat/0111417

Reply to Comment on ``Quantum Pump for Spin and Charge Transport in a Luttinger Liquid''

Prashant Sharma, Claudio Chamon

Published Nov 21, 2001• 0 citations
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Abstract

We show that Feldman and Gefen's comment revolves around a trivial issue - the relative magnitudes for the two crossover scales in the problem.
DOI
10.48550/arxiv.cond-mat/0111417

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We study the transport properties of a Luttinger liquid in the presence of several time-dependent weak pointlike impurities. Our starting point is the bosonized form of the Luttinger liquid Hamiltonian with a potential introduced by the impurities. We find the correction to the total current due to the backscattering of the electrons by the impurities in first order of perturbation theory for a general time-dependent impurity potential. We then apply this result to a single time-dependent impurity, and show that it reproduces the result obtained by Feldman and Gefen [Phys. Rev. B 67, 115337 (2003)], in particular that the current enhancement occurs only for strong repulsive electron-electron interactions. For the case of two impurities oscillating with the same frequency, we find that the dc component of the backscattering current is positive even for weak repulsive interactions, due to the presence of the interference term induced by spatial correlations in the Luttinger liquid. We show that the impurity frequencies at which the enhancement takes place form a bandlike structure. In the case of several impurities, the bands become broader, because of interference effects.
We study two different parametric pumps--one for pumping spin currents, the other for charge currents--in interacting quantum wires. We find that, as a function of pumping frequency, the spin or charge pumped per cycle has a nonuniversal crossover--depending on pumping details--between two universal fixed point values of 0 and twice the electronic spin or charge quantum number. The direction of flow between these two fixed points depends on whether the interactions are repulsive or attractive, while the quantization itself is a signature of interactions.