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arXiv:cond-mat/9707161 · Physical Review Letters

Oreg and Finkel'stein Reply:

Yuval Oreg, Alexander M. Finkel’stein

Published Jun 9, 1997• 10 citations
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Abstract

In their comment Fabrizio and Gogolin dispute our result of the enhancement of the tunneling density of states in a Tomonaga-Luttinger liquid at the location of a backward scattering defect [Phys. Rev. Lett. 76, 4230(1996); cond-mat/9601020]. They state that the anticommutativity of the fermion operators of the left and right moving electrons was not considered properly in the Letter. We show in the Reply that the result of the Letter can be reproduced following the Comment when its calculations are performed correctly. This clearly indicates that the question about the anticommutation relations was raised by Fabrizio and Gogolin without serious grounds.

DOI
10.1103/physrevlett.78.4528

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In their comment Fabrizio and Gogolin dispute our result of the enhancement of the tunneling density of states in a Tomonaga-Luttinger liquid at the location of a backward scattering defect [Phys. Rev. Lett. 76, 4230(1996); cond-mat/9601020]. They state that the anticommutativity of the fermion operators of the left and right moving electrons was not considered properly in the Letter. We show in the Reply that the result of the Letter can be reproduced following the Comment when its calculations are performed correctly. This clearly indicates that the question about the anticommutation relations was raised by Fabrizio and Gogolin without serious grounds.
In a recent Physical Review Letter, Oreg and Finkel'stein (OF) have calculated the electron density of states (DOS) for tunneling into a repulsive Luttinger liquid close to the location of an impurity. The result of their calculation is a DOS which is enhanced with respect to the pure system, and moreover diverging for not too strong repulsion. In this Comment we intend to show that OF's calculation suffers from a subtle flaw which, being corrected, results into a DOS not only vanishing at zero frequency but in fact suppressed in comparison with the DOS of a pure Luttinger liquid.
In a series of papers we combined the Bethe ansatz with a kinetic (Boltzmann) equation in order to compute exactly transport properties in a Luttinger liquid with an impurity. In a recent comment [cond-mat/9708163], Skorik claimed that while our results were correct in linear response, there was a ``serious flaw'' in our calculation at finite voltage. We explain here why Skorik's arguments are inappropriate, and that there is no flaw in our work [cond-mat/9408068; cond-mat/9505031; cond-mat/9503172].
We reply to the critique of our results raised by Aleiner, Altshuler and Gershenzon (AAG) in cond-mat/9808078 and cond-mat/9808053. We demonstrate that our path integral analysis fully reproduces the results of AAG if analyzed on a perturbative level. This should settle the issue of "missing diagrams" in our calculation. We, furthermore, demonstrate that our approach allows us to proceed beyond the Golden-rule-type perturbation theory employed by AAG. This explains the difference between our and AAG's results. We also comment on the comparison of our results with the experiments presented by AAG.