Transport in a one-dimensional Luttinger liquid

Details Transport in a one-dimensional Luttinger liquid Transport in a one-dimensional Luttinger liquid

1996-10-06

arxiv.org/abs/cond-mat/9610037v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

20 pages, including 7 Postscript figures. Paper to be published in "Mesoscopic Electron Transport", edited by L. Kowenhoven, G

Scientific paper

In this paper we review recent theoretical results for transport in a one-dimensional (1d) Luttinger liquid. For simplicity, we ignore electron spin, and focus exclusively on the case of a single-mode. Moreover, we consider only the effects of a single (or perhaps several) spatially localized impurities. Even with these restrictions, the predicted behavior is very rich, and strikingly different than for a 1d non-interacting electron gas. The method of bosonization is reviewed, with an emphasis on physical motivation, rather than mathematical rigor. Transport through a single impurity is reviewed from several different perspectives, as a pinned strongly interacting ``Wigner" crystal and in the limit of weak interactions. The existence of fractionally charged quasiparticles is also revealed. Inter-edge tunnelling in the quantum Hall effect, and charge fluctuations in a quantum dot under the conditions of Coulomb blockade are considered as examples of the developed techniques.

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