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Quantum Physics in One Dimension$
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Thierry Giamarchi

Print publication date: 2003

Print ISBN-13: 9780198525004

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198525004.001.0001

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BOUNDARIES AND ISOLATED IMPURITIES

BOUNDARIES AND ISOLATED IMPURITIES

Chapter:
(p.303) 10 BOUNDARIES AND ISOLATED IMPURITIES
Source:
Quantum Physics in One Dimension
Author(s):

Thierry Giamarchi

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198525004.003.0010

This chapter looks at the effects of individual impurities and boundaries in a Luttinger liquid. Such effects are especially important in Luttinger liquids realized in mesoscopic (or nanoscopic) devices. The discussion starts with the effects of a boundary, which can be produced either by the physical end of the device (such as in a nanotube) or by putting very strong impurities in the one-dimensional system. Such impurities will in effect cut the chain. For simplicity, the calculations are illustrated on spinless fermions. Similar results are obtained for fermions with spin. The case of a Luttinger liquid in which one has put a single impurity is also considered. Although such a description is not very realistic in a natural setting, it can be obtained easily in an artificial one, where one puts a constriction in the Luttinger liquid. Examples of such systems are presented.

Keywords:   boundaries, isolated impurities, Luttinger liquids, one-dimensional systems, carbon nanotubes, edge states, quantum Hall systems

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