Duality between Different Geometries of a Resonant Level in a Luttinger Liquid

Moshe Goldstein and Richard Berkovits
Phys. Rev. Lett. 104, 106403 – Published 10 March 2010

Abstract

We prove an exact duality between the side-coupled and embedded geometries of a single level quantum dot attached to a quantum wire in a Luttinger liquid phase by a tunneling term and interactions. This is valid even in the presence of a finite bias voltage. Under this relation the Luttinger liquid parameter g goes into its inverse, and transmittance maps onto reflectance. We then demonstrate how this duality is revealed by the transport properties of the side-coupled case. Conductance is found to exhibit an antiresonance as a function of the level energy, whose width vanishes (enhancing transport) as a power law for low temperature and bias voltage whenever g>1, and diverges (suppressing transport) for g<1. On-resonance transmission is always destroyed, unless g is large enough.

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  • Received 2 July 2009

DOI:https://doi.org/10.1103/PhysRevLett.104.106403

©2010 American Physical Society

Authors & Affiliations

Moshe Goldstein and Richard Berkovits

  • The Minerva Center, Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel

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Issue

Vol. 104, Iss. 10 — 12 March 2010

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