Duality between different geometries of a resonant level in a Luttinger liquid

Moshe Goldstein*, Richard Berkovits

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number106403
JournalPhysical Review Letters
Issue number10
StatePublished - 10 Mar 2010
Externally publishedYes


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