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

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

2009-07-02

arxiv.org/abs/0907.0424v2

Phys. Rev. Lett. 104, 106403 (2010)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4.5 pages, 3 figures; v2: published version

Scientific paper

10.1103/PhysRevLett.104.106403

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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