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

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.

4.5 pages, 3 figures; v2: published version

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• Quantum Dot in Interacting Environments
• Hierarchical equations of motion approach to transport through an Anderson impurity coupled to interacting Luttinger liquid leads
• Impurity Scattering in Luttinger Liquid with Electron-Phonon Coupling
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• Effect of electron-phonon coupling on transmission through Luttinger liquid hybridized with resonant level
• Nonequilibrium Quantum Critical Steady State: Transport Through a Dissipative Resonant Level
• Conductance of a Dissipative Quantum Dot: Nonequilibrium Crossover Near a Non-Fermi-Liquid Quantum Critical Point
• Non-Fermi Liquid Quantum Impurity Physics from non-Abelian Quantum Hall States
• Transparency enhancement in a double-barrier structure by the Fano antiresonance