Fano Resonances in Quantum Dots: A Non-Perturbative Role for Potential-Like Scattering

TL;DR

This paper provides an exact analysis of how potential-like scattering influences quantum dot transport, revealing quantum phase transitions and Fano resonances, especially in the Kondo regime, using a modified Anderson model solved via Bethe ansatz.

Contribution

It introduces a non-perturbative approach to study potential scattering effects in quantum dots, revealing phase transitions and resonance phenomena with exact solutions.

Findings

Potential scattering induces quantum phase transitions.

Transport is highly sensitive to potential scattering.

Fano resonances are explained through this model.

Abstract

We consider the physics of transport through quantum dots in the presence of two tunneling paths. The first path sees electrons hopping on and off the dot while the second path is modeled through a potential scattering-like term. To study the effects of potential scattering, we employ a modified version of the Anderson model. Such a model can be exactly solved through the Bethe ansatz, thus allowing a comprehensive and exact analysis of the zero temperature linear response conductance. We find transport properties to be extremely sensitive to the introduction of a potential scattering term. Indeed the presence of such a scattering term, inter alia, induces a series of first order quantum phase transitions. Focusing on the Kondo regime of the quantum dot, the non-perturbative effect of potential-like scattering can be directly tied to both the breaking of particle-hole symmetry and the interlinking of charge and spin degrees of freedom in the Anderson model. The sensitivity to potential scattering is also reflected in a set of complementary exact diagonalization computations. The consequences of this analysis extends to observations in general of Fano resonances in quantum dots as well as to the physics of transport through quantum dots embedded in Aharonov-Bohm rings.