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Quantum Impurity in Interacting Environments

Nathan Andrei

Jeudi 07 novembre 2019 à 11h, Moyen Amphi

Quantum impurities, when coupled to interacting systems, show a variety of striking phenomena. I will first discuss a quantum impurity – a local scattering center or a quantum dot - coupled to a Luttinger liquid wire, and in the second part of my talk I will discuss a Kondo impurity coupled to a superconducting wire.
In the first part I shall show how the interaction in Luttinger liquid affects the properties of the impurity. I will present exact solutions of the various systems by means of the Off Diagonal Bethe Ansatz approach. I will derive the spectra of the models for all coupling constant regimes and will calculate the impurity free energy and discuss in detail the high and low energy behavior of the system for both repulsive and attractive interactions. Among other things I will show that the competition between the tunneling and the backscattering leads to non-Fermi liquid exponents in the specific heat and capacitance of the dot.
I shall then turn to a Kondo impurity coupled to a 1-d superconductor. Here we consider a magnetic impurity coupled to a quantum wire with pairing interactions, which dynamically generate a mass gap. Solving the system exactly we find that it exhibits both screened and unscreened phases for an antiferromagnetic impurity. We determine the ground state density of states and magnetization in both phases as well as the excitations. In contrast to the well-studied case of magnetic impurities in mean-field superconductors, we find that there are no intragap bound states in the spectrum. The phase transition is not associated to a level crossing but to quantum fluctuations.


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