Numerical and analytic studies of Kondo effect in nanostructures

Abstract:  The Kondo effect is a strong correlation non-perturbative emergent phenomenon. It was first discovered in the bulk by analyzing magnetic impurities embedded in normal metal. With the progress of nanodevice fabrication a renewed interest in Kondo physics has been rekindled. To obtain reliable quantitative predictions for such experiments, unbiased numerical simulations such as various variants of quantum Monte Carlo (QMC), or numerical renormalization group (NRG) are widely used. On the other hand, analytic approaches are generally based on perturbative expansions taken beyond weak electron correlations by summing only specific subclasses of diagrams, a procedure that typically breaks conservation laws.
In this talk, I will present a thermodynamically self-consistent analytic theory for two-particle vertex functions which addresses the problem and apply it first to the Single impurity Anderson model (SIAM). The resulting spectral function is shown to qualitatively reproduce the Kondo critical scale of SIAM at half filling which is compared with numerical (NRG, QMC) and analytical results (Bethe ansatz). Extension to models with superconducting baths of electrons is briefly discussed.
In the second part of the talk, we analyze a magnetically tunable Kondo effect by using NRG as well as analytical methods (Schrieffer-Wolff transformation). The obtained results are carefully compared to experimental data obtained in a corresponding nanodevice investigated in the group of prof. Van der Zant at TU Delft.