Mesoscopic Kondo problem

– We study the effect of mesoscopic fluctuations on a magnetic impurity coupled to a spatially confined electron gas with a temperature in the mesoscopic range (i.e. between the mean level spacing ∆ and the Thouless energy ETh). Comparing “poor-man’s scaling” with exact Quantum Monte Carlo, we find that for temperatures larger than the Kondo temperature, many aspects of the fluctuations can be captured by the perturbative technique. Using this technique in conjunction with semi-classical approximations, we are able to calculate the mesoscopic fluctuations for a wide variety of systems. For temperatures smaller than the Kondo temperature, we find large fluctuations and deviations from the universal behavior. The nature of many-body interaction effects at the nanoscale has been of great interest recently. Examples include, for instance, charging and correlation in quantum dots [1], superconductivity or ferromagnetism in metallic grains [2], and transport through effectively onedimensional systems [3]. Since interference effects are ubiquitous at the nanoscale, it is natural to examine the interplay between interference and many-body interactions in these systems. A magnetic impurity coupled to an electron gas is a classic many-body problem, known as the Kondo problem [4]. In the simplest case, one takes a spin-(1/2) impurity coupled antiferromagnetically with an exchange constant J to an electron gas described by a constant density of states ρ0 within a bandwidth D. The physics has two distinct temperature regimes —at high T the electrons scatter off the impurity in inelastic spin-flip processes, while at low T there is only elastic scattering as the impurity is screened by electrons forming a bound state singlet. The crossover takes place at an energy scale T 0 K , which in the weak-coupling limit De−1/Jρ0 . All impurity properties (i.e. impurity contribution to thermodynamic quantities and impurity correlators) have temperature dependencies that are universal after rescaling with T 0 K . This simplest case corresponds to a bulk piece of metal in which there is no interference. More recently, the effect of interference on Kondo impurities has been studied in various open systems. In disordered metals, the presence of magnetic impurities affects the weaklocalization properties [5, 6], and the fact that each impurity sees a different local density of states may give rise to non-Fermi-liquid signatures in the metal-insulator transition [7]. In quantum point contacts, Friedel oscillations associated with the proximity of a boundary lead to a coupling between the magnetic impurity and the electron gas which depends on both the position of the impurity and the energy of the electron state; as a consequence, fluctuations of the Kondo properties are observed [8]. For closed systems, on the other hand, it is natural to ask: What is the effect of the confinement on the many-body physics? In ultra-small metal particles [2], for instance, the mean single-particle level spacing ∆ can be comparable to the bulk Kondo temperature T 0 K . Clearly, a magnetic impurity in such a particle will show new physical properties associated with the