Parity-dependent Kondo effect in ultrasmall metallic grains

– In this Letter we study the Kondo effect in an ultrasmall metallic grain, i.e. small enough to have a discrete energy-level spectrum, by calculating the susceptibility χ of the magnetic impurity. Our quantum Monte Carlo simulations, and analytic solution of a simple model, show that the behavior changes dramatically depending on whether the number of electrons in the grain is even or odd. We suggest that the measurements of χ provide an effective experimental way of probing the grain’s number parity. Small metallic particles, typically of dimensions of few nanometers, show properties which are intermediate between atomic and bulk condensed matter systems. Because of the finite dimensions, the quasi-continuous spectrum in the bulk splits into discrete energy levels. When the average level spacing δ is comparable with the other energy scales of the problem interesting new effects appear. For example the physical observables are parity dependent, i.e. differ if the number of electrons in the grain is even or odd. While metallic particles have been investigated in ensembles of grains in the past (see [1] and references therein), only recently spectroscopy of single grains [2] has been achieved experimentally. In the case of superconducting, ferromagnetic and/or antiferromagnetic systems, the effect of a finite level spacing is to enhance quantum fluctuations and consequently suppress the many-body condensation. As a result a superconductor will not possess a fully developed gap [3], the magnetization of a ferromagnet will not be macroscopically large [4], although distinct features reminiscent of the macroscopic order can be detected even in nanosize systems. Recently Thimm et al. [5], in their work on the so-called Kondo box, studied the effect of magnetic impurities in a small metal particle. They found that the Kondo resonance is strongly affected when the mean level spacing in the grain becomes larger than the Kondo temperature [5, 6, 7]. The Kondo box shows the parity effect as well. The Kondo effect [8] is a paradigm in correlated electron systems. It originates from the interaction between the localized spin of a single magnetic impurity and the free electrons of the metal. In bulk systems Kondo correlations manifest in an increase of the resistance for decreasing temperature