Parity Effects in Nanoscale Metallic Grain Including a Magnetic Impurity

Abstract

In ultrasmall systems such as nanoscale metallic grains, the discrete energy spectrum together with electron correlations may give dramatic properties at low temperatures. Among others, the Kondo effect has attracted considerable attention recently. In particular, parity effects should emerge depending on the number of total electrons: e.g., the Kondo effect appears (disappears) at low temperatures for an even (odd) number of electrons, yielding a finite (divergent) susceptibility when the Kondo temperature is smaller than the level spacing. More remarkable parity effects were pointed out by Thimm et al. in dynamical as well as transport properties when the mean level spacing is nearly equal to (or even smaller than) the Kondo temperature. They found that the Kondo resonance is discretized into a series of subpeaks with one main peak (two split peaks) at the Fermi level for an even (odd) number of electrons. They claimed that this behavior characterizes the Kondo effect in a metallic grain, which also leads to the oscillation behavior in the conductance. Although such parity effects are naturally expected, it is not clear how a single (double) peak structure is developed in the Kondo resonance depending on whether the electron count is even or odd. More generally we ask which aspect is universal in the parity effects. In this note we revisit this question about the Kondo effect in a metallic grain. Using the self-consistent second-order perturbation expansion, we demonstrate that although the parity effect indeed appears generically, the shape of the spectrum exhibits nonuniversal properties depending on a model system employed, in contrast to the claim of Thimm et al. In the nonequilibrium case, we find the oscillation behavior possessing the parity effect in the differential conductance. We consider a small metallic grain including a magnetic impurity described by the Anderson Hamiltonian,