Dimensional and band-structure effects on persistent currents in mesoscopic metallic rings

摘要

The effects of the number of channels on persistent currents in mesoscopic metallic rings induced by static magnetic fields are investigated by means of a Hamiltonian that incorporates diagonal disorder and first- and second-nearest neighbor interactions on finite clusters of the simple-cubic lattice (LxMxN) with a single atomic orbital per lattice site. In the fully ordered case with first-nearest neighbor interactions and as a consequence of quantum interference, the typical current shows oscillations as a function of the number of channels (N-ch=MxN). In two dimensions (N= 1) and half filling these oscillations lead to a current that does not increase with N-ch but for special sizes, for which quantum interference is almost suppressed. Away from half filling and in three dimensions, whereas the current also oscillates with N-ch, it increases (on average) approximately as N-ch(upsilon), with upsilon less than or similar to 1/2. Instead, the Drude peak increases linearly with N-ch both in two and three dimensions and for any filling. The Hamiltonian dependence of these results is clearly illustrated by showing that if only second nearest-neighbor interactions are included, the current in two dimensions and half filling is proportional to N-ch. Away fom half filling and in three dimensions, although the typical current also oscillates with N-ch, it increases faster than with only first nearest-neighbors interactions. We investigate band-structure effects by considering a chain with s-d hybridization. The results show that although completely filled bands give a finite persistent current, their contribution decreases exponentially with the length of the ring. Results for weakly disordered two-dimensional rings with a single atomic orbital per lattice site and nearest-neighbors interaction, are not very different from those obtained in the clean case. In particular, the typical current also oscillates with N-ch. These oscillations cast doubts on conclusions attained on the basis of calculations for only a few channels. [References: 21]