E. Louis et al., DIMENSIONAL AND BAND-STRUCTURE EFFECTS ON PERSISTENT CURRENTS IN MESOSCOPIC METALLIC RINGS, Physical review. B, Condensed matter, 58(11), 1998, pp. 6912-6919
The effects of the number of channels on persistent currents in mesosc
opic metallic rings induced by static magnetic fields are investigated
by means of a Hamiltonian that incorporates diagonal disorder and fir
st- 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 interacti
ons 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 fillin
g and in three dimensions, whereas the current also oscillates with N-
ch, it increases (on average) approximately as N-ch(upsilon), with ups
ilon less than or similar to 1/2. Instead, the Drude peak increases li
nearly 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 include
d, the current in two dimensions and half filling is proportional to N
-ch. Away fom half filling and in three dimensions, although the typic
al current also oscillates with N-ch, it increases faster than with on
ly first nearest-neighbors interactions. We investigate band-structure
effects by considering a chain with s-d hybridization. The results sh
ow that although completely filled bands give a finite persistent curr
ent, their contribution decreases exponentially with the length of the
ring. Results for weakly disordered two-dimensional rings with a sing
le atomic orbital per lattice site and nearest-neighbors interaction,
are not very different from those obtained in the clean case. In parti
cular, the typical current also oscillates with N-ch. These oscillatio
ns cast doubts on conclusions attained on the basis of calculations fo
r only a few channels.