We show exactly that small Hubbard rings exhibit unusual kink-like structures giving anomalous oscillations in persistent current. Singular behavior of persistent current disappears in some cases. In half-filled systems mobility gradually drops to zero with interaction, while it converges to some finite value in nonhalf-filled cases.

We present a detailed study of persistent current and low-field magnetic susceptibility in single isolated normal metal mesoscopic rings and cylinders in the tight-binding model with higher order hopping integral in the Hamiltonian. Our exact calculations show that order of magnitude enhancement of persistent current takes place even in presence of disorder if we include higher order hopping integral in the Hamiltonian. In strictly one-channel mesoscopic rings the sign of the low-field currents can be predicted exactly even in presence of impurity. We observe that perfect rings with both odd and even number of electrons support only diamagnetic currents. On the other hand in the disordered rings, irrespective of realization of the disordered configurations of the ring, we always get diamagnetic currents with odd number of electrons and paramagnetic currents with even number of electrons. In mesoscopic cylinders the sign of the low-field currents can't be predicted exactly since it strongly depends on the total number of electrons, N e , and also on the disordered configurations of the system. From the variation of persistent current amplitude with system size for constant electron density, we conclude that the enhancement of persistent current due to additional higher order hopping integrals are visible only in the mesoscopic regime.

To understand the role of electron correlation and disorder on persistent currents in isolated 1D rings threaded by magnetic flux φ, we study the behavior of persistent currents in aperiodic and ordered binary alloy rings. These systems may be regarded as disordered systems with well-defined long-range order so that we do not have to perform any configuration averaging of the physical quantities. We see that in the absence of interaction, disorder suppresses persistent currents by orders of magnitude and also removes its discontinuity as a function of φ. As we introduce electron correlation, we get enhancement of the currents in certain disordered rings. Quite interestingly we observe that in some cases, electron correlation produces kink-like structures in the persistent current as a function of φ. This may be considered as anomalous Aharonov-Bohm oscillations of the persistent current and recent experimental observations support such oscillations. We find that the persistent current converges with the size of the rings.

We have studied a one dimensional Hubbard superlattice with different Coulomb correlations at alternating sites for a half-filled band. Mean field calculations based on the Hartree-Fock approximation together with a real space renormalization group technique were used to study the ground state of the system. The phase diagrams obtained in these approaches agree with each other from the weak to the intermediate coupling regime. The mean field results show very quick convergence with system size. The renormalization group results indicate a spatial modulation of local moments that was identified in some previous work. Also we have studied the magnetoconductance of such superlattices which reveals several interesting points.

We show from exact calculations that a simple tight-binding Hamiltonian with diagonal disorder and long-range hopping integrals, falling off as a power µ of the inter-site separation, correctly describes the experimentally observed amplitude (close to the value of an ordered ring) and flux-periodicity (hc/e) of persistent currents in single-isolated-diffusive normal metal rings of mesoscopic size. Long-range hopping integrals tend to delocalize the electrons even in the presence of disorder resulting orders of magnitude enhancement of persistent current relative to earlier predictions. Keywords: Model Calculations, MagnetotransportThe phenomenon of persistent current in mesoscopic normal metal rings has generated a lot of excitement as well as controversy over the past years. In a pioneering work, Büttiker, Imry and Landauer [1] predicted that, even in the presence of disorder, an isolated 1D metallic ring threaded by magnetic flux φ can support an equilibrium persistent current with periodicity φ 0 = ch/e, the flux quantum. Later, experimental observations confirm the existence of persistent currents in isolated mesoscopic rings. However, these experiments yield many results that are not well-understood theoretically even today [2,3,4,5,6,7,8,9,10,11,12,13]. The results of the single loop experiments are significantly different from those for the ensemble of isolated loops. Persistent currents with expected φ 0 periodicity have been observed in isolated single Au rings [14] and in a GaAs-AlGaAs ring [15]. Levy et al. [16] found oscillations with period φ 0 /2 rather than φ 0 in an ensemble of 10 7 independent Cu rings. Similar φ 0 /2 oscillations were also reported for an ensemble of disconnected 10 5 Ag rings [17] as well as for an array of 10 5 isolated GaAs-AlGaAs rings [18]. In a recent experiment, Jariwala et al.[19] obtained both φ 0 and φ 0 /2 periodic persistent currents in an array of thirty diffusive mesoscopic Au rings. Except for the case of the nearly ballistic GaAs-AlGaAs ring [15], all the measured currents are in general one or two orders of magnitude larger than those expected from the theory [2,3,4,5,6,7,8,9,10,11,12]. The diamagnetic response of the measured φ 0 /2 oscillations of ensembleaveraged persistent currents near zero magnetic field also contrasts with most predictions [8,9].Free electron theory predicts that at T = 0, an or- * Corresponding author: Santanu K. Maiti E-mail: santanu@cmp.saha.ernet.in dered 1D metallic ring threaded by magnetic flux φ supports persistent current with maximum amplitude I 0 = ev F /L, where v F is the Fermi velocity and L is the circumference of the ring. Metals are intrinsically disordered which tends to decrease the persistent current, and the calculations show that the disorder-averaged current < I > crucially depends on the choice of the ensemble [3,4,5]. The magnitude of the current < I 2 > 1/2 is however insensitive to the averaging issues, and is of the order of I 0 l/L, l being the elastic mean free path of the electrons. This expression...