Spin and charge persistent currents in a Kane Mele-quantum ring.

We conduct a thorough study of different persistent currents in a spin-orbit coupled-(pseudospin-1) fermionic quantum ring (QR) that smoothly interpolates between graphene ( = 0, pseudospin-1/2) and a dice lattice ( = 1, pseudospin-1) in presence of an external perpendicular magnetic field. In particular, we have considered effects of intrinsic (ISOC) and Rashba spin-orbit couplings (RSOC) that are both inherent to two dimensional quantum structures and yield interesting consequences. The energy levels of the system comprise of the conduction bands, valence bands, and flat bands which show non-monotonic dependencies on the radius,of the QR, in the sense that, for small, the energy levels vary as1/R, while the variation is linear for large. The dispersion spectra corresponding to zero magnetic field are benchmarked with those for finite fields to enumerate the role played by the spin-orbit coupling terms therein. Further, it is noted that the flat bands demonstrate dispersive behavior, and hence is able to contribute to the transport properties only for finite ISOC. Moreover, RSOC yields spin-split bands, thereby contributing to the spin-resolved currents. The charge and the spin-polarized persistent currents are hence computed in presence of these spin-orbit couplings. The persistent currents in both the charge and spin sectors oscillate as a function of the magnetic field with a period equal to the flux quantum, as they should be; although they now depend upon the spin-orbit coupling parameters. Interestingly, the ISOC distorts the current profiles, owing to the distribution of the flat band caused by it, whereas RSOC alone preserves the flat band and hence a perfect periodicity of the current characteristic is maintained. Further, we have explored the role played by the parameterin our entire analysis to enable studies while interpolating from graphene to a dice lattice.