Persistent charge and spin currents in the long wavelength regime for graphene rings

We address the problem of persistent charge and spin currents on a Corbino disk built from a graphene sheet. We consistently derive the Hamiltonian including kinetic, intrinsic (ISO) and Rashba spin-orbit interactions in cylindrical coordinates. The Hamiltonian is carefully considered to reflect hermiticity and covariance. We compute the energy spectrum and the corresponding eigenfunctions separately for the intrinsic and Rashba spin-orbit interactions. In order to determine the charge persistent currents we use the spectrum equilibrium linear response definition. We also determine the spin and pseudo spin polarizations associated with such equilibrium currents. For the intrinsic case one can also compute the correct currents by applying the bare velocity operator to the ISO wavefunctions or alternatively the ISO group velocity operator to the free wavefunctions. Charge currents for both SO couplings are maximal in the vicinity of half integer flux quanta. Such maximal currents are protected from thermal effects because contributing levels plunge ($\sim$1K) into the Fermi sea at half integer flux values. Such a mechanism, makes them observable at readily accessible temperatures. Spin currents only arise for the Rashba coupling, due to the spin symmetry of the ISO spectrum. For the Rashba coupling, spin currents are cancelled at half integer fluxes but they remain finite in the vicinity, and the same scenario above protects spin currents

Charge and spin polarized currents in mesoscopic rings with Rashba spin-orbit interactions coupled to an electron reservoir

The electronic states of a mesoscopic ring are assessed in the presence of Rashba Spin Orbit coupling and a $U(1)$ gauge field. Spin symmetric coupling to an ideal lead is implemented following B\"uttiker's voltage probe. The exact density of states is derived using the reservoir uncoupled eigenstates as basis functions mixed by the reservoir coupling. The decay time of uncoupled electron eigenstates is derived by fitting the broadening profiles. The spin and charge persistent currents are computed in the presence of the SO interaction and the reservoir coupling for two distinct scenarios of the electron filling fraction. The degradation of the persistent currents depends uniformly on the reservoir coupling but nonuniformly in temperature, the latter due to the fact that currents emerge from different depths of the Fermi sea, and thus for some regimes of flux, they are provided with a protective gap. Such flux regimes can be tailored by the SO coupling for both charge and spin currents