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We address the problem of persistent charge and spin currents on a Corbinodisk built from a graphene sheet. We consistently derive the Hamiltonianincluding kinetic, intrinsic (ISO) and Rashba spin-orbit interactions incylindrical coordinates. The Hamiltonian is carefully considered to reflecthermiticity and covariance. We compute the energy spectrum and thecorresponding eigenfunctions separately for the intrinsic and Rashba spin-orbitinteractions. In order to determine the charge persistent currents we use thespectrum equilibrium linear response definition. We also determine the spin andpseudo spin polarizations associated with such equilibrium currents. For theintrinsic case one can also compute the correct currents by applying the barevelocity operator to the ISO wavefunctions or alternatively the ISO groupvelocity operator to the free wavefunctions. Charge currents for both SOcouplings are maximal in the vicinity of half integer flux quanta. Such maximalcurrents 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 onlyarise 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 butthey remain finite in the vicinity, and the same scenario above protects spincurrents.

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