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

Authors | Bolívar N, Medina E., Berche B. |

Reference | *Phys. Rev. B* **89** (2014) 125413 |

DOI | 10.1103/PhysRevB.89.125413 |

ArXiv | arxiv:1402.4103 |

Abstract | 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 (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. |