Effects of geometry and linearly polarized cavity photons on charge and spin currents in a quantum ring with spin-orbit interactions

We calculate the persistent charge and spin polarization current inside a finite-width quantum ring of realistic geometry as a function of the strength of the Rashba or Dresselhaus spin-orbit interaction. The time evolution in the transient regime of the two-dimensional (2D) quantum ring connected to electrically biased semi-infinite leads is governed by a time-convolutionless non-Markovian generalized master equation. The electrons are correlated via Coulomb interaction. In addition, the ring is embedded in a photon cavity with a single mode of linearly polarized photon field, which is polarized either perpendicular or parallel to the charge transport direction. To analyze carefully the physical effects, we compare to the analytical results of the toy model of a one-dimensional (1D) ring of non-interacting electrons with spin-orbit coupling. We find a pronounced charge current dip associated with many-electron level crossings at the Aharonov-Casher phase ΔΦ = π , which can be disguised by linearly polarized light. Qualitative agreement is found for the spin polarization currents of the 1D and 2D ring. Quantitatively, however, the spin polarization currents are weaker in the more realistic 2D ring, especially for weak spin-orbit interaction, but can be considerably enhanced with the aid of a linearly polarized electromagnetic field. Specific spin polarization current symmetries relating the Dresselhaus spin-orbit interaction case to the Rashba one are found to hold for the 2D ring, which is embedded in the photon cavity.