Ballistic spin-dependent transport of Rashba rings with multi-leads

Using the Landauer–Büttiker formula with the transfer matrix technique, we develop a formalism of the ballistic spin-dependent electron transport in the multi-lead Rashba rings. We give analytic formulas of the total conductance Gj, spin-σ   conductance gjσ and spin polarization Pj of each outgoing lead j, and their resonant and antiresonant conditions. Analytic studying with numerical investigating Rashba rings with several symmetric and asymmetric leads, we find that Gj, gjσ and Pj oscillate with the incoming electron energy and the spin–orbit interaction (SOI) strength, and their antiresonances depend on the incoming electron energy, the SOI strength and the outgoing-lead angle with the incoming lead. For the symmetric-lead rings, Gj, gjσ and Pj have some symmetries, Gj=GN-j,gjσ=gN-j-σ, and Pj = −PN−j for symmetric leads, j and N − j, where the angles between the symmetric outgoing leads j and N − j and the incoming lead are γN−j = 2π − γj. The spin polarization of the outgoing lead with γj = π is exactly zero for even-N-symmetric-lead rings. These symmetries originate from the lead symmetry and time reversal invariance. For asymmetry-lead rings these symmetries vanish.

Research highlights
► Transmission coefficients of each outgoing lead in multi-lead mesoscopic Rashba rings.
► Spin polarizations of each outgoing lead in multi-lead mesoscopic Rashba rings.
► Resonant and antiresonant conditions of spin polarization in multi-lead Rashba rings.
► Symmetries of conductance and spin polarization of symmetric multi-lead Rashba rings.