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 G_j, spin-σ conductance and spin polarization P_j 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 G_j, and P_j 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, G_j, and P_j have some symmetries, , and P_j = −P_N−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 γ_N−j = 2π − γ_j. The spin polarization of the outgoing lead with γ_j = 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.