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Spin filtering effect in Rashba ring conductors F. Romeo Università di Salerno Dip. di Fisica “E. R. Caianiello” Italy In collaboration with: M. Marinaro, R. Citro and S. Cojocaru Outline Introduction and Motivations Effective 1D Ring Hamiltonian with spin-orbit (SO) interaction Solution of the single particle scattering problem Transmittance and Conductance Results: zero-pole structure, spin filtering Conclusions Introduction and Motivations Spintronics (spin-based electronic): In order to make a spintronic device, the primary requirement is to have a system that can generate a current of spin polarised electrons, and a system that is sensitive to the spin polarization of the electrons. The simplest method of generating a spin polarised current is to inject the current through a ferromagnetic material (Giant magnetoresistance devices, spin valves etc) Applications: spin transistor (for example experimental implementation of S. Datta-B. Das model *), spin filters, MRAM (Magnetic Random Access Memory) * Semiconductor-based Spin Orbit devices Spin-interference device, J. Nitta et al., Appl. Phys. Lett. 75, 695 (1999) Spin interference effect in ring conductors subject to Rashba coupling, D. Frustaglia and K. Richter, Phys. Rev. B 69, 235310 (2004) Effective 1D Ring Hamiltonian with spinorbit (SO) interaction F. E. Meijer et al., Phys. Rev. B 69, 035308 (2004) From 2D to 1D Electric and magnetic field along z SO-Ring SO-AB Ring in presence of a tunnel barrier J. Nitta et. al., Phys. Rev. Lett. 78, 1335 (1997) Eigenstates, eigenvalues and single particle scattering problem Mòlnar et al. , Phys. Rev. B 69, 155335 (2004) Y Aharonov and A Casher, Phys. Rev. Lett. 53, 319 (1984) Scattering problem By imposing: Continuity of the wave functions at the junctions Proper boundary condition for delta barrier potential Spin/charge current conservation Transmittance and Conductance Landauer-Buttiker Formula Mòlnar et al. , Phys. Rev. B 69, 155335 (2004), Equation (28) Real zeros conductance Z= 0 Z different from 0 |n| even integer (breaking of Inversion symmetry with respect to up in down and viceversa) Similar to U. Aeberhard et al. , Phys. Rev. B 72, 075328 (2005) Effect of z: Inversion symmetry Breaking u IS L R d u ISB L u R d L R L R d Effect of AB-flux: TRS Breaking Resonances Conductance Poles Im(x) Simple cases Pole structure insensitive to the spin variables Re(x) |x|2 =1 pole Vanishing coefficients for power : x , x 2, x 3 KL zero Spin filtering: how to compensate the interference zeros An interference zero can be compensated by a pole at the same position: The zeros in the transmittance do not necessarily correspond to a zero in the conductance. In principle it is possible to obtain a pole in one spin channel at xp The above condition is independent from z The displacement of the structural zeros does not affect the position of the pole at xp=1. Switching effect Poles at x =1 in both spin channel In this configuration we cant distinguish between different spin channels because of a vanishing spin dependence of the transmittance. pole zero pole zero pole zero pole zero Conclusions We showed the possibility of making a momentum-resolved spin filter by means of 1D ring with SO interaction using the present semiconductor technology. Differently from other proposals, the presence of the tunnel barrier in the model allows us to have a complete control of the filtering properties in a selected spin channel simply acting on a gate voltage. This provides a more convenient way to control the transport properties of the structure. The arrangement could be used also as quantum pump in order to generate pure spin current (~30 pA @ 100 MHz). Additional investigations are needed to clarify the role of disorder, electron correlations etc. on the performances described. Appendix : Scattering Equations Spin and charge conservation laws at each junctions Appendix : zero in complex plane Zero-pole structure in complex energy plane Zeros Interference zeros When z = 0 the zeros are x = 1 and x = -1 When |x|2-1= 0 real zeros appears in the conductance curves z-dependent zeros Condition for real zeros In the limit of integer/half-integer effective flux and z different from zero we obtain: Appendix : Complex plane picture Appendix : Complex plane picture (AB-flux different from 0) Appendix : Complex plane picture (z different from 0) Appendix : Simple pole structure