Spin filtering effect in Rashba ring conductors

1. 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

2. 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

3. * 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)

4. 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)

5. Effective 1D Ring Hamiltonian with spin-orbit (SO) interaction • F. E. Meijer et al., Phys. Rev. B 69, 035308 (2004)

6. From 2D to 1D

7. Electric and magnetic field along z • SO-Ring • J. Nitta et. al., Phys. Rev. Lett. 78, 1335 (1997) • SO-AB Ring in presence of a tunnel barrier

8. 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)

9. Scattering problem By imposing: • Continuity of the wave functions at the junctions • Proper boundary condition for delta barrier potential • Spin/charge current conservation

10. Transmittance and Conductance Landauer-Buttiker Formula • Mòlnar et al. , Phys. Rev. B 69, 155335 (2004), Equation (28)

11. 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)

12. L R IS u d u u L R L R L R ISB d d Effect of z: Inversion symmetry Breaking

13. Effect of AB-flux: TRS Breaking

14. Im(x) K L Re(x) |x|2 =1 pole zero Resonances Conductance • Poles • Simple cases • Pole structure insensitive to the spin variables • Vanishing coefficients for power : x , x 2, x 3

15. 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.

16. 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.

17. pole zero

18. pole zero

19. pole zero

20. pole zero

21. 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.

22. Appendix : Scattering Equations • Spin and charge conservation laws at each junctions

23. Appendix : zero in complex plane • Zero-pole structure in complex energy plane • Zeros Interference zeros z-dependent zeros • When z = 0 the zeros are x = 1 and x = -1 • When |x|2-1= 0 real zeros appears in the conductance curves

24. Condition for real zeros • In the limit of integer/half-integer effective flux and z different from zero we obtain:

25. Appendix : Complex plane picture

26. Appendix : Complex plane picture (AB-flux different from 0)

27. Appendix : Complex plane picture (z different from 0)

28. Appendix : Simple pole structure