Transcript Diapositiva 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
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