1. Electron transport in quantum wires subjected to the Rashba SOI
Almas Sadreev, Lab. of Theory of Nonlinear Processes,
Institute of Physics, Siberian Branch of Russian Academy of Sciences
Krasnoyarsk, Russia
My thanks to
Karl-Fredrik Berggren and Ivan Shelykh for invitation
And to whom I collaborate and collaborated :
Karl-Fredrik Berggren (Linkoping University, Sweden)
Evgeny Bulgakov and Konstantin Pichugin (Institite of Physics, Krasnoyarsk, Russia)
Pavel Exner, Pavel Streda and Petr Seba (Chech Rep.)
Evgeny Sherman (University of Basque Country, Bilbao, Spain)
Stockholm, Nordita workshop 2012, September

2. Spintronics (nickname for spin-based electronics):
We want to use spins of single electrons for
storage,
transfer,
and manipulation of information and not only ...
Stockholm, Nordita workshop 2012, September

3. Spin-orbit interaction

4. From Nitta’s lecture
Stockholm, Nordita workshop 2012, September

5. E U 2DEG z GaAs AlGaAs n - AlGaAs GaAs
Stockholm, Nordita workshop 2012, September

6. Stockholm, Nordita workshop 2012, September

7. Stockholm, Nordita workshop 2012, September

8. >
Stockholm, Nordita workshop 2012, September

9. The Razhba spin-orbit interaction
In infinite interface electric field is uniform and directed perpendicular to the interface.
Emmanuil Rashba
where a ~ Ez
The Razhba spin-orbit interaction
E.I. Razhba, Sov. Phys. Solid State 2, 1224 (1960)
Stockholm, Nordita workshop 2012, September

10. Lusakowski et al, PRB68,081201R (2003)
Stockholm, Nordita workshop 2012, September

11. SOI in 2DEG
J. Phys. C (2007)
Stockholm, Nordita workshop 2012, September

12. Stockholm, Nordita workshop 2012, September
Infinite 1d wire

13. S. Datta, Quantum transport: Atom to transistor
Supriyo Datta, Purdue Univ.
Datta-Das spin transistor
S.Datta, Electronic Transport in Mesoscopic Systems (Cambridge University Press, Cambridge, England, 1995).
S. Datta, Quantum transport: Atom to transistor
Stockholm, Nordita workshop 2012, September

14. Datta-Das spin transistor
Stockholm, Nordita workshop 2012, September

15. In 2007 Albert Fert (France) and Peter Grunberg (Germany) have got Nobel prize for discovery of giant magnetoresistance in multilayers of Fe/Cr, one after the other. Chromium of order of 1nm of thickness. The resistance increase between the parallel and anti-parallel configurations of the layers of iron went up to 80%!
Albert Fert
Peter Grunberg
Stockholm, Nordita workshop 2012, September

16. Stockholm, Nordita workshop 2012, September

17. Quasi 1d wire Datta& Das, Appl. Phys. Lett.(1989);
Stockholm, Nordita workshop 2012, September
Quasi 1d wire
Datta& Das, Appl. Phys. Lett.(1989);
Perroni et al J. Phys. C (2007);
SJeong&Lee PRB (2006);
Zhang, Brusheim and Xu, PRB (2005)
Mireles& Kirczenow, PRB (2001);
Knobbe&Schapers PRB (2005);
Moroz & Barnes, PRB (1999) ;
Pramanik et al PRB (2007);
Debald&Kramer, PRB (2005);
Governale&Zulicke PRB (2002);
Rodriguez, Puente and Serra (2003)
Erlingsson et al PRB (2010);

18. Approximate by two channels
Stockholm, Nordita workshop 2012, September

19. Two-band (two-channel) model
We take into account the exact solution of the quantum wire in the absence of SOI, then we study its effect on the sub-bands. Because of SOI, a coupling between sub-bands with opposite spins occurs. In order to study the effects of this coupling, we will discuss the results within the first- and second-order perturbation theory approach with respect to the SOI.
This assumption is valid if the wire is very narrow. Moreover, this simple system is studied since it provides a simple understanding of the transport properties.
Stockholm, Nordita workshop 2012, September

20. Two-band model Energy is measured in terms of
Stockholm, Nordita workshop 2012, September

21. two band model n=1,s=1 n=1,s=-1 n=2,s=-1 n=2,s=1
Stockholm, Nordita workshop 2012, September

22. Two-band model (wave functions)
Stockholm, Nordita workshop 2012, September

23. Current induced spin polarization –spin Hall effect
Reynoso, Usaj, and Balseiro, PRB70, (2004); PRB73, (2006)
Stockholm, Nordita workshop 2012, September

24. Charge- and spin-density modulations in semiconductor quantum wires
PHYSICAL REVIEW B 72,
Charge- and spin-density modulations in semiconductor quantum wires
Minchul Lee and Christoph Bruder
Stockholm, Nordita workshop 2012, September

25. J. Nitta, T. Akazaki, H. Takayanagi, and T. Enoki, PRL (1999)
Gate Control of Spin-Orbit Interaction in an Inverted In0.53Ga0.47AsIn0.52Al0.48As Heterostructure
J. Nitta, T. Akazaki, H. Takayanagi, and T. Enoki, PRL (1999)
Stockholm, Nordita workshop 2012, September

26. Quantum wire Hamiltonian
Finger gate potential (Davies, Larkin, and Sukhorukov, J. Appl. Phys.
77, 4504 (1995).

27. The simplest model of ballistic transport

28. Parabolic wire Strong SOI weak SOI
Stockholm, Nordita workshop 2012, September

29. Is the only integral of motion
A. V. Moroz and C. H. W. Barnes
Phys. Rev.B60,14272 (1999); B61, R2464 (2000)
Is the only integral of motion
GaAs
AlGaAs
n-AlGaAs
2 D E G
gates
1d wire x

30. From parabolic potential
Asymmetry of heterostructure

31. Landauer two-probe conductance with spin splitting

32. Curvilinear wire Bulgakov &Sadreev PRB 66 (2002)
Stockholm, Nordita workshop 2012, September

33. Stockholm, Nordita workshop 2012, September

34. General solution is
Two channels of transmission
Let electron is injecting with spin directed along the z-axis

35. Stockholm, Nordita workshop 2012, September

37. Spin polarization by magnetic field or ferromagnetic layer
No spin flip
Stockholm, Nordita workshop 2012, September

38. Spin polarization by Rashba SOI
Kisilev&Kim J. Appl. Phys. (2001); (2003)
Bulgakov &Sadreev PRB (2002)
Zhai &Xu, PRL 94, (2005).
Time reversal
Stockholm, Nordita workshop 2012, September

39. Spin filtering
Spin polarization
Therefore, for the single channel transmission through the two-terminal QD with the
Rashba spin-orbit interaction there is NO spin polarization (filtering).

40. Unitarity of S-matrix:

41. Spin transistor Kisilev&Kim J. Appl. Phys. (2001); (2003)
Bulgakov &Sadreev PRB (2002)
Liu et al PRB (2007)
Spin transistor
Perroni et al J. Phys. (2007)

42. The Hall like effect, induced by the Rashba spin-orbit.
Landau&Liphshitz, Quantum Mechanics. s n n s
Stockholm, Nordita workshop 2012, September

43. Four-terminal structure Bulgakov et al, PRL (1999)
Two effects
output
1) Spin polarization
2) Hall-like effect
SOI
output
output
Stockholm, Nordita workshop 2012, September

44. Stockholm, Nordita workshop 2012, September

45. Stockholm, Nordita workshop 2012, September

46. Nitta et al, Gate Control of Spin-Orbit Interaction in an Inverted
In0.53Ga0.47AsIn0.52Al0.48As Heterostructure , PRL (1997,1999)
Three-terminal
Yokoyama&Eto PRB (2009)
Four-terminal
Stockholm, Nordita workshop 2012, September

47. Theory and experiments by Nitta group
Physica E(2005)
Stockholm, Nordita workshop 2012, September

48. Bulgakov&Sadreev, JETP Lett. (2001):
Exact solution for circular QD with Rashba SOI
Spin polarization 90% by circular polarized laser field
PRB (2004): Exact solution with Rashba SOI and magnetic field f R
Stockholm, Nordita workshop 2012, September

49. Stockholm, Nordita workshop 2012, September

50. Eigen energies
Stockholm, Nordita workshop 2012, September

51. Laser field with circular polarization
Stockholm, Nordita workshop 2012, September

52. Stockholm, Nordita workshop 2012, September

53. 1d packet:
t=0
t=1.5
t=7
Stockholm, Nordita workshop 2012, September

54. 2d case

55. Landauer conductance