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Electrical Means of Manipulating Electron Spins in Semiconductors

NCTU. Electrical Means of Manipulating Electron Spins in Semiconductors. C. S. Chu Dept. of Electrophysics National Chiao Tung University. Collaborators: A.G. Mal’shukov (RAS) L. Y. Wang (NCTU). NCTU. NCTU.

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Electrical Means of Manipulating Electron Spins in Semiconductors

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  1. NCTU Electrical Means of ManipulatingElectron Spins in Semiconductors C. S. Chu Dept. of Electrophysics National Chiao Tung University Collaborators: A.G. Mal’shukov (RAS)L. Y. Wang (NCTU) NTHU Colloquium 11.22.2006

  2. NCTU NTHU Colloquium 11.22.2006

  3. NCTU Quoted from the abstract of “Spintronics: Fundamentals and applications” Spintronics, or spin electronics, involves the study of active control and manipulation of spin degrees of freedom in solid-state systems. in Reviews of Modern Physics, vol. 76, p.323-410, 2004, by I. Žutić, J. Fabian, and S. Das Sarma. NTHU Colloquium 11.22.2006

  4. NCTU How about transport of spins in non-magnetic semiconductor using only electrical control? Schemes making use of spin Hall effect Schemes other than spin Hall effect NTHU Colloquium 11.22.2006

  5. NCTU A simplest version of a spin Hall effect: An electrical current passes through a sample with spin-orbit interaction, and induces a spin polarization near the lateral edges, with opposite polarization at opposing edges (M.I. D’yakonov and V.I. Perel’, JEPT Lett., 13, 467 (1971)). This effect does not require an external magnetic field or magnetic order in the equilibrium state before the current is applied. M.I. D’yakonov and V.I. Perel’ (1971) proposed an extrinsic mechanism for the spin Hall effect in the paper: “Possibility of orienting electron spins with current”. cond-mat/0603306 H. Engel, E.I. Rashba, B.I. Halperin NTHU Colloquium 11.22.2006

  6. NCTU V.M. Edelstein, Solid State Commun. 73, 233 (1990)“Spin polarization of conduction electrons induced by electric current in two-dimensional asymmetric electron systems” S. Murakami, N. Nagaosa, S.C. Zhang, Science 301, 1348 (2003)“Dissipationless quantum spin current at room temperature” J. Sinova, D. Culcer, Q. Niu, N.A. Sinitsyn, T. Jungwirth, and A.H. MacDonald, Physical Review Letters 92, 126603 (2004)“Universal Intrinsic Spin Hall Effect” NTHU Colloquium 11.22.2006

  7. NCTU A simple picture for the extrinsic spin Hall effect J.E. Hirsch, PRL 83, 1834 (1999) NTHU Colloquium 11.22.2006

  8. NCTU Potential energy More on the simple picture for the extrinsic spin Hall effect For electron incident upon theLHS of the attractive scatterer, again the spin up particle is deflected more tothe left and the spin down particle is deflected more to the right. NTHU Colloquium 11.22.2006

  9. NCTU A “simple picture” for the intrinsic spin Hall effect PRL 92, 126603 (2004)J. Sinova, D. Culcer, Q. Niu et al. NTHU Colloquium 11.22.2006

  10. Asymmetric heterostructure that has Spin-orbit interaction Schematic layer structure of an inverted In0.53Ga0.47As / In0.52Al0.48As heterostructure.(Nitta et al. Phys. Rev. Lett.78, 1355(1997)) Calculated conduction band diagram (solid line) and electron distribution (dash line). (Nitta et al. Physica E, 2, 527(1998)) NTHU Colloquium 11.22.2006

  11. 2DEG InGaAs InAlAs Structure inversion asymmetry: E Rashba effect (spin-orbit interaction ) Heterostructure: E analog NTHU Colloquium 11.22.2006

  12. Effective magnetic field induced by the effective current I. An electron moves between two charged plane I V E Beff I In Lab. frame In the rest frame of an electron The SOI hamiltonian is given by where is called the Rashba constant. NTHU Colloquium 11.22.2006

  13. + E ky kx Fig.3.Dispersion relation for a 2D Rashba-type system and the Rashba constant . NTHU Colloquium 11.22.2006

  14. Rashba spin-orbit interaction (SOI) • SOI is significant in narrow gap semiconductor heterostructures. • Large variation (up to 50%) of the SOI coupling constant , tuned by metal gates, has been observed experimentally. • [ Nitta et. al. PRL 78 (1997) • Engels et. al. PRB 55 (1997) • Grundler, PRL 84 (2000) ] • Static gate control of  has been • the focus of previous proposals on spin polarized transistors.[ Datta et. al. APL 56 (1990), ……] NTHU Colloquium 11.22.2006

  15. Tuning of the coupling constant by a metal gate Gate InGaAs Spin-orbit coupling parameter of the first (circle) and second (square) subband as a function of the gate voltage: including (solid) and not including (open) band nonparabolicity correlation. (Nitta. et al. Phys.Rev.B 60,7736(1999)) InAlAs 2DEG NTHU Colloquium 11.22.2006

  16. NCTU J. Sinova, et al PRL 92, 126603 (2004) A “simple picture” for the intrinsic spin Hall effect This picture is subject to change since it has not incorporated the scattering picture as well as the form of the spin-orbit interaction NTHU Colloquium 11.22.2006

  17. Experimental observation of extrinsic spin Hall Effect in thin 3D layersY.K. Kato, R.C.Myers, A.C. Gossard, D.D. Awschalom, Science 306, 1910 (2004) NTHU Colloquium 11.22.2006

  18. Experimental confirmation of spin Hall Effect in a 2D hole gasJ. Wunderlich, B. Kaestner, J. Sinova, and T. Jungwirth, Phys. Rev. Lett. 94, 047204 (2005) NTHU Colloquium 11.22.2006

  19. NTHU Colloquium 11.22.2006

  20. SHE in n-type Rashba spin-orbit systems vanishes in the presence of weak disorder J.I. Inoue, et al, Phys. Rev. B 70, 041303 (2004)E.I. Rashba, Phys. Rev. B 70, 201309 (2004)O. Chalaev et al, Phys. Rev. B 71, 245318 (2005)E.G. Mishchenko, et al, Phys. Rev. Lett. 93, 226602 (2004)A.A. Burkov, et al, Phys. Rev. B 70, 155308 (2004)O.V. Dimitrova, Phys. Rev. B 71, 245327 (2005)R. Raimondi et al, Phys. Rev. B 71, 033311 (2005)A.G. Mal’shukov et al, Phys. Rev. B 71, 121308(R) (2005)B.A. Bernevig and S.C. Zhang, Phys. Rev. Lett. 95, 016801 (2005) Vertex correction is important ! NTHU Colloquium 11.22.2006

  21. Would the entire intrinsic spin Hall story collapse due to the presence of impurities? SHE is found in Dresselhaus-type spin-orbit systemsA.G. Mal’shukov et al, Phys. Rev. B 71, 121308(R) (2005) SHE is found in cubic Rashba-type hole systemsB.A. Bernevig and S.C. Zhang, Phys. Rev. Lett. 95, 016801 (2005) NTHU Colloquium 11.22.2006

  22. NCTU Thus far, the research on spin Hall focused onphysical quantities such as:spin current; spin Hall conductivity. The system of interest was mostly Rashba-typerather than Dresselhaus-type. Spin accumulation at the edges was essentially obtained from the bulk spin current plus someplausible arguments. Explicit calculation of the spin accumulation at the edges in a diffusive sample was in order at the time. NTHU Colloquium 11.22.2006

  23. Question: What sort of spin accumulation could instrinsic Rashba SOI or Dresselhaus SOI induce near a diffuse sample boundaries? Outline: Derivation of a diffusion equation for the spin and charge densities in a 2D strip Spin accumulation at the strip edges and its symmetry properties Connection between the spin flux and the spin densities Summary NTHU Colloquium 11.22.2006

  24. 2DEG InGaAs InAlAs Derivation of a diffusion equation for the spin and charge densities in a 2D strip Rashba SOI: Asymmetric heterostructure Dresselhaus SOI: Symmetric quantum well NTHU Colloquium 11.22.2006

  25. Random distribution of Isotropic scatterers NTHU Colloquium 11.22.2006

  26. Linear response: < ….. > denotes averaging over impurity configuration NTHU Colloquium 11.22.2006

  27. NTHU Colloquium 11.22.2006

  28. NTHU Colloquium 11.22.2006

  29. Ladder diagrams do not contribute NTHU Colloquium 11.22.2006

  30. NCTU NTHU Colloquium 11.22.2006

  31. NTHU Colloquium 11.22.2006

  32. +….. + + + + + +…. Treating the disorder within the ladder diagram approximation NTHU Colloquium 11.22.2006

  33. NCTU + + +…. NTHU Colloquium 11.22.2006

  34. Treating the disorder within the ladder diagram approximation NTHU Colloquium 11.22.2006

  35. To get some feeling, let’s consider the case h0: NTHU Colloquium 11.22.2006

  36. Need to evaluate up to first order in . Angular average Precession of the inhomogeneous spin polarization about the effective SOI field. NTHU Colloquium 11.22.2006

  37. It is diagonal, and is nonzero for i, s limited to x, y, and z. NTHU Colloquium 11.22.2006

  38. D’akonov-Perelspin relaxation Charge-spin coupling NTHU Colloquium 11.22.2006

  39. NTHU Colloquium 11.22.2006

  40. x E y Rashba-type strip Equation for the spin densities for Rashba-typesemiconductor strip Bulk spin density : Sx = Sz = 0 V.M. Edelstein Solid State Comm. 1990J.I. Inoue et al, PRB 2003 NTHU Colloquium 11.22.2006

  41. What boundary conditions do we have for the solving of the spin densities ? Answer: Connecting spin flux and spin densities NTHU Colloquium 11.22.2006

  42. Connecting spin flux and spin densities NTHU Colloquium 11.22.2006

  43. Rashba-type strip NO Spin Accumulation at edges for Rashba-type strip. NTHU Colloquium 11.22.2006

  44. x E y Rashba-type strip Equation for the spin densities for Rashba-typesemiconductor strip Bulk spin density : Sx = Sz = 0 V.M. Edelstein Solid State Comm. 1990J.I. Inoue et al, PRB 2003 NTHU Colloquium 11.22.2006

  45. x E y Dresselhaus-type strip Equation for the spin densities for Dresselhaus-typesemiconductor strip Bulk spin density : Sy = Sz = 0 NTHU Colloquium 11.22.2006

  46. Dresselhaus-type strip Spin density diffusion equation in a 2D stripdriven by a homogeneous electric field Edges of the strip are at y = ± d/2 NTHU Colloquium 11.22.2006

  47. Dresselhaus-type strip Spin density diffusion equation in a 2D stripdriven by a homogeneous electric field Edges of the strip are at y = ± d/2 NTHU Colloquium 11.22.2006

  48. Spin densities for i = x, z as a functions of its width d. The inset shows the dependence of Sz(y) on the transverse coordinate y. Lengths are measured in unit of . (PRL.95, 146601(2005)) NTHU Colloquium 11.22.2006

  49. NCTU (a) (b) Spin densities of Sz are of odd parity in a 2D strip with /k=1.3 for the strip width d = (a) 1; (b) 10, respectively. NTHU Colloquium 11.22.2006

  50. NCTU Summary • A diffusion approximation has been derived for the spin density. • Spin accumulation at the two edges of a Dresselhaus 2D strip associated with the spin Hall effect is obtained. • The spin accumulation exhibits damped oscillations as a function of the strip width. • Our analysis shows that the spin current decreases as τ2 whereas the strip spin density decrease as τ. This explains why we still obtain noticeable spin polarization in our dirty regime examples. NTHU Colloquium 11.22.2006

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