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Electrical Means of Manipulating Electron Spins in Semiconductors

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Electrical Means of Manipulating Electron Spins in Semiconductors

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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

NTHU Colloquium 11.22.2006

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

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

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

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

A simple picture for the extrinsic spin Hall effect

J.E. Hirsch, PRL 83, 1834 (1999)

NTHU Colloquium 11.22.2006

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

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

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

InGaAs

InAlAs

Structure inversion asymmetry:

E

Rashba effect (spin-orbit interaction )Heterostructure:

E

analog

NTHU Colloquium 11.22.2006

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

E

ky

kx

Fig.3.Dispersion relation for a 2D Rashba-type system and the Rashba constant .

NTHU Colloquium 11.22.2006

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

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

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

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

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

NTHU Colloquium 11.22.2006

SHE in 11.22.2006n-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

Would the entire intrinsic spin Hall story collapse 11.22.2006due 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

NCTU 11.22.2006

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

Question: What sort of spin accumulation 11.22.2006 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

2DEG 11.22.2006

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

Random distribution of Isotropic scatterers 11.22.2006

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Linear response: 11.22.2006

< ….. > denotes averaging over impurity configuration

NTHU Colloquium 11.22.2006

NTHU Colloquium 11.22.2006

NTHU Colloquium 11.22.2006

Ladder diagrams do not contribute 11.22.2006

NTHU Colloquium 11.22.2006

NCTU 11.22.2006

NTHU Colloquium 11.22.2006

NTHU Colloquium 11.22.2006

+….. 11.22.2006

+

+

+

+

+

+….

Treating the disorder within the ladder diagram approximation

NTHU Colloquium 11.22.2006

Treating the disorder within the ladder diagram approximation

NTHU Colloquium 11.22.2006

To get some feeling, let’s consider the case approximationh0:

NTHU Colloquium 11.22.2006

Need to evaluate up to first order in . approximation

Angular average

Precession of the inhomogeneous spin polarization about the effective SOI field.

NTHU Colloquium 11.22.2006

It is diagonal, and is nonzero for approximation i, s limited to x, y, and z.

NTHU Colloquium 11.22.2006

NTHU Colloquium 11.22.2006

x 11.22.2006

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

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

Connecting spin flux and spin densities spin densities ?

NTHU Colloquium 11.22.2006

Rashba-type strip spin densities ?

NO Spin Accumulation at edges for Rashba-type strip.

NTHU Colloquium 11.22.2006

x spin densities ?

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

x spin densities ?

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

Dresselhaus-type strip spin densities ?

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

Dresselhaus-type strip spin densities ?

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

Spin densities 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

NCTU spin densities ?

(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

NCTU spin densities ?

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