Spin-dependent transport phenomena in strongly spin-orbit coupled mesoscopic systems: spin Hall effect and Aharonov-Casher Hong Kong, August 17 th 2005 JAIRO SINOVA Collaborators supported by: Collaborators: Allan MacDonald, Dimitri Culcer, Ewelina Hankeiwc, Qian Niu, Kentaro Nomura, Nikolai Sinitsyn, Laurens Molenkamp, Hartmut Buhmann, Charlie Becker, Volker Daumer, Yongshen Gui Matthias König, Jian Liu, Markus Schäfer, Joerg Wunderlich, Bernd Kästner, Tomas Jungwirth, Branislav Nikolic, Satofumi Souma, Liviu Zarbo, Mario Borunda

OUTLINE Spin dependent transport in SO coupled systems: Das-Datta transistor paradigm Spin dependent transport in SO coupled systems: Das-Datta transistor paradigm Spin-Hall effect Spin-Hall effect Basic pheonemonlogy Basic pheonemonlogy Some settled issues: mini-workshop on spin-Hall effect Some settled issues: mini-workshop on spin-Hall effect Spin Hall effect in the mesoscopic regime Spin Hall effect in the mesoscopic regime Why study the mesoscopic regime Why study the mesoscopic regime Transport indications of SHE in the mesoscopic regime Transport indications of SHE in the mesoscopic regime Spin accumulation in ballistic and coherent systems Spin accumulation in ballistic and coherent systems Aharonov-Casher effect in mesoscopic rings Aharonov-Casher effect in mesoscopic rings

Spin-orbit coupling interaction (one of the few echoes of relativistic physics in the solid state) Ingredients: -“Impurity” potential V(r) - Motion of an electron Produces an electric field In the rest frame of an electron the electric field generates and effective magnetic field This gives an effective interaction with the electron’s magnetic moment CONSEQUENCES If part of the full Hamiltonian quantization axis of the spin now depends on the momentum of the electron !! If treated as scattering the electron gets scattered to the left or to the right depending on its spin!!

Spin Hall effect like-spin Spin-orbit coupling “force” deflects like-spin particles I _ F SO _ _ _ V=0 non-magnetic Spin-current generation in non-magnetic systems without applying external magnetic fields Spin accumulation without charge accumulation excludes simple electrical detection Take now a PARAMAGNET instead of a FERROMAGNET: Carriers with same charge but opposite spin are deflected by the spin-orbit coupling to opposite sides. Refs: Dyakonov and Perel (71), J. E. Hirsch (99)

INTRINSIC SPIN-HALL EFFECT: INTRINSIC SPIN-HALL EFFECT: Murakami et al Science 2003 (cond-mat/ ) Sinova et al PRL 2004 (cont-mat/ ) as there is an intrinsic AHE (e.g. Diluted magnetic semiconductors), there should be an intrinsic spin-Hall effect!!! Inversion symmetry  no R-SO Broken inversion symmetry  R-SO (differences: spin is a non-conserved quantity, define spin current as the gradient term of the continuity equation. Spin-Hall conductivity: linear response of this operator) n, q n’  n, q

Disorder effects: beyond the finite lifetime approximation for Rashba 2DEG Question: Are there any other major effects beyond the finite life time broadening? Does side jump contribute significantly? Inoue, Bauer, Molenkamp PRB 04 Ladder partial sum vertex correction: Also: Mishchenko et al, PRL 04 Raimondi et al, PRB 04, Dimitrova PRB05, Loss et al, PRB 05 NOTE: the vertex corrections are zero for 3D hole systems (Murakami 04) and 2DHG (Bernevig and Zhang 05)

Experimental observations Wunderlich, Kästner, Sinova, Jungwirth, cond-mat/ PRL in press: Experimental observation of the spin-Hall effect in a two dimensional spin-orbit coupled semiconductor system Co-planar spin LED in GaAs 2D hole gas: ~1% polarization CP [%] Light frequency (eV) Kato, Myars, Gossard, Awschalom, Science Nov 04 Observation of the spin Hall effect bulk in semiconductors Local Kerr effect in n-type GaAs and InGaAs: ~0.03% polarization (weaker SO-coupling, stronger disorder)

SHE controversy Does the SHE conductivity vanish due to scattering? Seems to be the case in 2DRG+Rashba (Inoue et al 04), does not for any other system studied Dissipationless vs. dissipative transport Is the SHE non-zero in the mesoscopic regime? What is the best definition of spin-current to relate spin-conductivity to spin accumulation ……

APCTP Workshop on Semiconductor Nano-Spintronics: Spin-Hall Effect and Related Issues August 8-11, 2005 APCTP, Pohang, Korea A COMMUNITY WILLING TO WORK TOGETHER

Semantics agreement: The intrinsic contribution to the spin Hall conductivity is the the spin Hall conductivity in the limit of strong spin orbit coupling and  >>1. This is equivalent to the single bubble contribution to the Hall conductivity in the weakly scattering regime. General agreement The spin Hall conductivity in a 2DEG with Rashba coupling vanishes in the absence of a magnetic field and spin-dependent scattering. The intrinsic contribution to the spin Hall conductivity is identically cancelled by scattering (even weak scattering). This unique feature of this model can be traced back to the specific spin dynamics relating the rate of change of the spin and the spin current directly induced, forcing such a spin current to vanish in a steady non-equilibrium situation. The cancellation observed in the 2DEG Rashba model is particular to this model and in general the intrinsic and extrinsic contributions are non-zero in all the other models studied so far. In particular, the vertex corrections to the spin-Hall conductivity vanish for p-doped models.

OUTLINE Spin dependent transport in SO coupled systems: Das-Datta transistor paradigm Spin dependent transport in SO coupled systems: Das-Datta transistor paradigm Spin-Hall effect Spin-Hall effect Basic pheonemonlogy Basic pheonemonlogy Some settled issues: mini-workshop on spin-Hall effect Some settled issues: mini-workshop on spin-Hall effect Spin Hall effect in the mesoscopic regime Spin Hall effect in the mesoscopic regime Why study the mesoscopic regime Why study the mesoscopic regime Transport indications of SHE in the mesoscopic regime Transport indications of SHE in the mesoscopic regime Spin accumulation in ballistic and coherent systems Spin accumulation in ballistic and coherent systems Aharonov-Casher effect in mesoscopic rings Aharonov-Casher effect in mesoscopic rings

Non-equilibrium Green’s function formalism (Keldysh-LB) Advantages: No worries about spin-current definition. Defined in leads where SO=0 Well established formalism valid in linear and nonlinear regime Easy to see what is going on locally SHE in the mesoscopic regime

Spin Hall effect in the mesoscopic regime, simplifying the debate Hankiewicz, Molenkamp, Jungwirth, Sinova, PRB 70, (R) (2004). Also: Sheng et al, PRL 05 Nikolic et al, PRB 05 6

Actual gated H-bar sample HgTe-QW  R = 5-15 meV 5  m ohmic Contacts Gate- Contact Unfortunately the device is too large to observe coherent transport

Nikolic, Souma, Zarbo, and Sinova, PRL 05 Spin accumulation in mesoscopic systems

x100, E F =-3.8t, t so =0.1t Non-linear regime Rashba Model

OUTLINE Spin dependent transport in SO coupled systems: Das-Datta transistor paradigm Spin dependent transport in SO coupled systems: Das-Datta transistor paradigm Spin-Hall effect Spin-Hall effect Basic pheonemonlogy Basic pheonemonlogy Some settled issues: mini-workshop on spin-Hall effect Some settled issues: mini-workshop on spin-Hall effect Spin Hall effect in the mesoscopic regime Spin Hall effect in the mesoscopic regime Why study the mesoscopic regime Why study the mesoscopic regime Transport indications of SHE in the mesoscopic regime Transport indications of SHE in the mesoscopic regime Spin accumulation in ballistic and coherent systems Spin accumulation in ballistic and coherent systems Aharonov-Casher effect in mesoscopic rings Aharonov-Casher effect in mesoscopic rings

HgTe Ring-Structures Three phase factors: Aharonov-Bohm Berry Aharonov-Casher

High Electron Mobility  > 3 x 10 5 cm 2 /Vsec

Rashba Effect in HgTe Rashba splitting energy 8 x 8 k  p band structure model A. Novik et al., PRB 72, (2005). Y.S. Gui et al., PRB 70, (2004).

HgTe Ring-Structures Modeling E. Hankiewicz, J. Sinova, Concentric Tight Binding Model + B-field

CONCLUSION Spin Hall effect is robust in the mesoscopic regime Spin Hall effect is robust in the mesoscopic regime Coherent transport can in principle be used as a spin injector. Coherent transport can in principle be used as a spin injector. Need to connect the two regimes (bulk, mesoscopic) Need to connect the two regimes (bulk, mesoscopic) Need a consistent spin-accumulation theory (in terms of the chiral states) Need a consistent spin-accumulation theory (in terms of the chiral states) Aharonov-Casher effect in HgTe ring nanostructure consistent with theory Aharonov-Casher effect in HgTe ring nanostructure consistent with theory

Rashba Splitting (Bychkov-Rashba) subband splitting due to macroscopic asymmetric potential spin orbit coupling in an asymetric potential  Rashba hamiltonian Rashba term  : effective mass parameter  : vector of Pauli spin matrices E : confining electric field energy dispersion in case of a hole system

Band Structure of HgTe QWs 4 nm QW 15 nm QW normal semiconductor E2 H1 H2 L1 inverted semiconductor

First Data Asymmetric HgTe-QW  R = 5-15 meV

Inverted Bandstructure type-III QW

First Data HgTe-QW  R = 5-15 meV Signal due to depletion...

Other Wafer Symmetric HgTe-QW  R = 0-5 meV Signal less than 10 -4

HgTe: Semimetal or Semiconductor D.J. Chadi et al. PRB, 3058 (1972) zero gap: fundamental gap bandstructure

Using SO: Datta-Das spin FET V - v B eff - v - v V/2

HgTe Quantum-Well wellbarrier VBO = 570 meV