Disorder effects on the spin-Hall current in a diffusive Rashba two-dimensional heavy-hole system

Liu, S. Y.; Lei, X. L.

doi:10.1103/physrevb.72.155314

Cited by 35 publications

(14 citation statements)

References 30 publications

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“…For example, taking ζ = 0 and H α,h , with N = Ñ = 3 , we see that the sign of σ SH in Equation [Equation ( 32)] is opposite to the case of isotropic scattering [Equation ( 31)]. Similarly, Liu and Lei (2005) found in a numerical study of system with spin-orbit coupling H α,h that σ SH strongly depends on the type of the scattering potential. Therefore, the spin Hall conductivity is not a universal quantity, as its numerical prefactor and its sign depend on sample parameters.…”

Section: Spin Currents In Bulkmentioning

confidence: 63%

Theory of Spin Hall Effects in Semiconductors

Engel

Rashba

Halperin

2007

Handbook of Magnetism and Advanced Magnetic Materials

173

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Spin Hall effects are a collection of phenomena, resulting from spin-orbit coupling, in which an electrical current flowing through a sample can lead to spin transport in a perpendicular direction and spin accumulation at lateral boundaries. These effects, which do not require an applied magnetic field, can originate in a variety of intrinsic and extrinsic spin-orbit coupling mechanisms and depend on geometry, dimension, impurity scattering, and carrier density of the system-making the analysis of these effects a diverse field of research. In this article, we give an overview of the theoretical background of the spin Hall effects and summarize some of the most important results. First, we explain effective spin-orbit Hamiltonians, how they arise from band structure, and how they can be understood from symmetry considerations; including intrinsic coupling due to bulk inversion or structure asymmetry or due to strain, and extrinsic coupling due to impurities. This leads to different mechanisms of spin transport: spin precession, skew scattering, and side jump. Then we present the kinetic (Boltzmann) equations, which describe the spin-dependent distribution function of charge carriers, and the diffusion equation for spin polarization density. Next, we define the notion of spin currents and discuss their relation to spin polarization. Finally, we explain the electrically induced spin effects; namely, spin polarization and currents in bulk and near boundaries (the focus of most current theoretical research efforts), and spin injection, as well as effects in mesoscopic systems and in edge states.

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Section: Spin Currents In Bulkmentioning

confidence: 63%

Theory of Spin Hall Effects in Semiconductors

Engel

Rashba

Halperin

2007

Handbook of Magnetism and Advanced Magnetic Materials

173

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“…µ is the chemical potential, and α is the cubic Rashba term which can be adjusted experimentally. [72][73][74][75] Due to the SOC, the single particle eigenenergy splits from simple degenerate parabolic bands to two branches,…”

Section: Model Hamiltonianmentioning

confidence: 99%

Tunable correlation effects of magnetic impurities by the cubic Rashba spin-orbit couplings

Peng¹,

Lin²,

Chen³

et al. 2023

Preprint

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We theoretically study the influence of the k-cubic Rashba spin-orbit coupling (SOC) on the correlation effects of magnetic impurities by combining the variational method and the Hirsch-Fye quantum Monte Carlo (HFQMC) simulations. Markedly different from the normal k-linear Rashba SOC, even a small cubic Rashba term can greatly alter the band structure and induce a Van Hove singularity in a wide range of energy, thus the single impurity local moment becomes largely tunable. The cubic Rashba SOC adopted in this work breaks the rotational symmetry, but the host material is still invariant under the operations R z (π), IR z (π/2), Mxz, Myz, where R z (θ) is the rotation of angle θ about the z-axis, I is the inversion operator and Mxz (Myz) is the mirror reflection about the x-z (y-z) principal plane. Saliently, various components of spin-spin correlation between the single magnetic impurity and the conduction electrons show three-or sixfold rotational symmetry. This unique feature is due to the triple winding of the spins with a 2π rotation of k, which is a hallmark of the cubic Rashba effect, and can possibly be an identifier to distinguish the cubic Rashba SOC from the normal k-linear Rashba term in experiments. Although the cubic Rashba term drastically alters the electronic properties of the host, we find that the spatial decay rate of the spin-spin correlation function remains essentially unchanged. Moreover, the carrier-mediated Ruderman-Kittel-Kasuya-Yosida interactions between two magnetic impurities show twisted features, the ferromagnetic diagonal terms dominate when two magnetic impurities are very close, but the off-diagonal terms become important at long distances.

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“…Recently, this 2D heavy-hole gas with cubic Rashba SOC has been extensively studied. In such heavy-hole systems, the spin Hall effect [29,[31][32][33][34][35] and spin polarization [15,36] have been carried out theoretically, and the experimental observation of the spin Hall effect was reported [8]. Moreover, controlled spin rotation in a spin field-effect transistor setup [37] and anisotropic magnetoresistance [38] were also studied.…”

Section: Hamiltonianmentioning

confidence: 99%

“…To carry out the transport quantities, such as conductivity and spin polarization, it is necessary to derive the kinetic equation for a lesser Green function. Following the procedure presented in [17] and [32], we first carry out the Dyson equations for the real-space lesser Green functions in the spin basis and then introduce the center-of-mass time, T = (t 1 + t 2 )/2, and the relative time, τ = t 1 −t 2 . After that, the Fourier and the unitary transformations are performed and the equation reduces to the kinetic equation in the helicity basis.…”

Section: Kinetic Equationmentioning

confidence: 99%

Spin polarization induced by in-plane electric and magnetic fields in two-dimensional heavy-hole systems

Wang

Liu

Qing-fu

et al. 2010

J. Phys.: Condens. Matter

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Using a nonequilibrium Green function approach, we systematically investigate the current induced spin polarization (CISP) in a two-dimensional heavy-hole system with cubic Rashba spin-orbit coupling, driven by in-plane electric and magnetic fields. We find that when a magnetic field is applied along the direction of electric field, the longitudinal conductivity drops monotonously with an increase of magnetic-field strength or of hole density. The spin polarization along the electric-field direction is just the Pauli paramagnetism and it quadratically increases with an increase of hole density. The nonvanishing out-of-plane component of spin polarization emerges for both short-range and long-range disorders, and it changes sign with the variation of magnetic field, especially for long-range hole-impurity scattering. In the magnetic-field dependences of this out-of-plane CISP and of the in-plane CISP perpendicular to the electric field, there are singular magnetic fields, below or above which the effects of magnetic field are completely different.

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Disorder effects on the spin-Hall current in a diffusive Rashba two-dimensional heavy-hole system

Cited by 35 publications

References 30 publications

Theory of Spin Hall Effects in Semiconductors

Theory of Spin Hall Effects in Semiconductors

Tunable correlation effects of magnetic impurities by the cubic Rashba spin-orbit couplings

Spin polarization induced by in-plane electric and magnetic fields in two-dimensional heavy-hole systems

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