Understanding spin Hall effect in two-dimensional fermionic systems with generic spin–orbit interaction in III–V heterostructures

Paul, Boudhayan; Ghosh, Tarun Kanti

doi:10.1016/j.physleta.2014.11.060

Cited by 5 publications

(3 citation statements)

References 37 publications

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“…We note that a similar derivation was proposed in Ref. [21], in which the effective magnetic field is replaced by a pseudo-magnetic field derived from the spin force. In the following section, we solve s ′ by acquiring the boundary conditions for Eqs.…”

Section: D Hamiltonian and Drude Modelmentioning

confidence: 68%

The semiclassical theory for spin dynamics in a disordered system

Chen¹,

Hsu²

2020

Preprint

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We investigate the Drude model of spin dynamics in two-dimensional spin-orbit coupled systems. In the absence of an applied electric field, the spin aligns with the k-dependent effective magnetic field. The influence of disorder (the momentum relaxation time τ ) on the system is considered. In the presence of an electric field, the change in momentum causes a change in the effective magnetic field. The in-plane spin can precess around the successive change in the orientation of the effective magnetic field. We find that up to the linear order of the electric field, the spin orientation undergoes Larmor-like and non-Larmor like precession. Furthermore, we find that the non-Larmor motion over a very short time (t ≪ τ ) exactly equals the result obtained from the Kubo formula. This means that the Kubo formula only captures the system's response over a very short evolution. The spin-Hall conductivity for Larmor and non-Larmor precession in the Rashba system is analytically calculated. We find that the intrinsic spin-Hall current is not a universal constant and correctly drops to zero when the Rashba spin-orbit coupling drops to zero. We also calculate the time-averaged Larmor and non-Larmor spin-Hall conductivities (SHCs) for the k-cubic Rashba system and compare them to experimental values. The time-averaged Larmor SHC vanishes and the non-Larmor SHC is given by 2.1(q/8π) which is very close to the experimental value 2.2(q/8π) by Wunderlich et al. [Phys. Rev. Lett. 94, 047204 (2005)].

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Section: D Hamiltonian and Drude Modelmentioning

confidence: 68%

The semiclassical theory for spin dynamics in a disordered system

Chen¹,

Hsu²

2020

Preprint

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“…For β = 0, one can obtain the following approximate expressions for the expectation values: x ≃ (3/2k 0 )[1 − cos(ω 0 t)], v x ≃ (3αk 2 0 / ) sin(ω 0 t), S y ≃ (3 /2) sin(ω 0 t), S z ≃ (3 /2) cos(ω 0 t), and F x ≃ f 0 cos(ω 0 t) where ω 0 = 2αk 3 0 / and f 0 = 6m * α 2 k 5 0 / 2 . Due to the presence of SOI, an effective Lorentz-like magnetic field [54] can be obtained in the following form B s = 2m * 2 α 2 p 4 g(θ)σ z ẑ/(e 7 ). In the a 0 ≫ 1 limit and when β = 0 we obtain B s ≃ B 0 cos(ω 0 t) where B 0 = 6m * 2 α 2 k 4 0 /(e 3 ).…”

Section: Persistent Zitterbewegung and Possible Detectionmentioning

confidence: 99%

Zitterbewegung of a heavy hole in presence of spin-orbit interactions

2015

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We study the zitterbewegung of a heavy hole in presence of both cubic Rashba and cubic Dresselhaus spin-orbit interactions. On contrary to the electronic case, zitterbewegung does not vanish for equal strength of Rashba and Dresselhaus spin-orbit interaction. This non-vanishing of zitterbewegung is associated with the Berry phase. Due to the presence of the spin-orbit coupling the spin associated with the heavy hole precesses about an effective magnetic field. This spin precession produces a transverse spin-orbit force which also generates an electric voltage associated with zitterbewegung. We have estimated the magnitude of this voltage for a possible experimental detection of zitterbewegung.

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“…In a spin-orbit coupled system, an electrical charge current can yield a transverse pure spin current with polarization perpendicular to the plane of the charge and spin current. This is known as spin Hall current which arises mainly due to an intrinsic mechanism governed by the geometry of the Bloch wave functions [26][27][28][29][30]. Further, it may appear because of the extrinsic mechanism such as the skew scattering [31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Role of Berry curvature in the generation of spin currents in Rashba systems

Kapri,

Dey,

Ghosh

2021

Preprint

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We study the background (equilibrium), linear and nonlinear spin currents in 2D Rashba spinorbit coupled systems with Zeeman splitting and in 3D noncentrosymmetric metals using modified spin current operator by inclusion of the anomalous velocity. The linear spin Hall current arises due to the anomalous velocity of charge carriers induced by the Berry curvature. The nonlinear spin current occurs due to the band velocity and/or the anomalous velocity. For 2D Rashba systems, the background spin current saturates at high Fermi energy (independent of the Zeeman coupling), linear spin current exhibits a plateau at the 'Zeeman' gap and nonlinear spin currents are peaked at the gap edges. The magnitude of the nonlinear spin current peaks enhances with the strength of Zeeman interaction. The linear spin current is polarized out of plane, while the nonlinear ones are polarized in-plane. We witness pure anomalous nonlinear spin current with spin polarization along the direction of propagation. In 3D noncentrosymmetric metals, background and linear spin currents are monotonically increasing functions of Fermi energy, while nonlinear spin currents vary non-monotonically as a function of Fermi energy and are independent of the Berry curvature. These findings may provide useful information to manipulate spin currents in Rashba spin-orbit coupled systems.

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Understanding spin Hall effect in two-dimensional fermionic systems with generic spin–orbit interaction in III–V heterostructures

Cited by 5 publications

References 37 publications

The semiclassical theory for spin dynamics in a disordered system

The semiclassical theory for spin dynamics in a disordered system

Zitterbewegung of a heavy hole in presence of spin-orbit interactions

Role of Berry curvature in the generation of spin currents in Rashba systems

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