Spin Hall effect and Berry phase of spinning particles

Bérard, Alain; Mohrbach, Hervé

doi:10.1016/j.physleta.2005.11.071

Cited by 135 publications

(212 citation statements)

References 40 publications

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“…The Berry phase approach has been successfully adopted to explain various quantum mechanical/semiclassical aspects of different systems in condensed matter physics [22][23][24][25][26][27]. In particular, the studies on momentum space Berry phase associated to spin Hall effect [28][29][30][31]has become a topic of great recent interest . One of the avenues to investigate the motion of spins through gauge theories entails the study of the gauge fields, which naturally couples to the spin.…”

Section: Introductionmentioning

confidence: 99%

The effect of inertia on the Dirac electron, the spin Hall current and the momentum space Berry curvature

Chowdhury¹,

Basu²

2013

Annals of Physics

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We have studied the spin dependent force and the associated momentum space Berry curvature in an accelerating system. The results are derived by taking into consideration the non relativistic limit of a generally covariant Dirac equation under the presence of electromagnetic field where the methodology of Foldy-Wouthuysen transformation is applied to achieve the non relativistic limit. Spin currents appear due to the combined action of the external electric field, crystal field and the induced inertial electric field via the total effective spin-orbit interaction. In an accelerating frame, the crucial role of momentum space Berry curvature in the spin dynamics has also been addressed from the perspective of spin Hall conductivity. For time dependent acceleration, the expression for the spin polarization has been derived.

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Section: Introductionmentioning

confidence: 99%

The effect of inertia on the Dirac electron, the spin Hall current and the momentum space Berry curvature

Chowdhury¹,

Basu²

2013

Annals of Physics

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“…At the same time, recent studies have shown, that even in isotropic smoothly inhomogeneous medium the ray equations acquire additional terms of the first order in GO µ [5−11]. These terms are caused by the spin-orbit interaction of photons (also responsible for the Berry phase) [5,8] and provide for the conservation of the total angular momentum of a wave, including its spin part [8,9]. Due to spinorbit interaction of photons a smoothly inhomogeneous isotropic medium can be considered as a weakly anisotropic one in the first approximation in GO µ [6].…”

Section: Introductionmentioning

confidence: 99%

“…is a pure gauge potential in the p -space, induced by the local gauge transformation (9) and ′ = + R R A Ż (13) is the operator of covariant coordinates corresponding to the center of the semiclassical wave packet [7,8,10].…”

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confidence: 99%

Non-Abelian evolution of electromagnetic waves in a weakly anisotropic inhomogeneous medium

2007

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A theory of electromagnetic wave propagation in a weakly anisotropic smoothly inhomogeneous medium is developed, based on the quantum-mechanical diagonalization procedure applied to Maxwell equations. The equations of motion for the translational (ray) and intrinsic (polarization) degrees of freedom are derived ab initio. The ray equations take into account the optical Magnus effect (spin Hall effect of photons) as well as trajectory variations owing to the medium anisotropy. Polarization evolution is described by the precession equation for the Stokes vector. In generic case, the evolution of wave turns out to be non-Abelian: it is accompanied by mutual conversion of the normal modes and periodic oscillations of the ray trajectories analogous to electron zitterbewegung. The general theory is applied to examples of wave evolution in media with circular and linear birefringence.

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“…The results reveal the nature of the spin-Hall effect -the spin-dependent geometric phase of partial waves brings about a spin-dependent transverse shift of the resulting confined wave field. In contrast to semiclassical theories implying paraxial confined waves [ 15,16,18,21], our experiment dealt with a highly nonparaxial field. As a result, the transverse shift is comparable with the focal spot width and is readily detected.…”

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confidence: 99%

Coriolis Effect in Optics: Unified Geometric Phase and Spin-Hall Effect

et al. 2008

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We examine the spin-orbit coupling effects that appear when a wave carrying intrinsic angular momentum interacts with a medium. The Berry phase is shown to be a manifestation of the Coriolis effect in a non-inertial reference frame attached to the wave. In the most general case, when both the direction of propagation and the state of the wave are varied, the phase is given by a simple expression that unifies the spin redirection Berry phase and the Pancharatnam-Berry phase. The theory is supported by the experiment demonstrating the spin-orbit coupling of electromagnetic waves via a surface plasmon nano-structure. The measurements verify the unified geometric phase, demonstrated by the observed polarization-dependent shift (spin-Hall effect) of the waves.PACS numbers: 03.65. Vf, 41.20.Jb, Introduction.-Geometric phase is an inherent feature of the polarization optics that appears under evolution of electromagnetic waves in inhomogeneous and anisotropic media [1]. There are two types of geometric phases: (i) the spin redirection Rytov-Vladimirskii-Berry phase associated with the parallel transport of the wave field under SO(3) variations of the direction of propagation of the wave [2,3] and (ii) the Pancharatnam-Berry phase that occurs under SU(2) manipulations with the polarization state of light [4,5]. In the general case, when both the direction of propagation and polarization state of the wave are varied, the geometric phase becomes more intricate [6,7,8,9], and a unified geometrical description of the phase requires the tricky Majorana representation [8].

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Spin Hall effect and Berry phase of spinning particles

Cited by 135 publications

References 40 publications

The effect of inertia on the Dirac electron, the spin Hall current and the momentum space Berry curvature

The effect of inertia on the Dirac electron, the spin Hall current and the momentum space Berry curvature

Non-Abelian evolution of electromagnetic waves in a weakly anisotropic inhomogeneous medium

Coriolis Effect in Optics: Unified Geometric Phase and Spin-Hall Effect

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