Spin Hall effect and Berry phase of spinning particles

2004/04/30 by Alain Bérard, Herve Mohrbach, Hervé Mohrbach · 9 citations
Physics and Astronomy · #Berry connection and curvature #Classical mechanics #Dirac equation #Gauge theory #Geometric phase #Mathematical physics #Noncommutative and Quantum Gravity Theories #Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum electrodynamics #Quantum mechanics #Spin (aerodynamics) #Topological Materials and Phenomena #cond-mat.other #hep-th

paper · pdf · doi:10.1016/j.physleta.2005.11.071

published as Phys.Lett. A352 (2006) 190-195 · published with the following title: Spin Hall effect and Berry phase of spinning particles

openalex publication_date 2005/12/02 · arxiv created 2006/03/27 · arxiv updated 2016/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We consider the adiabatic evolution of the Dirac equation in order to compute its Berry curvature in momentum space. It is found that the position operator acquires an anomalous contribution due to the non Abelian Berry gauge connection making the quantum mechanic algebra noncommutative. A generalization to any known spinning particles is possible by using the Bargmann-Wigner equation of motions. The noncommutativity of the coordinates is responsible of the topological spin transport of spinning particle similarly to the spin Hall effect in spintronic physics or the Magnus effect in optics. As an application we predict new dynamics for nonrelativistic particles in an electric field and for photons in a gravitational field.

Citations

• String theory and noncommutative geometry
• Modified geometrical optics of a smoothly inhomogeneous isotropic medium: The anisotropy, Berry phase, and the optical Magnus effect
• The Non-commutative Landau Problem
• THE LANDAU PROBLEM AND NONCOMMUTATIVE QUANTUM MECHANICS
• New varying speed of light theories
• Topological spin transport of photons: the optical Magnus effect and Berry phase
• Dissipationless Quantum Spin Current at Room Temperature
• Topological Nature of Anomalous Hall Effect in Ferromagnets
• Quantal phase factors accompanying adiabatic changes
• Hydrogen Atom Spectrum and the Lamb Shift in Noncommutative QED

Cited by

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• Spinning-particle model for the Dirac equation and the relativistic Zitterbewegung
• Paraxial propagation in disclinated amorphous media
• Noncommutative configuration space: classical and quantum mechanical aspects
• Spin Hall effect of photons in a static gravitational field
• Transverse and longitudinal angular momenta of light
• Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium
• Geometrical Optics of Beams with Vortices: Berry Phase and Orbital Angular Momentum Hall Effect
• Non-Abelian evolution of electromagnetic waves in a weakly anisotropic inhomogeneous medium