Topological spin transport of relativistic electron

Abstract

We derive the semiclassical (with accuracy of $\hslash$) motion equation for relativistic electron, which follow from the Dirac equation. We determine both the evolution equation for electron polarization, which takes the non-Abelian Berry phase into account, and Hamiltonian equations for trajectories of the particle (wave packet) center in the phase space. The equations have covariant form with respect to U(2) gauge transformations and contain topological spin terms that are connected to the Berry gauge field arising during the diagonalization of the Dirac equation. The trajectory equations obtained are substantially different from the traditional ones (for instance, those that follow from the Pauli Hamiltonian) and correspond to contemporary ideas of topological spin transport of particles.

10 pages, to appear in Europhysics Letters

References in corpus (16)

• Dissipationless Quantum Spin Current at Room Temperature
• Experimental observation of the spin-Hall effect in a two dimensional spin-orbit coupled semiconductor system
• Hall Effect of Light
• Wave-packet dynamics in slowly perturbed crystals: Gradient corrections and Berry-phase effects
• First Principles Calculation of Anomalous Hall Conductivity in Ferromagnetic bcc Fe
• Berry phase, hyperorbits, and the Hofstadter spectrum: semiclassical dynamics in magnetic Bloch bands
• Dissipationless Anomalous Hall Current in the Ferromagnetic Spinel CuCr${}_2$Se${}_{4-x}$Br${}_x$
• Semiclassical theory of spin transport in spin-orbit coupled systems
• Topological spin transport of photons: the optical Magnus Effect and Berry Phase
• A semiclassical approach to the Dirac equation
• Modified geometrical optics of a smoothly inhomogeneous isotropic medium: the anisotropy, Berry phase, and the optical Magnus effect
• Spin Gauge Fields: from Berry Phase to Topological Spin Transport and Hall Effects
• Monopole and Berry Phase in Momentum Space in Noncommutative Quantum Mechanics
• Semiclassical limit of the Dirac equation and spin precession
• Topological spin transport of photons: "magnetic monopole" gauge field in Maxwell equations and polarization splitting of rays in periodically inhomogeneous media
• Topological spin pumps I

Cited by in corpus (63)

• Berry Phase Effects on Electronic Properties
• Theory and applications of free-electron vortex states
• Semiclassical Dynamics of Electron Wave Packet States with Phase Vortices
• Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium
• Relativistic Electron Vortex Beams: Angular Momentum and Spin-Orbit Interaction
• Chiral transport equation from the quantum Dirac Hamiltonian and the on-shell effective field theory
• Spin Hall effect of Photons in a Static Gravitational Field
• Kinetic theory of chiral relativistic plasmas and energy density of their gauge collective excitations
• Relativistic Hall Effect
• Semi-relativistic effects in spin-1/2 quantum plasmas
• Non-Abelian evolution of electromagnetic waves in a weakly anisotropic inhomogeneous medium
• Berry Phase, Lorentz Covariance, and Anomalous Velocity for Dirac and Weyl Particles
• Semiclassical Diagonalization of Quantum Hamiltonian and Equations of Motion with Berry Phase Corrections
• Polarization Transport of Transverse Acoustic Waves: Berry Phase and Spin Hall Effect of Phonons
• Spin and orbital Hall effects for diffracting optical beams in gradient-index media
• General method of the relativistic Foldy-Wouthuysen transformation and proof of validity of the Foldy-Wouthuysen Hamiltonian
• Quantum Mechanics with a Momentum-Space Artificial Magnetic Field
• Position and spin in relativistic quantum mechanics
• Semiclassical Dynamics of Electrons in Magnetic Bloch Bands: a Hamiltonian Approach
• General properties of the Foldy-Wouthuysen transformation and applicability of the corrected original Foldy-Wouthuysen method
• Semiclassical dynamics and transport of the Dirac spin
• Semiclassical Dynamics of Dirac particles interacting with a Static Gravitational Field
• Relativistic quantum dynamics of twisted electron beams in arbitrary electric and magnetic fields
• Position, spin and orbital angular momentum of a relativistic electron
• Comparative analysis of direct and "step-by-step" Foldy-Wouthuysen transformation methods
• Berry Curvature in Graphene: A New Approach
• Relativistic Spin-Orbit Interactions of Photons and Electrons
• Exact form of the exponential Foldy-Wouthuysen transformation operator for an arbitrary-spin particle
• On the Hamiltonian nature of semiclassical equations of motion in the presence of an electromagnetic field and Berry curvature
• General relativity effects in precision spin experimental tests of fundamental symmetries
• Recursive Diagonalization of Quantum Hamiltonians to all order in $\hslash$
• Relativistic electron vortex beams in a laser field
• Berry phase and anomalous velocity of Weyl fermions and Maxwell photons
• Effective Quantum Theories for Transport in Inhomogeneous Systems with Non-trivial Band Structure
• High-order Foldy-Wouthuysen transformations of the Dirac and Dirac-Pauli Hamiltonians in the weak-field limit
• Semiclassical quantization of electrons in magnetic fields: the generalized Peierls substitution
• Relativistic quantum mechanics of a Proca particle in Riemannian spacetimes
• Diagonal Representation for a Generic Matrix Valued Quantum Hamiltonian
• Electron vortex beams in a magnetic field and spin filter
• Correspondence between classical and Dirac-Pauli spinors in view of the Foldy-Wouthuysen transformation
• Black hole mirages: electron lensing and Berry curvature effects in inhomogeneously tilted Weyl semimetals
• Semiclassical dynamics of Dirac and Weyl particles in rotating coordinates
• Foldy-Wouthuysen transformation for a Dirac-Pauli dyon and the Thomas-Bargmann-Michel-Telegdi equation
• Non-relativistic expansion of single-nucleon Dirac equation: Comparison between Foldy-Wouthuysen transformation and similarity renormalization group
• Electronic transport and the related anomalous effects in silicene-like hexagonal lattice
• Exact Foldy-Wouthuysen transformation of the Dirac-Pauli Hamiltonian in the weak-field limit by the method of direct perturbation theory
• Spin dynamics with non-abelian Berry gauge fields as a semiclassical constrained hamiltonian system
• The geometric phase and the geometrodynamics of relativistic electron vortex beams
• Topology of Generalized Spinors and Chiral Anomaly
• Helicity of spin-extended chiral particles
• Momentum-space Landau levels in driven-dissipative cavity arrays
• Theory of wavepacket transport under narrow gaps and spatial textures: non-adiabaticity and semiclassicality
• Appearance of Gauge Fields and Forces beyond the adiabatic approximation
• Artificial Magnetic Fields in Momentum Space in Spin-Orbit Coupled Systems
• Transverse force generated by an electric field and transverse charge imbalance in spin-orbit coupled systems
• Appearance of Gauge Fields and Forces beyond the adiabatic approximation
• Topological Force and Torque in Spin-Orbit Coupling System
• Leading correction to the relativistic Foldy-Wouthuysen Hamiltonian
• Hidden momentum of electrons, nuclei, atoms and molecules
• Spin Currents of Charged Dirac Particles in Rotating Coordinates
• Relativistic properties of a molecule: energy, linear momentum, angular momentum and boost momentum to order $1/c^2$
• Thomas precession, persistent spin currents and quantum forces
• A Quantum Mechanical Approach To The Polarization Transport of Photons