Non-Abelian gauge fields in the gradient expansion: generalized Boltzmann and Eilenberger equations

Abstract

We present a microscopic derivation of the generalized Boltzmann and Eilenberger equations in the presence of non-Abelian gauges, for the case of a non-relativistic disordered Fermi gas. A unified and symmetric treatment of the charge $[U(1)]$ and spin $[SU(2)]$ degrees of freedom is achieved. Within this framework, just as the $U(1)$ Lorentz force generates the Hall effect, so does its $SU(2)$ counterpart give rise to the spin Hall effect. Considering elastic and spin-independent disorder we obtain diffusion equations for charge and spin densities and show how the interplay between an in-plane magnetic field and a time dependent Rashba term generates in-plane charge currents.

11 pages, 1 figure; some corrections and updated/extended references

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Cited by in corpus (61)

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• Theory of the spin-galvanic effect and the anomalous phase-shift ${\phi }_0$ in superconductors and Josephson junctions with intrinsic spin-orbit coupling
• Spin-orbit interaction in a two-dimensional electron gas: a SU(2) formulation
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• Persistent Skyrmion Lattice of Noninteracting Electrons with Spin-Orbit Coupling
• Theory of coupled spin-charge transport due to spin-orbit interaction in inhomogeneous two-dimensional electron liquids
• Quasiclassical theory of magnetoelectric effects in superconducting heterostructures in the presence of the spin-orbit coupling
• Long-Range Spin-Triplet Correlations and Edge Spin Currents in Diffusive Spin-Orbit Coupled SNS Hybrids with a Single Spin-Active Interface
• Ballistic spin transport in the presence of interfaces with strong spin-orbit coupling
• Theory of current-induced spin polarizations in an electron gas
• Onsager relations in a two-dimensional electron gas with spin-orbit coupling
• Optical Spintronics in Organic-Inorganic Perovskite Photovoltaics
• Generation of pure superconducting spin current in magnetic heterostructures via non-locally induced magnetism due to Landau Fermi-liquid effects
• Engineering Chiral and Topological Orbital Magnetism of Domain Walls and Skyrmions
• Transport equations for superconductors in the presence of spin interaction
• Usadel equation in the presence of intrinsic spin-orbit coupling: A unified theory of magneto-electric effects in normal and superconducting systems
• Spin Hall effects due to phonon skew scattering
• Superconductivity near a magnetic domain wall
• Nonlinear $\sigma$-model for disordered systems with intrinsic spin-orbit coupling
• Quantum kinetics of anomalous and nonlinear Hall effects in topological semimetals
• Intrinsic spin-orbit interaction in diffusive normal wire Josephson weak links: supercurrent and density of states
• Intrinsic spin Hall effect in systems with striped spin-orbit coupling
• Intrinsic Spin Torque Without Spin-Orbit Coupling
• Effective Quantum Theories for Transport in Inhomogeneous Systems with Non-trivial Band Structure
• Supercurrent generation by spin injection in an s-wave superconductor-Rashba metal bilayer
• Theory of the inverse spin galvanic effect in quantum wells
• Spin-orbit induced equilibrium spin currents in materials
• Room temperature spin thermoelectrics in metallic films
• Spin-charge coupled dynamics driven by a time-dependent magnetization
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• Theory of inverse Rashba-Edelstein effect induced by spin pumping into a two-dimensional electron gas
• Semiclassical kinetic theory for systems with non-trivial quantum geometry and the expectation value of physical quantities
• Quantum Kinetic Theory of the Linear Response for Weakly Disordered Multiband Systems
• Nonlocal magnetolectric effects in diffusive conductors with spatially inhomogeneous spin-orbit coupling
• A Unified Description of Spin Transport, Weak Antilocalization and Triplet Superconductivity in Systems with Spin-Orbit Coupling
• Boltzmann approach to spin-orbit-induced transport in effective quantum theories
• Interplay between superconductivity and spin-dependent fields in nanowire-based systems
• Theory of the inverse Rashba-Edelstein effect induced by thermal spin injection
• Magnetoelectric effects in diffusive two-dimensional superconductors studied by the nonlinear $\sigma$ model
• Quasiclassical theory of the spin-orbit magnetoresistance of three-dimensional Rashba metals
• Current-induced spin polarization in InGaAs and GaAs epilayers with varying doping densities
• Sinusoidal magnetic field induced topological excitations in a spin-orbit coupled spinor condensate
• Nonuniversality of the intrinsic inverse spin-Hall effect in diffusive systems
• Electric field effect on electron gas spins in two-dimensional magnets with strong spin-orbit coupling
• Probing the Spin-Momentum Locking in Rashba Surfaces via Spin Current
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• Quantum kinetic equations and anomalous non-equilibrium Cooper pair spin accumulation in Rashba wires with Zeeman splitting
• Spin Hall magnetoresistance and spin Nernst magnetothermopower: role of the inverse spin galvanic effect
• The spin Hall effect
• Spin polarization induced by an electric field in the presence of weak localization effects
• Dynamical Spin-Orbit-Based Spin Transistor
• Thermodynamics and emergent thermomechanical response of a quantum ring with nonminimal spin--orbit coupling
• Gradient expansion of the non-Abelian gauge-covariant Moyal star-product