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 (32)

• Spontaneous Edge Accumulation of Spin Currents in Finite-Size Two-Dimensional Diffusive Spin-Orbit Coupled SFS Heterostructures
• Theory of coupled spin-charge transport due to spin-orbit interaction in inhomogeneous two-dimensional electron liquids
• 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
• Nonlinear $\sigma$-model for disordered systems with intrinsic spin-orbit coupling
• Quantum kinetics of anomalous and nonlinear Hall effects in topological semimetals
• Supercurrent generation by spin injection in an s-wave superconductor-Rashba metal bilayer
• Spin-orbit induced equilibrium spin currents in materials
• Spin-charge coupled dynamics driven by a time-dependent magnetization
• A generalized Stoner criterion and versatile spin ordering in two-dimensional spin-orbit coupled electron systems
• Room temperature spin thermoelectrics in metallic films
• Spin Hall and inverse spin galvanic effects in graphene with strong interfacial spin-orbit coupling: a quasi-classical Green's function approach
• The Higgs-Amplitude mode in the optical conductivity in the presence of a supercurrent: Gauge-invariant formulation with disorder
• Spin current swapping and Hanle spin Hall effect in the two dimensional electron gas
• Quantum Kinetic Theory of the Linear Response for Weakly Disordered Multiband Systems
• 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
• A Unified Description of Spin Transport, Weak Antilocalization and Triplet Superconductivity in Systems with Spin-Orbit Coupling
• Current-induced spin polarization in InGaAs and GaAs epilayers with varying doping densities
• Magnetoelectric effects in diffusive two-dimensional superconductors studied by the nonlinear $\sigma$ model
• Theory of the inverse Rashba-Edelstein effect induced by thermal spin injection
• Interplay between superconductivity and spin-dependent fields in nanowire-based systems
• Sinusoidal magnetic field induced topological excitations in a spin-orbit coupled spinor condensate
• 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
• Spin-conserving Boltzmann theory for carriers and excitons in organic semiconductors
• Driving spin and charge in quantum wells by surface acoustic waves
• Quantum kinetic equations and anomalous non-equilibrium Cooper pair spin accumulation in Rashba wires with Zeeman splitting
• The spin Hall effect
• 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