Gauge Fields in the Theory of Condensed Matter and Helicity Conservation
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RETICAL AND MATHEMATICAL PHYSICS
Gauge Fields in the Theory of Condensed Matter and Helicity Conservation M. Iv. Trukhanova* Department of Physics, Moscow State University, Moscow, 119991 Russia Received November 23, 2019; revised December 23, 2019; accepted December 24, 2019
Abstract—A model of the quantum hydrodynamics of a charged particle in an external electromagnetic field is considered with account for the spin–orbit interaction and the influence of the Zeeman energy. The model is based on the formalism of introducing non-Abelian Yang–Mills gauge fields. It is shown that non-Abelian gauge fields generate forces, that act on the spin and spin current. It is demonstrated that the helicity of a particle moving on the background of such fields, that create forces that depend on the spin of the particle, is not conserved. A two-fluid model of quantum hydrodynamics is developed for systems of electrons in spin-up and spin-down states moving against the background of the magnetic structure of a skyrmion with a nontrivial topology. A system of continuity equations, momentum balance, and evolution equations of spin density is constructed, and the helicity conservation for electron fluxes is proved in the framework of the proposed two-fluid model. Keywords: gauge fields, quantum hydrodynamics, magnetic skyrmions, electron–skyrmion interaction. DOI: 10.3103/S0027134920020137
INTRODUCTION In studying the properties of the Rashba–Dresselhaus spin–orbit coupling and the interaction of charged particles with nontrivial magnetic structures, it is rather convenient to introduce gauge fields and consider the evolution of particles that move on the background of these fields [1]. In the nonrelativistic case, the formalism of this approach is based on the Pauli equation for a particle moving on the background of Maxwell’s electromagnetic field U (1) and the Yang–Mills gauge field SU (2) [2, 3]. The model of evolution of spin and charge currents in the medium with the Rashba–Dresselhaus spin– orbit coupling was formulated based on the fourdimensional U (1) × SU (2) gauge theory. It has been shown, that the total spin current containing the contribution of the Yang–Mills field intensity is conserved [2]. One interesting area of application of the method of introducing gauge fields is the investigation of behavior of topologically nontrivial magnetic structure of skyrmions [4–8], especially, its interaction with the charge current. The electrons may interact with the local magnetic moments of a skyrmion via the strong Hund coupling, which tends to orient the electron *
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spins in the direction of local moments due to the spin transfer torque mechanism. We may consider such coupling by using the formalism of gauge fields, when the electron moves in the adiabatic approximation in the background of Abelian gauge fields capturing the Berry phase [9–13]. An electron in such a model regards the spin structure of a skyrmion as the source of a gauge “magnetic” field and the moving skyrmion as the source of a gauge “electric” field
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