Pure Gauge Spin-Orbit Couplings

Abstract

Planar systems with a general linear spin-orbit interaction (SOI) that can be cast in the form of a non-Abelian pure gauge field are investigated using the language of non-Abelian gauge field theory. A special class of these fields that, though a $2\times 2$ matrix, are Abelian are seen to emerge and their general form is given. It is shown that the unitary transformation that gauges away these fields induces at the same time a rotation on the wavefunction about a fixed axis but with a space-dependent angle, both of which being characteristics of the SOI involved.The experimentally important case of equal-strength Rashba and Dresselhaus SOI (R+D SOI) is shown to fall within this special class of Abelian gauge fields, and the phenomenon of Persistent Spin Helix (PSH) that emerges in the presence of this latter SOI in a plane is shown to fit naturally within the general formalism developed. The general formalism is also extended to the case of a particle confined to a ring. It is shown that the Hamiltonian on a ring in the presence of equal-strength R+D SOI is unitarily equivalent to that of a particle subject to only a spin-independent but $\theta$-dependent potential with the unitary transformation relating the two being again the space-dependent rotation operator characteristic of R+D SOI.

arXiv comment7 pages

References in corpus (16)

• Spintronics: Fundamentals and applications
• Non-ballistic spin field-effect transistor
• An Exact SU(2) Symmetry and Persistent Spin Helix in a Spin-Orbit Coupled System
• Emergence of the persistent spin helix in semiconductor quantum wells
• Direct mapping of the formation of a persistent spin helix: Supplementary information
• Spin states and persistent currents in mesoscopic rings: spin-orbit interactions
• Equilibrium spin currents: Non-Abelian gauge invariance and color diamagnetism in condensed matter
• SU(2)xU(1) unified theory for charge, orbit and spin currents
• Mesoscopic rings with Spin-Orbit interactions
• Non-Abelian spin-orbit gauge: Persistent spin helix and quantum square ring
• Gauge symmetry breaking and topological quantization for the Pauli Hamiltonian
• Classical Yang-Mills theory in condensed matter physics
• Hamiltonian for a particle in a magnetic field on a curved surface in orthogonal curvilinear coordinates
• Hermitian spin-orbit Hamiltonians on a surface in orthogonal curvilinear coordinates: a new practical approach
• Hermitian and Gauge-Covariant Hamiltonians for a particle in a magnetic field on Cylindrical and Spherical Surfaces
• Gauge Covariance and Spin Current Conservation in the Gauge Field Formulation of Systems with Spin-Orbit Coupling

Cited by in corpus (2)

• Skin effect and dynamical delocalization in non-Hermitian quasicrystals with spin-orbit interaction
• Geometric effects resulting from square and circular confinements for a particle constrained to a space curve