Particles in non-Abelian gauge potentials - Landau problem and insertion of non-Abelian flux

Abstract

We study charged spin-1/2 particles in two dimensions, subject to a perpendicular non-Abelian magnetic field. Specializing to a choice of vector potential that is spatially constant but non-Abelian, we investigate the Landau level spectrum in planar and spherical geometry, paying particular attention to the role of the total angular momentum J = L +S. After this we show that the adiabatic insertion of non-Abelian flux in a spin-polarized quantum Hall state leads to the formation of charged spin-textures, which in the simplest cases can be identified with quantum Hall Skyrmions.

24 pages, 10 figures (with corrected legends)

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Cited by in corpus (20)

• Non-Abelian gauge potentials in graphene bilayers
• The spin Hall effect in a quantum gas
• Ultracold Spin-Orbit Coupled Bose-Einstein Condensate in a Cavity: Route to Magnetic Phases Through Cavity Transmission
• WKB estimate of bilayer graphene's magic twist angles
• Ultracold atoms in U(2) non-Abelian gauge potentials preserving the Landau levels
• Focus on topological quantum computation
• Effective field theory for deformed odd-mass nuclei
• Vortex lattices for ultracold bosonic atoms in a non-Abelian gauge potential
• Fragility of the fractional quantum spin Hall effect in quantum gases
• Wong's Equations and Charged Relativistic Particles in Non-Commutative Space
• The Geometry of (non-Abelian) Landau levels
• Simulating Higher-Order Topological Insulators in Density Wave Insulators
• Strongly correlated states of trapped ultracold fermions in deformed Landau levels
• Landau-like states in neutral particles
• Noncompact dynamical symmetry of a spin-orbit coupled oscillator
• Effective field theories for collective excitations of atomic nuclei
• The N = 1 Supersymmetric Wong Equations and the Non-Abelian Landau Problem
• Cavity Optomechanics with Ultra Cold Atoms in Synthetic Abelian and Non-Abelian Gauge Field
• Line of magnetic monopoles and an extension of the Aharonov-Bohm effect
• Landau Quantization for $\Lambda$-Type Neutral Atoms in an Homogeneous Spin-Dependent Gauge Potential