Skyrmion quantum spin Hall effect

Abstract

The quantum spin Hall effect is conventionally thought to require a strong spin-orbit coupling, producing an effective spin-dependent magnetic field. However, spin currents can also be present without transport of spins, for example, in spin-waves or skyrmions. In this paper, we show that topological skyrmionic spin textures can be used to realize a quantum spin Hall effect. From basic arguments relating to the single-valuedness of the wave function, we deduce that loop integrals of the derivative of the Hamiltonian must have a spectrum that is integer multiples of $2\pi$. By relating this to the spin current, we form a new quantity called the quantized spin current which obeys a precise quantization rule. This allows us to derive a quantum spin Hall effect, which we illustrate with an example of a spin-1 Bose-Einstein condensate.

7 pages, 2 figures (published in PRB)

References in corpus (12)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Skyrmion Hall Effect Revealed by Direct Time-Resolved X-Ray Microscopy
• The Quantum Spin Hall Effect: Theory and Experiment
• On A Proper Definition of Spin Current
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• Skyrmion Lattice in Two-Dimensional Chiral Magnet
• Topological Magnons and Edge States in Antiferromagnetic Skyrmion Crystals
• Quantum Hall physics in rotating Bose-Einstein condensates
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• Integer and Fractional Quantum Anomalous Hall Effect in a Strip of Stripes Model

Cited by in corpus (2)

• Majorana braiding gates for topological superconductors in a one dimensional geometry
• Self-dual compact gauged baby skyrmions in a continuous medium