Quantum skyrmion Hall effect

Field: condensed matter physics
Keywords: topology, electron-based quantum skyrmions, spin, Berry curvature

Abstract: Topological skyrmion phases of matter are recently-introduced topological phases of electronic systems in equilibrium, in which a system with more than one degree of freedom (e.g. spin and orbital degrees of freedom) realizes a topological state for a subset of the degrees of freedom (e.g. only spin). For topological skyrmion phases of spin, this topology is relevant even if spin is not conserved due to non-negligible atomic spin-orbit coupling, and is distinguished by a skyrmion forming in the spin texture over the Brillouin zone, distinct from a skyrmion forming in the texture of the projector onto occupied states over the Brillouin zone.
We present results on three band Bloch Hamiltonians realizing this non-trivial spin topology, and outline some bulk-boundary correspondence features, such as gapless edge states corresponding to zero net charge—but finite spin angular momentum—pumped across the bulk gap. Tracing out the orbital degree of freedom, we can identify this spin pumping with pumping of spin point charges, and local curvature of the k-space spin skyrmion with a Berry curvature of these spin point charges. That is, the spin pumping is identified with pumping of spin magnetic skyrmions, which reduce to point magnetic charges after tracing out the orbital degree of freedom.
We therefore identify topological skyrmion phases as lattice counterparts of quantized transport of quantum magnetic skyrmions, a quantum skyrmion Hall effect. This indicates that the theory of the quantum Hall effect must be generalized, by relaxing the assumption of point charges.