Quantum skyrmion Hall effect

Abstract: Motivated by recent discovery of additional topologically non-trivial phases of matter in lattice models beyond established classification schemes, we generalize the framework of the quantum Hall effect (QHE) to that of the quantum skyrmion Hall effect (QSkHE). This generalization may be stated in terms of Landau level projection. Considering particles on a two-sphere, which see a U(1) monopole, one can project to the lowest Landau level (LLL). Upon performing such a projection, the possible position coordinates of the particles reduce to the quantum numbers of the single-particle orbitals of the LLL. The key generalization of the QSkHE is that an almost point-like LLL, corresponding to matrix representation size for the position operators of N by N, with N small and correspondingly small orbital degeneracy, can still host an intrinsically 2+1 dimensional, topologically non-trivial many-body state (2 space dimensions and 1 time dimension). Equivalently, in regimes in which spin has previously been treated only as a label of quantum states (small N), spin more generally encodes some finite number of spatial dimensions. This many-body state hosted by the almost point-like LLL can play the role, in the QSkHE, that a charged particle plays in the QHE. We discuss the relevance of these findings for HgTe quantum wells and Van der Waals heterostructure materials.

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Walter

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