Color degeneracy of competing orders near topological defects cores in planar quadratic band touching systems
arXiv:2004.13043 · doi:10.1103/8dnx-qsyx
Abstract
We study two-dimensional fermionic systems, displaying quadratic band touching in the normal state, in the presence of vortices and skyrmions of insulating and superconducting masses in the ordered phase. A prototypical example of such systems is the Bernal bilayer graphene that supports eight zero-energy modes in the presence of a mass vortex with the requisite U(1) symmetry. Near the vortex core, additional ten masses that close an SO(5) algebra can develop local expectation values by splitting the manifold of zero modes in five and ten different ways by lifting its SO(4) and SU(2) chiral symmetries, respectively. In particular, each SU(2) chiral symmetry can be broken by three distinct copies of chiral-triplet mass orders, giving rise to the notion of the color degeneracy among the competing orders near the vortex core. By contrast, a skyrmion of three anticommuting masses supports additional six masses in its core, and possesses an SU(2) isospin quantum number, besides the usual generalized U(1) charge. Consequently, charge Kekulé pair density waves can develop in the skyrmion core of Néel layer antiferromagnet, while a skyrmion of quantum spin Hall insulator in addition supports an wave pairing. We also analyze the internal algebra of competing orders in the core of these defects on checkerboard or Kagome lattice that supports only a single copy of quadratic band touching in the normal state.
arXiv commentPublished version in PRB: 17 Pages, 4 Figures, 2 Tables
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