Color degeneracy of topological defects in quadratic band touching systems
Abstract
We study twodimensional fermionic quadratic band touching (QBT) systems in the presence of vortex and skyrmion of insulating and superconducting masses. A prototypical example of such systems is the Bernal bilayer graphene that supports eight zeroenergy modes in the presence of a mass vortex with the requisite U(1) symmetry. Inside the vortex core, additional ten masses that close an SO(5) algebra can develop local expectation values by splitting the 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 chiraltriplet mass orders, giving rise to the notion of the color or flavor degeneracy among the competing orders. 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 $4e$ Kekule pairdensitywaves can develop in the skyrmion core of Néel layer antiferromagnet, while a skyrmion of quantum spin Hall insulator in addition supports a mundane $s$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 QBT.
 Publication:

arXiv eprints
 Pub Date:
 April 2020
 arXiv:
 arXiv:2004.13043
 Bibcode:
 2020arXiv200413043R
 Keywords:

 Condensed Matter  Mesoscale and Nanoscale Physics;
 Condensed Matter  Strongly Correlated Electrons;
 Condensed Matter  Superconductivity
 EPrint:
 14 Pages, 4 Figures, 2 Tables