平面二次能带接触系统中拓扑缺陷核心处竞争序的颜色退化
Color degeneracy of competing orders near topological defects cores in planar quadratic band touching systems
AI总结：
研究二维费米系统在拓扑缺陷核心处的竞争序退化现象，通过分析不同序参量的对称性破缺，揭示颜色退化机制及序参量的内部代数结构。
摘要：
我们研究了在有序相中存在绝缘体和超导质量涡旋和Skyrmion的二维费米系统，其正常态显示二次能带接触。伯纳尔双层石墨烯是此类系统的典型例子，其在具有必要U(1)对称性的质量涡旋存在下支持八个零能态。在涡旋核心附近，额外的十个质量通过分裂零模的曼陀罗空间，以不同的方式形成局部期望值，从而打破SO(4)和SU(2)手性对称性，分别产生SO(5)代数。特别是，每个SU(2)手性对称性可通过三种不同的手性三重质量序来打破，从而在涡旋核心附近产生竞争序之间的颜色退化。相比之下，三个反交换质量的Skyrmion在核心内支持额外的六个质量，并具有除了通常的广义U(1)电荷外的SU(2)异旋量子数。因此，Néel层反铁磁体的Skyrmion核心中可以发展出电荷4e的Kekulé配对密度波，而量子自旋霍尔绝缘体的Skyrmion还支持s波配对。我们还分析了这些缺陷核心在支持仅单个二次能带接触的checkerboard或Kagome晶格上的竞争序内部代数。
英文摘要：
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 $4e$ 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 $s$ 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 quadratic band touching in the normal state.
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