Isospin of topological defects in Dirac systems
Isospin of topological defects in Dirac systems
复制标题
狄拉克系统拓扑缺陷的同位旋
DOI：
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发表时间：
2011
期刊：
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通讯作者：
I. Herbut
中科院分区：
文献类型：
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作者：
I. Herbut
我们研究的狄拉克准粒子在$d$维晶格系统中的电子畴壁（$d=1$），涡旋（$d=2$），或刺猬（$d=3$）的超导和/或绝缘，序参数，出现在狄拉克方程中的质量项的存在。已知这种拓扑缺陷携带非平凡的量子数，例如电荷和自旋。在这里，我们讨论他们的额外的内部自由度：不管空间的维数和性质的订单，支持缺陷，一个额外的质量序参量被发现出现在他们的核心。证明了封闭两个相互交换的三维Clifford代数的六个线性无关局部序是一般可能的。我们展示了粒子-空穴对称性如何限制缺陷总是携带单个有效同位旋1/2的量子数，而与它们的电荷或真实自旋的值无关。这种新的自由度在石墨烯和拓扑绝缘体的表面上的例子进行了讨论。
We study the Dirac quasiparticles in $d$-dimensional lattice systems of electrons in the presence of domain walls ($d=1$), vortices ($d=2$), or hedgehogs ($d=3$) of superconducting and/or insulating, order parameters, which appear as mass terms in the Dirac equation. Such topological defects have been known to carry nontrivial quantum numbers, such as charge and spin. Here we discuss their additional internal degree of freedom: irrespective of the dimensionality of space and the nature of orders that support the defect, an extra mass order parameter is found to emerge in their core. Six linearly independent local orders, which close two mutually commuting three-dimensional Clifford algebras, are proven to be in general possible. We show how the particle-hole symmetry restricts the defects to always carry the quantum numbers of a single effective isospin 1/2, quite independently of the values of their electric charge or true spin. Examples of this new degree of freedom in graphene and on surfaces of topological insulators are discussed.