Kitaev chain with a fractional twist
Kitaev chain with a fractional twist
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DOI：
10.1103/physrevb.106.125109
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发表时间：
2022-04
影响因子：
3.7
通讯作者：
Bora Basa;Gabriele La Nave;P. Phillips
中科院分区：
文献类型：
--
作者：
Bora Basa;Gabriele La Nave;P. Phillips
物质绝缘相的拓扑非平凡性现在通过拓扑K理论得到了很好的理解，其中狄拉克算子的指数被组装成拓扑类。我们认为在Kitaev链的背景下，一个广义狄拉克算子的概念，相关的Clifford代数的中心扩展。我们证明，通过采取合理的运营商的权力出现在相应的BdG哈密顿的泡利矩阵，实现了中心扩展。这样做会在拓扑相图中引入伪金属成分，其中绕组数的值为$\mathbb Q$。我们发现，这一阶段主机的模式，仍然在弱无序的存在下扩展，激发一个非整数绕组数的拓扑解释。我们注意到，这是在对应的Ref。[J. Differential Geom. 74（2）：265-292]证明了在没有自旋$^\mathbb C$结构的情况下定义的投射狄拉克算子具有有理指数。
The topological non-triviality of insulating phases of matter is by now well understood through topological K-theory where the indices of the Dirac operators are assembled into topological classes. We consider in the context of the Kitaev chain a notion of a generalized Dirac operator where the associated Clifford algebra is centrally extended. We demonstrate that the central extension is achieved via taking rational operator powers of Pauli matrices that appear in the corresponding BdG Hamiltonian. Doing so introduces a pseudo-metallic component to the topological phase diagram within which the winding number is valued in $\mathbb Q$. We find that this phase hosts a mode that remains extended in the presence of weak disorder, motivating a topological interpretation of a non-integral winding number. We remark that this is in correspondence with Ref.[J. Differential Geom. 74(2):265-292] demonstrating that projective Dirac operators defined in the absence of spin$^\mathbb C$ structure have rational indices.