Time-reversal symmetric Kitaev model and topological superconductor in two dimensions
Time-reversal symmetric Kitaev model and topological superconductor in two dimensions
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DOI：
10.1103/physrevb.85.155119
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发表时间：
2011-11
影响因子：
3.7
通讯作者：
Ryota Nakai;S. Ryu;A. Furusaki
中科院分区：
文献类型：
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作者：
Ryota Nakai;S. Ryu;A. Furusaki
介绍了一种时间反转不变的kitaev型模型，其中方形晶格上的自旋（Dirac矩阵）通过各向异性最近邻和次近邻交换相互作用进行相互作用。通过将该模型映射到自由马约拉纳费米子与静态Z_2规范场耦合的紧密结合模型上，精确求解了该模型。马约拉纳费米子模型可以看作是一个时间反转不变超导体模型，在Altland-Zirnbauer分类中被归为对称类DIII的成员。基态相图有两个拓扑上不同的间隙相，它们由Z_2拓扑不变量来区分。拓扑非平凡相既支持边界处的Kramers‘对无间隙的Majorana边缘模式，也支持在\pi-flux背景中束缚在0通量涡旋上的Kramers’对零能量的Majorana状态。考虑了无间隙马约拉纳边缘模式，得到了沿边缘自旋的幂律衰减相关函数。在一维阶梯上也定义了模型，在这种情况下，基态相图同样具有Z_2平凡相和非平凡相。
A time-reversal invariant Kitaev-type model is introduced in which spins (Dirac matrices) on the square lattice interact via anisotropic nearest-neighbor and next-nearest-neighbor exchange interactions. The model is exactly solved by mapping it onto a tight-binding model of free Majorana fermions coupled with static Z_2 gauge fields. The Majorana fermion model can be viewed as a model of time-reversal invariant superconductor and is classified as a member of symmetry class DIII in the Altland-Zirnbauer classification. The ground-state phase diagram has two topologically distinct gapped phases which are distinguished by a Z_2 topological invariant. The topologically nontrivial phase supports both a Kramers' pair of gapless Majorana edge modes at the boundary and a Kramers' pair of zero-energy Majorana states bound to a 0-flux vortex in the \pi-flux background. Power-law decaying correlation functions of spins along the edge are obtained by taking the gapless Majorana edge modes into account. The model is also defined on the one-dimension ladder, in which case again the ground-state phase diagram has Z_2 trivial and non-trivial phases.