Photonic realization of the (2+1)-dimensional parity anomaly
Photonic realization of the (2+1)-dimensional parity anomaly
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DOI：
10.1103/physrevb.86.075152
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发表时间：
2012-08-28
影响因子：
3.7
通讯作者：
Ochiai, Tetsuyuki
中科院分区：
文献类型：
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作者：
Ochiai, Tetsuyuki
我们提出了一个光子实现的宇称异常最初发现在（2+1）维狄拉克费米子。我们首先利用群论推导出三角形、蜂窝形和kagome晶格光子晶体布里渊区拐角处的有效狄拉克哈密顿量。在有效理论的框架下，解析地导出了一个由空间反演和时间反演对称性破缺引起的拓扑相变。这种相变与二维电子系统在周期性磁通作用下的Halfton模型密切相关，Halfton模型实现了凝聚态系统的宇称反常。我们还得到了一个有效的理论周围的布里渊区中心，在动量空间的二次简并发生。那里的有效理论预言了与宇称反常类似的现象。结果表明，即使在磁通量交错排列的情况下，也能预测出拓扑非平凡相和手征边缘态。数值模拟也证实了预测。
We present a photonic realization of the parity anomaly originally found in the (2+1)-dimensional Dirac fermion. We first derive an effective Dirac Hamiltonian around the Brillouin zone corner of triangular-, honeycomb-, and kagome-lattice photonic crystals using group theory. A topological phase transition by broken space-inversion and time-reversal symmetries is derived analytically within the effective theory on the honeycomb lattice. The phase transition is closely related to the Haldane model of the two-dimensional electron system under periodic magnetic flux, which realizes the parity anomaly in a condensed-matter system. We also derive an effective theory around the Brillouin zone center, where quadratic degeneracy in momentum space take places. The effective theory there predicts a similar phenomenon as the parity anomaly. As a result, a topologically nontrivial phase and a chiral edge state are predicted even for staggered configuration of applied magnetic flux. A numerical simulation is also presented to confirm the prediction.