# Z2 -projective translational symmetry protected topological phases

@article{Zhao2020Z2T, title={Z2 -projective translational symmetry protected topological phases}, author={Y. X. Zhao and Yue-Xin Huang and Shengyuan A. Yang}, journal={Physical Review B}, year={2020}, volume={102}, pages={161117} }

Symmetry is fundamental to topological phases. In the presence of a gauge field, spatial symmetries will be projectively represented, which may alter their algebraic structure and generate novel physics. We show that the ${\mathbb{Z}}_{2}$ projectively represented translational symmetry operators adopt a distinct anticommutation relation. As a result, each energy band is twofold degenerate, and carries a varying spinor structure for translation operators in momentum space, which cannot be…

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