$\mathbb{Z}_2$-projective translational symmetry protected topological
phases
- URL: http://arxiv.org/abs/2007.00575v3
- Date: Wed, 28 Oct 2020 08:10:53 GMT
- Title: $\mathbb{Z}_2$-projective translational symmetry protected topological
phases
- Authors: Y. X. Zhao, Yue-Xin Huang and Shengyuan A. Yang
- Abstract summary: In the presence of a gauge field, spatial symmetries will be projectively represented.
Our work opens a new arena of research for exploring topological phases protected by projectively represented space groups.
- Score: 0.2578242050187029
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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 topological phases. We show that
the $\mathbb{Z}_2$ projectively represented translational symmetry operators
adopt a distinct commutation relation, and become momentum dependent analogous
to twofold nonsymmorphic symmetries. Combined with other internal or external
symmetries, they give rise to many exotic band topology, such as the degeneracy
over the whole boundary of the Brillouin zone, the single fourfold Dirac point
pinned at the Brillouin zone corner, and the Kramers degeneracy at every
momentum point. Intriguingly, the Dirac point criticality can be lifted by
breaking one primitive translation, resulting in a topological insulator phase,
where the edge bands have a M\"{o}bius twist. Our work opens a new arena of
research for exploring topological phases protected by projectively represented
space groups.
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