3 years ago

$(d-2)$-dimensional edge states of rotation symmetry protected topological states.

Chen Fang, Zhong Fang, Zhida Song

We study fourfold rotation invariant gapped topological systems with time-reversal symmetry in two and three dimensions ($d=2,3$). We show that in both cases nontrivial topology is manifested by the presence of the $(d-2)$-dimensional edge states, existing at a point in 2D or along a line in 3D. For fermion systems without interaction, the bulk topological invariants are given in terms of the Wannier centers of filled bands, and can be readily calculated using a Fu-Kane-like formula when inversion symmetry is also present. The theory is extended to strongly interacting systems through explicit construction of microscopic models having robust $(d-2)$-dimensional edge states.

Publisher URL: http://arxiv.org/abs/1708.02952

DOI: arXiv:1708.02952v4

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