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Phys Rev Lett. 2017 Dec 15;119(24):246402. doi: 10.1103/PhysRevLett.119.246402. Epub 2017 Dec 11.

(d-2)-Dimensional Edge States of Rotation Symmetry Protected Topological States.

Song Z1,2, Fang Z1,3, Fang C1.

Author information

1
Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.
2
University of Chinese Academy of Sciences, Beijing 100049, China.
3
Collaborative Innovation Center of Quantum Matter, Beijing 100084, China.

Abstract

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 the explicit construction of microscopic models having robust (d-2)-dimensional edge states.

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