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

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

v5, accepted in prl, the explicit Z8 Fu-Kane-like formulas provided

References in corpus (7)

• Topological Crystalline Insulators
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Reflection symmetric second-order topological insulators and superconductors
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Wannier representation of Z_2 topological insulators
• Quantum Spin Hall Effect in Strip of Stripes Model
• Integer and Fractional Quantum Anomalous Hall Effect in a Strip of Stripes Model

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