Shift insulators: rotation-protected two-dimensional topological crystalline insulators

We study a two-dimensional tight-binding model of a topological crystalline insulator protected by rotation symmetry. The model is built by stacking two Chern insulators with opposite Chern numbers which transform under conjugate representations of the rotation group, e.g. p_± orbitals. Despite its apparent similarity to the Kane-Mele model, it does not host stable gapless surface states. Nevertheless the model exhibits topological responses including the appearance of quantized fractional charge bound to rotational defects (disclinations) and the pumping of angular momentum in response to threading an elementary magnetic flux, which are described by a mutual Chern-Simons coupling between the electromagnetic gauge field and an effective gauge field corresponding to the rotation symmetry. We show that although the filled bands of the model do not admit a symmetric Wannier representation, this obstruction is removed on addition of appropriate atomic orbitals, which implies 'fragile' topology. As a result, the response of the model can be derived by representing it as a superposition of atomic orbitals with positive and negative integer coefficients.
Ref: S. Liu, A. Vishwanath, E. Khalaf, arXiv: 1809.01636.