Defect Response in 2D Delicate Topological Insulators

We investigate the dislocation response in a mirror-symmetric, 2-band, 2D delicate topological insulator (DTI) with a bulk returning Thouless pump (RTP). Little is known about the effects of lattice disclinations and other types of defects on DTIs. Our model can be realized in 2D as photonic crystal made of stacked Su-Schrieffer-Heeger chains. This model has a trivial Chern number, instead being characterized by $2\pi$-quantized Berry phase differences between high-symmetry lines in the Brillouin zone. By stitching together lattices of the RTP DTI with different sizes, disclinations corresponding to uncoupled sites in the lattice could be generated. Using a second-quantization tight binding model, defect response could be calculated computationally. We find that each dislocation had a topologically robust charge distribution at half-filling. We also find that each disclination site hosted only one protected edge mode corresponding to the symmetry eigenvalues of the dislocation. We show that our computational results align with theoretical predictions.