Topological insulation in a ladder model with particle-hole and reflection symmetries

A two-legged ladder model, one dimensional, exhibiting the parity anomaly is constructed. The model belongs to the C and CI symmetry classes, depending on the parameters, but, due to reflection, it exhibits topological insulation. The model consists of two superimposed Creutz models with onsite potentials. The topological invariants of each Creutz model sum to give the mirror winding number, with winding numbers which are nonzero individually but equal and opposite in the topological phase, and both zero in the trivial phase. We demonstrate the presence of edge states and quantized Hall response in the topological region. Our model exhibits two distinct topological regions, distinguished by the different types of reflection symmetries.