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

Abstract: 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 for both cases are {\it mirror winding numbers,} which are nonzero individually in the topological phase, but sum to zero overall in both phases. 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.