Topological phase transition in a ladder of the dimerized Kitaev superconductor chains

We investigate the topological properties of a ladder model of the dimerized Kitaev superconductor chains. The topological class of the system is determined by the relative phase θ between the inter- and intra-chain superconducting pairing. One topological class is the class BDI characterized by the ℤ index, and the other is the class D characterized by the ℤ₂ index. For the two different topological classes, the topological phase diagrams of the system are presented by calculating two different topological numbers, i.e., the ℤ index winding number W and the ℤ₂ index Majorana number ℳ , respectively. In the case of θ =0, the topological class belongs to the class BDI, multiple topological phase transitions accompanying the variation of the number of Majorana zero modes are observed. In the case of θ = π /2 it belongs to the class D. Our results show that for the given value of dimerization, the topologically nontrivial and trivial phases alternate with the variation of chemical potential. (paper)