Extension of the Kitaev model on the square lattice

We study an extension of the Kitaev model [1] on the square lattice, where two types of Gamma matrices on neighboring sites have interaction that respects time reversal symmetry. A family of Kitaev models can be classified as the topological insulator/superconductor when described by Majorana fermions [2]. Our model is in class DIII in Altland-Zirnbauer classification, and thus a Z$_{2}$ invariant characterizes two distinct phases. There appear helical Majorana edge modes in the topological phase. The same model on the one-dimensional ladder is also studied. \\[4pt] [1] A. Kitaev, Annals of Physics 321, 2 (2006).\\[0pt] [2] S. Ryu, Phys. Rev. B 79, 075124 (2009).