Topological phases of the two-leg Kitaev ladder

We study the phase diagram of the two-leg Kitaev model. Different topological phases can be characterized by either the number of Majorana modes for a deformed chain of the open ladder, or by a winding number related to the ‘h  -loop’ in the momentum space. By adding a three-spin interaction term to break the time-reversal symmetry, two originally different phases are glued together, so that the number of Majorana modes reduce to 0 or 1, namely, the topological invariant collapses to Z2Z2 from an integer Z. These observations are consistent with a recent general study [S. Tewari, J.D. Sau, arXiv:1111.6592v2].

► We study the phase diagram of the two-leg Kitaev model.
► Different phases can be described by the numbers of Majorana modes or winding numbers.
► The topological invariant is an integer Z   rather than the commonly used Z2Z2.
► The topological invariant collapses to Z2Z2 by adding terms breaking the time-reversal symmetry.