Topological indices, defects, and Majorana fermions in chiral superconductors

We study theoretically the role of topological invariants to protect the Majorana fermions in a model of two-dimensional (2D) chiral superconductors which belong to class D of the topological periodic table. A rich phase diagram is revealed. Each phase is characterized by the topological invariants for 2D (Z) and 1D (Z₂), which lead to the Majorana fermion at the edge dislocation and the core of the vortex. Interference of the Majorana fermions originating from the different topological invariants is studied. The stability of the Majorana fermion with respect to the interlayer coupling, i. e. , in 3D, is also examined.