Driving topological phases by spatially inhomogeneous pairing centers

We investigate the effect of periodic and disordered distributions of pairing centers in a one-dimensional itinerant system to obtain the microscopic conditions required to achieve an end Majorana mode and the topological phase diagram. Remarkably, the topological invariant can be generally expressed in terms of the physical parameters for any pairing center configuration. Such a fundamental relation allows us to unveil hidden local symmetries and to identify trajectories in the parameter space that preserve the nontrivial topological character of the ground state. We identify the phase diagram with topologically nontrivial domains where Majorana modes are completely unaffected by the spatial distribution of the pairing centers. These results are general and apply to several systems where inhomogeneous perturbations generate stable Majorana modes.