Nested defects on the boundary of topological superconductors

Helical Majorana edge states at the 2D boundaries of 3D topological superconductors can be gapped by a surface Zeeman field. Here we study the effect nested defects imprinted on the Zeeman field can have on the edge states. We demonstrate that depending on the configuration of the field, we can induce dimensional reduction of gapless Majorana modes from 2D to 1D or quasi-0D at magnetic domain walls. We determine the nature of the Majorana localization on these defects as a function of the magnitude and configuration of the Zeeman field. Finally, we observe a generalization of the index theorem governing the number of gapless modes at the interface between topologically nontrivial systems with partial Chern numbers.