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Helical Majorana edge states at the 2D boundaries of 3D topologicalsuperconductors can be gapped by a surface Zeeman field. Here we study theeffect nested defects imprinted on the Zeeman field can have on the edgestates. We demonstrate that depending on the configuration of the field we caninduce dimensional reduction of gapless Majorana modes from 2D to 1D orquasi-0D at magnetic domain walls. We determine the nature of the Majoranalocalisation on these defects as a function of the magnitude and configurationof the Zeeman field. Finally, we observe a generalisation of the index theoremgoverning the number of gapless modes at the interface between topologicallynon-trivial systems with partial Chern numbers.

Nested Defects on the Boundary of Topological Superconductors