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In this work we discuss the formation of zero energy vortex and chiral edgemodes in a fermionic representation of the Kitaev honeycomb model. We introducethe representation and show how the associated Jordan-Wigner procedurenaturally defines the so called branch cuts that connect the topological vortexexcitations. Using this notion of the branch cuts we show how to, in thenon-Abelian phase of the model, describe the Majorana zero mode structureassociated with vortex excitations. Furthermore we show how, by intersectingthe edges between Abelian and non-Abelian domains, the branch cuts dictate thecharacter of the chiral edge modes. In particular we will see in whatsituations the exact zero energy Majorana edge modes exist. On a cylinder, andfor the particular instances where the Abelian phase of the model is the fullvacuum, we have been able to exactly solve for the systems edge energyeigensolutions and derive a recursive formula that exactly describes the edgemode structure. Penetration depth is also calculated and shown to be dependenton the momentum of the edge mode. These solutions also describe the overallcharacter of the fully open non-Abelian domain and are excellent approximationsat moderate distances from the corners.

Zero energy and chiral edge modes in a p-wave magnetic spin model