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Antiferromagnetic Topological Superconductor and Electrically Controllable Majorana Fermions

We investigate the realization of a topological superconductor in a generic bucked honeycomb system equipped with four types of mass-generating terms, where the superconductor gap is introduced by attaching the honeycomb system to an $s$-wave superconductor. Constructing the topological phase diagram, we show that Majorana modes are formed in the phase boundary. In particular, we analyze the honeycomb system with antiferromagnetic order in the presence of perpendicular electric field $E_{z}$. It becomes topological for $|E_{z}|>E_{z}^{\text{cr}}$ and trivial for $|E_{z}|<E_{z}^{\text{cr}}$, with $E_{z}^{\text{cr}}$ a certain critical field. It is possible to create a topological spot in a trivial superconductor by controlling applied electric field. One Majorana zero-energy bound state appears at the phase boundary. We can arbitrarily control the position of the Majorana fermion by moving the spot of applied electric field, which will be made possible by a scanning tunneling microscope probe.