  The external controllability of topological superconductors and Majorana
fermions would be important both for fundamental and practical interests. Here
we predict the electric-field control of Majorana fermions in two-dimensional
topological superconductors utilizing a topological insulator thin film
proximity coupled to a conventional $s$-wave superconductor. With ferromagnetic
ordering, the tunable structure inversion asymmetry by vertical electric field
could induce topological quantum phase transition and realize a chiral
topological superconductor state. A zero-energy Majorana bound state appears at
the boundary of an applied electric field spot, which can be observed by
scanning tunneling microscopy. Furthermore, the structure inversion asymmetry
could also enlarge the helical topological superconductor state in the phase
diagram, making the realization of such an exotic state more feasible. The
electrical control of topological phases could further apply to van der Waals
materials such as two-dimensional transition metal dichalcogenides.
