  Half-integer conductance, the signature of Majorana edge modes, has been
recently observed in a quantum anomalous Hall insulator/superconductor
heterostructure. Here, we analyze a scheme for gate-tunable control of
degenerate ground states of Majorana zero modes (MZM) in thin film topological
superconductors. Gating the top surface of a thin film magnetic topological
insulator controls the topological phase in the region underneath the gate. The
voltage of the transition depends on the gate width, and narrower gates require
larger voltages. Relatively long gates are required, on the order of a micron,
to prevent hybridization of the end modes and to allow the creation of MZMs at
low gate voltages. Applying a voltage to T{shaped and I{shaped gates localizes
the Majoranas at their ends. This scheme may provide a facile method for
implementing quantum gates for topological quantum computing.
