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.
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