Manipulation of Majorana fermions by point-like gate voltage in the Vortex state of a topological superconductor

A vortex in a topological superconductor induces two Majorana fermions (MFs), one in the core and the other at the sample edge. Here we demonstrate that edge MFs can be transported and braided by turning gate voltages on and off at the point-like constriction junctions between samples. The controllable high mobility of edge MFs is due to the topological property, namely an edge MF appears when the sample perimeter includes odd vorticity, and disappears for even vorticity. As shown explicitly by solving the time-dependent Bogoliubov-de Gennes equation, disturbance to the quantum coherence of MFs during braiding is negligibly small in this scheme due to the point-like application of the gate voltage. The present work bridges for the first time the fundamental topological features of edge MFs and their adiabatic dynamics which is important for performing topological quantum computation.