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The list of quantum mechanical systems with non-Abelian statistics hasrecently been expanded by including generic spin-orbit-coupled semiconductorse.g., InAs) in proximity to a s-wave superconductor. Demonstration of theanyonic statistics using Majorana fermion interferometry in this system is anecessary first step towards topological quantum computation (TQC). However,since all isolated chiral edges that can be created in the semiconductor arecharge neutral, it is not clear if electrically controlled interferometry ispossible in this system. Here we show that when two isolated chiral Majoranaedges are brought into close contact, the resultant interface supports chargecurrent, enabling electrically controlled Majorana fermion interferometry inthe semiconductor structure. Such interferometry experiments on thesemiconductor are analogous to similar interferometry experiments on the$\nu=5/2$ fractional quantum Hall systems and on the surface of a 3D strongtopological insulator, illustrating the usefulness of the 2D semiconductorheterostructure as a suitable TQC platform. In particular, we proposed Majoranainterferometers may be the most direct method for establishing non-Abelianbraiding statistics in topological superconductors.

Probing non-Abelian statistics with Majorana fermion interferometry in spin-orbit-coupled semiconductors