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Under appropriate external conditions a semiconductor nanowire in proximityto an s-wave superconductor can be in a topological superconducting (TS) phase.This phase supports localized zero-energy Majorana fermions at the ends of thewire. However, the non-Abelian exchange statistics of Majorana fermions isdifficult verify because of the one-dimensional topology of such wires. In thispaper we propose a scheme to transport Majorana fermions between the ends ofdifferent wires using tunneling, which is shown to be controllable by gatevoltages. Such tunneling-generated hops of Majorana fermions can be used toexchange the Majorana fermions. The exchange process thus obtained is describedby a non-Abelian braid operator that is uniquely determined by thewell-controlled microscopic tunneling parameters.

Controlling non-Abelian statistics of Majorana fermions on Majorana dimer lattices