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We study the generation of Majorana fermions in a two-dimensional topologicalsuperconductor placed in a transverse magnetic field B. A topologicalinsulator/superconductor heterostructure and a two-dimensional p-wavesuperconductor are discussed. It is demonstrated that in these systems a singlevortex creates two Majorana fermions, one hosted at the vortex core. The wavefunction of the second Majorana state is localized in the superconductor volumealong a circle of radius $r^* \propto B^{-1}$ centered at the vortex core. Inthe case of many vortices, the sensitivity of $r^*$ to the magnetic field B maybe used to control the coupling between the Majorana fermions. The latterproperty could be an asset for quantum computations.

Majorana fermion from Landau quantization in 2D topological superconductors