  We study the generation of Majorana fermions in a two-dimensional topological
superconductor placed in a transverse magnetic field B. A topological
insulator/superconductor heterostructure and a two-dimensional p-wave
superconductor are discussed. It is demonstrated that in these systems a single
vortex creates two Majorana fermions, one hosted at the vortex core. The wave
function of the second Majorana state is localized in the superconductor volume
along a circle of radius $r^* \propto B^{-1}$ centered at the vortex core. In
the case of many vortices, the sensitivity of $r^*$ to the magnetic field B may
be used to control the coupling between the Majorana fermions. The latter
property could be an asset for quantum computations.

Mesoscale and Nanoscale Physics