  We investigate a topological insulator -- superconductor heterostructure with
an Abrikosov vortex in a magnetic field. Large Zeeman field causes a
topological phase transition in the system. We found that a Majorana fermion
exists at the vortex core in the phase with zero first Chern number and does
not exist at the phase with non-trivial first Chern number. This result is
supported by the index theorem. This system provides an example in which a
Majorana fermion emerges in a system with zero first Chern number.
