  Majorana fermions are the only fermionic particles that are expected to be
their own antiparticles. While elementary particles of the Majorana type were
not identified yet, quasi-particles with Majorana like properties, born from
interacting electrons in the solid, were predicted to exist. Here, we present
thorough experimental studies, backed by numerical simulations, of a system
composed of an aluminum superconductor in proximity to an indium arsenide
nanowire, with the latter possessing strong spin-orbit coupling. An induced 1d
topological superconductor - supporting Majorana fermions at both ends - is
expected to form. We concentrate on the characteristics of a distinct zero bias
conductance peak (ZBP), and its splitting in energy, both appearing only with a
small magnetic field applied along the wire. The ZBP was found to be robustly
tied to the Fermi energy over a wide range of system parameters. While not
providing a definite proof of a Majorana state, the presented data and the
simulations support strongly its existence.
