Majorana fermions are the only fermionic particles that are expected to be their own antiparticles. Although elementary particles of the Majorana type have not been identified yet, quasi-particles with Majorana-like properties, born from interacting electrons in the solid, have been predicted to exist. I will present results of experimental studies of a system composed of an aluminium superconductor in proximity to an indium arsenide nanowire, with the latter possessing strong spin-orbit coupling and Zeeman splitting. An induced one-dimensional topological superconductor,

supporting Majorana fermions at both ends, is expected to form.

I will concentrate on the characteristics of a distinct zero-bias conductance peak and its splitting in energy - both appearing only with a small magnetic field applied along the wire. The zero-bias conductance peak was found to be robustly tied to the Fermi energy over a wide range of system parameters. Although not providing definite proof of a Majorana state, the presented data and the simulations support its existence.