The search for topologically degenerate Majorana modes in
Majorana fermions are fermion-like excitations that were originally proposed in particle physics by Ettore Majorana and are characterized asbeing their own anti-particle. In condensed matter systems Majorana fermions occur as fractionalized excitations with topologicallyprotected degeneracy associated with such excitations. In this talk, I will discuss a recent set of proposals for realizing Majorana modes in alarge class of spin-orbit coupled, time-reversal symmetry broken superconducting systems. The simplicity of this class of systems hasresulted in several experimental attempts, which have successfully observed preliminary evidence for the Majorana modes in the form ofzero-bias conductance peaks and doubled Shapiro steps. Following this I will then discuss future possibilities in terms of modifications to theexperiments to help confirm the presence of Majorana modes.