  Majorana Fermions, strange particles that are their own antiparticles, were
predicted in 1937 and have been sought after ever since. In condensed matter
they are predicted to exist as vortex core or edge excitations in certain
exotic superconductors. These are topological superconductors whose order
parameter phase winds non-trivially in momentum space. In recent years, a new
and promising route for realizing topological superconductors has opened due to
advances in the field of topological insulators. Current proposals are based on
semiconductor heterostructures, where spin-orbit coupled bands are split by a
band gap or Zeeman field and superconductivity is induced by proximity to a
conventional superconductor. Topological superconductivity is obtained in the
interface layer. The proposed heterostructures typically include two or three
layers of different materials. In the current work we propose a device based on
materials with inherent spin-orbit coupling and an intrinsic tendency for
superconductivity, eliminating the need for a separate superconducting layer.
We study a lattice model that includes spin-orbit coupling as well as on-site
and nearest neighbor interaction. Within this model we show that topological
superconductivity is possible in certain regions of parameter space. These
regions of non-trivial topology can be understood as a nodeless superconductor
with d-wave symmetry which, due to the spin-orbit coupling, acquires an extra
phase twist of $2\pi$.
