  We model theoretically a two-dimensional electron gas (2DEG) covered by a
superconductor and demonstrate that topological superconducting channels are
formed when stripes of the superconducting layer are removed. As a consequence,
Majorana bound states (MBS) are created at the ends of the stripes. We
calculate the topological invariant and energy gap of a single stripe, using
realistic values for an InAs 2DEG proximitized by an epitaxial Al layer. We
show that the topological gap is enhanced when the structure is made
asymmetric. This can be achieved by either imposing a phase difference (by
driving a supercurrent or using a magnetic-flux loop) over the strip or by
replacing one superconductor by a metallic gate. Both strategies also enable
control over the MBS splitting, thereby facilitating braiding and readout
schemes based on controlled fusion of MBS. Finally, we outline how a network of
Majorana stripes can be designed.
