  We propose a planar Josephson junction setup to host Majorana modes where the
semiconductor is sandwiched between superconductors on both surfaces. While the
studied configuration is related to both devices proposed for use with
topological insulators as well as other proposals for Majorana modes without
applied magnetic fields, we find that placing the superconductor on both
surfaces allows us to replace the topological insulator by a wider variety of
spin-orbit coupled semiconductors. Application of an electric field in the
junction together with appropriate superconducting phase differences allows
different Fermi surfaces to be subject to different phase differences. We find
that these conditions can drive the system into a class-D topological
superconductor with a pair of Majorana modes at the two ends of the junction.
Additionally, class-DIII topological superconductors with helical Majorana
modes also occur in other parts of the phase diagram. We simulate our setup on
HgTe near the valence band edge described by the well-known 8-band Kane model
with realistic parameters and find phase diagram can be achieved. The
topological gap can remain comparable to the bulk superconducting gap
throughout the fermi surface.
