  Planar Josephson junctions comprising semiconductors with strong spin-orbit
interaction (SOI) are promising platforms to host Majorana bound states (MBSs).
Previous works on MBSs in planar Josephson junctions have focused on electron
gases, where SOI is linear in momentum. In contrast, a two-dimensional hole gas
in planar germanium (Ge) exhibits SOI that is cubic in momentum. Nevertheless,
we show here that due to the particularly large SOI, Ge is a favorable
material. Using a discretized model, we numerically simulate a Ge planar
Josephson junction and demonstrate that also cubic SOI can lead to the
emergence of MBSs. Interestingly, we find that the cubic SOI yields an
asymmetric phase diagram as a function of the superconducting phase difference
across the junction. We also find that trivial Andreev bound states can imitate
the signatures of MBSs in a Ge planar Josephson junction, therefore making the
experimental detection of MBSs difficult. We use experimentally realistic
parameters to assess if the topological phase is accessible within experimental
limitations. Our analysis shows that two-dimensional Ge is an auspicious
candidate for topological phases.
