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Recent experiments on Bernal bilayer graphene (BLG) deposited on monolayerWSe$_2$ revealed robust, ultra-clean superconductivity coexisting with sizableinduced spin-orbit coupling. Here we propose BLG/WSe$_2$ as a platform toengineer gate-defined planar topological Josephson junctions, where the normaland superconducting regions descend from a common material. More precisely, weshow that if superconductivity in BLG/WSe$_2$ is gapped and emerges from aparent state with inter-valley coherence, then Majorana zero modes can form inthe barrier region upon applying weak in-plane magnetic fields. Our resultsspotlight a potential pathway for `internally engineered' topologicalsuperconductivity that minimizes detrimental disorder andorbital-magnetic-field effects.

Gate-Defined Topological Josephson Junctions in Bernal Bilayer Graphene