Motivated by the presentation of Yuval Oreg at Bound states 2023 workshop, I present some promising setups giving rise to topological superconductivity and Majorana zero modes. Based on paper [I], we review several proposal that rely on controlling the phase of the superconducting order parameter, either as the sole mechanism for time-reversal symmetry breaking, or as an additional handy knob used to reduce the applied magnetic field. In paper [II], the authors offer a general prescription for inducing topological superconductivity in planar superconductor-normal-superconductor-normal-superconductor (SNSNS) Josephson junctions without applying any magnetic fields on the junctions. The phase differences between the three superconductors define a parameter plane which includes large topological regions.
[I] arXiv:2112.06766v1 [II] arXiv:2206.13537v1