Bending effect on the Majorana bound states in planar Josephson junctions

We consider the bending effect on the formation of Majorana bound states in planar Josephson junctions where the normal stripe is tilted in a V shape. Our results show that the Majorana bound states remain robust for moderate bending angles. Beyond some critical angles, the degradation of Majorana bound states can be revealed by its eigenspectrum as well as the Majorana polarization. Our results show that the parameter space of bending angle for robust Majorana bound states can be significantly enlarged by tuning the superconducting phase difference across the Josephson junction. These findings suggest that the interplay of the junction geometry and the device parameters provides richer degree of freedom in designing topological superconducting devices for future applications. The Majorana polarization analysis is an indispensable tool for characterizing the Majorana states.