Transition from 2D to 1D topological superconductivity in a triangular island of p-wave superconductor

We study the connection between 0D and 1D Majorana modes in a triangular island of a model topological superconductor, with the motivation of designing a flexible platform for performing braiding operations on Majorana zero modes for topological quantum computation. Using the mean-field Bogoliubov-de Gennes theory, we solve a tight-binding model with Rashba spin-orbit coupling, out-of-plane Zeeman field, and s-wave pairing on an equilateral triangle, which hosts chiral Majorana edge modes. Using an eigen-value solver we were able to show breaking of the three-fold rotation symmetry of the model by applying an additional in-plane Zeeman field, which is expected to result in an effectively 1D topological superconductor. To further understand the evolution of the pseudo-Majorana states at the corners we treat the corner as a wedge with open boundary conditions and solve the BdG equation analytically.