Enhanced Topological Superconductivity in an Asymmetrical Planar Josephson Junction


 As a platform for holding Majorana zero models (MZMs) that can be used as carriers for topological quantum computing, a two-dimensional planar topological Josephson junction faces some challenges. One is a combination of mirror and time-reversal symmetry may make the system hold multiple pairs of MZMs. Other is that a soft gap dominated by a large momentum that occurs in a clean system. To solve these problems, asymmetric junction can be introduced. Breaking this symmetry changes the symmetry class from class BDI to class D, and only a single pair of MZMs can be left at the boundary of the system. We numerically study four cases that create an asymmetric system and find out that different superconducting pairing potential, different coupling coefficients between two-dimensional electron gases(2DEGs) and two superconducting bulks, different widths of two superconducting bulks make the gap of the system decrease at the optimal value, but make the gap at the minimum value increase. And the zigzag-shape quasi-one-dimensional junction eliminates the large momentum parallel to the junction and enhances the gap at the large momentum. However, the zigzag-shape junction cannot increase the gap at the region of multiple pairs of MZMs in a symmetric system. We show that by combining zigzag-shape junction with different coupling coefficients, the system can maintain a large gap(≈0.2Δ) in a wide region of the parameter space.