Enhanced Topological Superconductivity in an Asymmetrical Planar Josephson Junction

As a platform for holding Majorana zero models (MZMs), the two-dimensional planar topological Josephson junction that can be used as carriers for topological quantum computing faces some challenges. One is a combination of mirror and time-reversal symmetries may make the system hold multiple pairs of MZMs. The other is that a soft gap dominated by a large momentum 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 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 increases. 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 (≈0.2 Δ ) in a wide region of the parameter space.