Pinning of Andreev bound states to zero energy in two-dimensional superconductor- semiconductor Rashba heterostructures

We consider a two-dimensional electron gas (2DEG) with Rashba spin-orbit interaction (SOI) partially covered by an s-wave superconductor, where the uncovered region remains normal but is exposed to a perpendicular Zeeman field. We find analytically and numerically Andreev bound states (ABSs) formed in the normal region and show that, by tuning the SOI to certain values, one can reach a regime where the energy of the lowest ABS becomes pinned close to zero as a function of Zeeman field. In addition, we also consider a configuration with a superconducting vortex and find again ABSs pinned close to zero energy in the topologically trivial phase for a wide range of parameters. Thus, ABSs and Majorana bound states show similar behavior in such structures.