  We consider a two-dimensional electron gas with Rashba spin-orbit interaction
(SOI) partially covered by an s-wave superconductor, where the uncovered region
remains normal but is exposed to an effective Zeeman field applied
perpendicular to the plane. We find analytically and numerically Andreev bound
states (ABSs) formed in the normal region and show that, due to SOI and by
tuning the parameters of the system deeply into the topologically trivial
phase, one can reach a regime where the energy of the lowest ABS becomes pinned
close to zero as a function of Zeeman field. The energy of such an ABS is shown
to decay as an inverse power-law in Zeeman field. We also consider a
superconductor-semiconductor heterostructure with a superconducting vortex at
the center and in the presence of strong SOI, and find again ABSs that can get
pinned close to zero energy in the non-topological phase.
