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Robust topologically trivial low-energy Andreev bound states (ABSs) inducedby position-dependent effective potentials have recently come under renewedfocus, in light of a remarkable set of experiments observing robust quantizedzero-bias conductance plateaus in semiconductor-superconductorheterostructures. We show that (1) the partial spatial separation of the wavefunctions of the component Majorana bound states (MBSs) is crucial for thecreation and stability of topologically trivial near-zero-energy Andreev boundstates, (2) the signs of the spin polarizations of the component MBSs can beeither the same or opposite, depending on the profile of the inducingpotential, and (3) the spin polarizations do not play a fundamental role ingenerating vastly different coupling strengths to local probes and/or ensuringthe robustness of the near-zero-energy ABS. Consequently, in contrast to recenttheoretical claims (Vuik et al., arXiv:1806.02801), we find that a robust,quantized zero-bias conductance plateau of height 2e^2/h measured in thetopologically trivial regime necessarily requires partially separated ABSs(ps-ABSs), independent of the relative signs of the spin-polarizations. Inaddition, we show that (4) well-defined energy splitting oscillations involveMBSs characterized by exponential tails pointing toward each other, and (5)ps-ABSs generated by the tunnel barrier itself produce zero-bias conductancepeaks with a characteristic width that increases strongly with the appliedmagnetic field. Finally, we propose (6) a quantitative scheme for analyzing thestability of Majorana modes based on probability distributions of splittingsusceptibilities and show that a ps-ABS mode can be remarkably robust whenjudged based on its signature in a charge tunneling experiment, but, inessence, is topologically unprotected.

physical review. b./physical review. b

Robust low-energy Andreev bound states in semiconductor-superconductor  heterostructures: Importance of partial separation of component Majorana  bound states