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Motivated by an important recent experiment [Deng et al., Science 354, 1557(2016)], we theoretically consider the interplay between Andreev boundstates(ABSs) and Majorana bound states(MBSs) in quantum dot-nanowiresemiconductor systems with proximity-induced superconductivity(SC), spin-orbitcoupling and Zeeman splitting. The dot induces ABSs in the SC nanowire whichshow complex behavior as a function of Zeeman splitting and chemical potential,and the specific question is whether two such ABSs can come together forming atopological MBS. We consider physical situations involving the dot beingnon-SC, SC, or partially SC. We find that the ABSs indeed tend to coalescetogether producing near-zero-energy midgap states as Zeeman splitting and/orchemical potential are increased, but this mostly happens in thenon-topological regime although there are situations where the ABSs could cometogether forming a topological MBS. The two scenarios(two ABSs forming anear-zero-energy non-topological ABS or a zero-energy topological MBS) aredifficult to distinguish by tunneling conductance spectroscopy due toessentially the same signatures. Theoretically we distinguish them by knowingthe critical Zeeman splitting for the topological quantum phase transition orby calculating the topological visibility. We find that the "sticking together"propensity of ABSs to produce a zero-energy midgap state is generic in class Dsystems, and by itself says nothing about the topological nature of theunderlying SC nanowire. One must use caution in interpreting tunnelingconductance measurements where the midgap sticking-together behavior of ABSscannot be construed as definitive evidence for topological SC with non-AbelianMBSs. We also suggest some experimental techniques for distinguishing betweentrivial and topological ZBCPs.

physical review. b./physical review. b

Andreev bound states versus Majorana bound states in quantum  dot-nanowire-superconductor hybrid structures: Trivial versus topological  zero-bias conductance peaks