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

Motivated by an important recent experiment, we theoretically consider the interplay between Andreev bound states(ABSs) and Majorana bound states(MBSs) in quantum dot-nanowire semiconductor systems with proximity-induced superconductivity(SC), spin-orbit coupling and Zeeman splitting. The dot induces ABSs in the SC nanowire which show complex behavior, and the specific question is whether two such ABSs can come together forming a topological MBS. We find that the ABSs indeed tend to coalesce together producing near-zero-energy states, but this mostly happens in the trivial regime although there are situations where the ABSs could come together forming a MBS. The two scenarios are difficult to distinguish by tunnel conductance. The "sticking together" propensity of ABSs to produce a zero-energy state is generic in class D systems, and by itself says nothing about the topological nature of the SC nanowire. Thus conductance measurements with the midgap sticking-together behavior of ABSs cannot be construed as definitive evidence for topological SC. We also suggest experimental techniques for distinguishing between trivial and topological ZBCPs.