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

TLDR

Motivated by a recent experiment, we theoretically study the interplay between Andreev bound states and Majorana bound states in quantum‑dot nanowire–superconductor hybrids with spin–orbit coupling and Zeeman splitting. The central question is whether two ABSs can merge to form a topological Majorana bound state. We analyze non‑SC, SC, and partially SC dot configurations, identify the critical Zeeman splitting for the topological transition or compute topological visibility, and propose experimental techniques to distinguish trivial from topological zero‑bias conductance peaks. We find that ABSs coalesce into near‑zero‑energy midgap states as Zeeman splitting or chemical potential increase, a behavior that occurs mainly in the non‑topological regime but can also produce a topological MBS, yet tunneling conductance signatures of the two scenarios are essentially indistinguishable, so the generic sticking‑together propensity of ABSs in class D systems provides no definitive evidence for topological superconductivity and requires careful interpretation of conductance measurements.

Abstract

Motivated by an important recent experiment [Deng et al., Science 354, 1557 (2016)], 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 as a function of Zeeman splitting and chemical potential, and the specific question is whether two such ABSs can come together forming a topological MBS. We consider physical situations involving the dot being non-SC, SC, or partially SC. We find that the ABSs indeed tend to coalesce together producing near-zero-energy midgap states as Zeeman splitting and/or chemical potential are increased, but this mostly happens in the non-topological regime although there are situations where the ABSs could come together forming a topological MBS. The two scenarios(two ABSs forming a near-zero-energy non-topological ABS or a zero-energy topological MBS) are difficult to distinguish by tunneling conductance spectroscopy due to essentially the same signatures. Theoretically we distinguish them by knowing the critical Zeeman splitting for the topological quantum phase transition or by calculating the topological visibility. We find that the "sticking together" propensity of ABSs to produce a zero-energy midgap state is generic in class D systems, and by itself says nothing about the topological nature of the underlying SC nanowire. One must use caution in interpreting tunneling conductance measurements where the midgap sticking-together behavior of ABSs cannot be construed as definitive evidence for topological SC with non-Abelian MBSs. We also suggest some experimental techniques for distinguishing between trivial and topological ZBCPs.