In semiconducting-superconducting hybrid devices, Andreev bound states (ABSs) can mediate the coupling between quantum dots, allowing for the realization of artificial Kitaev chains. In order to engineer Majorana bound states (MBSs) in these systems, one must control the energy of the ABSs. In this Letter, we show how extended ABSs in a flux-tunable Josephson junction can be used to control the coupling between distant quantum dots separated by ≃1  μm. In particular, we demonstrate that the combination of electrostatic control and phase control over the ABSs increases the parameter space in which MBSs are observed. Finally, by employing an additional spectroscopic probe in the hybrid region between the quantum dots, we gain information about the spatial distribution of the Majorana wave function in a two-site Kitaev chain.

Majorana zero modes are non-Abelian quasiparticles predicted to emerge at the edges of topological superconductors. A one-dimensional topological superconductor can be realized with the Kitaev model—a chain of spinless fermions coupled via p-wave superconductivity and electron hopping—which becomes topological in the long-chain limit. Here we realize a three-site Kitaev chain using semiconducting quantum dots coupled by superconducting segments in a hybrid InSb/Al nanowire. We investigate the robustness of Majorana zero modes under varying coupling strengths and electrochemical potentials, comparing two- and three-site chains realized within the same device. We observe that extending the chain to three sites enhances the stability of the zero-energy modes, especially against variations in the coupling strengths. This experiment lacks superconducting phase control, yet numerical conductance simulations with phase averaging align well with our observations. Our results demonstrate the scalability of quantum-dot-based Kitaev chains and its benefits for Majorana stability.

A chain of quantum dots (QDs) in semiconductor–superconductor hybrid systems can form an artificial Kitaev chain hosting Majorana bound states (MBSs). These zero-energy states are expected to be localized on the edges of the chain, at the outermost QDs. The remaining QDs, comprising the bulk, are predicted to host an excitation gap that protects the MBSs at the edges from local on-site perturbations. Here we demonstrate this connection between the bulk and edges in a minimal system, by engineering a three-site Kitaev chain in a two-dimensional electron gas. Through direct tunnelling spectroscopy on each site, we show that the appearance of stable zero-bias conductance peaks at the outer QDs is correlated with the presence of an excitation gap in the middle QD. Furthermore, we show that this gap can be controlled by applying a superconducting phase difference between the two hybrid segments and that the MBSs are robust only when the excitation gap is present. We find a close agreement between experiments and the original Kitaev model, thus confirming key predictions for MBSs in a three-site chain.

Majorana bound states are expected to appear in one-dimensional semiconductor-superconductor hybrid systems, provided they are homogeneous enough to host a global topological phase. In order to experimentally investigate the uniformity of the system, we study the spatial dependence of the local density of states in multiprobe devices where several local tunneling probes are positioned along a gate-defined wire in a two-dimensional electron gas. Spectroscopy at each probe reveals a hard induced gap and an absence of subgap states at zero magnetic field. However, subgap states emerging at a finite magnetic field are not always correlated between different probes. Moreover, we find that the extracted critical field and effective g-factor vary significantly across the length of the wire. Upon studying several such devices, we do however find examples of striking correlations in the local density of states measured at different tunnel probes. We discuss possible sources of variation across devices.