How to systematically map out a Majorana island*

As a high-quality hybrid system, InSb nanowires with epitaxial-grown Al shells reveal ballistic superconductivity and quantized zero-bias conductance peak. This holds great promise for the realization of Majorana-based topological quantum computing. The building block for a topological qubit is a superconductor-semiconductor island hosting a pair of Majorana zero modes (called Majorana island). The state of the topological qubit is the combination of the even/odd parity of such Majorana islands. Therefore, to understand the status of the topological qubit, systematic studies of a Majorana island are crucial. First, by performing tunnelling spectroscopy measurements, we use the ballistic superconductivity and quantized zero-bias peak to support the high-quality and potential ‘Majorana’ properties of the island. Secondly, the even-odd ground state phase diagram as a function of chemical potential is mapped out and provides a guideline for the topological qubit. Thirdly, how the superconducting gap and effective g-factor influence the phase diagram is also studied. Such a systematic mapping of the Majorana island is also suitable for double islands, leading towards topological qubits based on multiple islands.