Phase Diagram of Majorana Island

Scalable topological qubit proposals based on semiconductor-superconductor systems are built on Majorana islands hosting pairs of Majorana zero modes. Here, by systematically measuring the periodicity of Coulomb blockade oscillations of InSb/Al island, we reconstruct the ground state parity of the island over large ranges of magnetic field and plunger gate voltage (Vpg). The resulting phase diagram can be divided into three regimes compared with numerical simulations. For negative Vpg, sub-gap states are absent due to strong proximity effect, so the 2e to 1e-periodic transition happens at high B-fields, indicating the poisoning of the superconducting state. For positive Vpg, the 2e-1e transition happens instead at a constant but small B-field. The reason is un-proximitized states quickly disperse below the charging energy due to the orbital effect of the magnetic field. The two regimes are separated by an intermediate regime where the 2e-1e transition field varies smoothly with Vpg, which is the most promising for locating a robust topological phase according to simulations. In this regime, we observe correlated oscillating peak spacing and heights. This complete phase diagram of Majorana island can lead to a guideline to set up a topological qubit in more complicated devices.