Full parity phase diagram of a proximitized nanowire island

TL;DR

This study maps the charge periodicity transition in a hybrid nanowire island under varying magnetic fields and gate voltages, highlighting conditions favorable for Majorana zero modes and the importance of comprehensive phase space exploration.

Contribution

It provides the first detailed phase diagram of charge periodicity in a proximitized nanowire, combining experimental measurements with numerical simulations to identify optimal conditions for Majorana modes.

Findings

Charge periodicity transitions from 2e to 1e with magnetic field.

Correlated oscillations of conductance peak spacings and heights.

Non-topological states influence the 2e-1e transition at positive gate voltages.

Abstract

We measure the charge periodicity of Coulomb blockade conductance oscillations of a hybrid InSb-Al island as a function of gate voltage and parallel magnetic field. The periodicity changes from $2e$ to $1e$ at a gate-dependent value of the magnetic field, $B^*$, decreasing from a high to a low limit upon increasing the gate voltage. In the gate voltage region between the two limits, which our numerical simulations indicate to be the most promising for locating Majorana zero modes, we observe correlated oscillations of peak spacings and heights. For positive gate voltages, the $2e$-$1e$ transition with low $B^*$ is due to the presence of non-topological states whose energy quickly disperses below the charging energy due to the orbital effect of the magnetic field. Our measurements demonstrate the importance of a careful exploration of the entire available phase space of a proximitized nanowire as a prerequisite to define future topological qubits.