Parity transitions in the superconducting ground state of hybrid InSb-Al Coulomb islands

TL;DR

This study investigates the ground state parity transitions in hybrid InSb-Al superconducting islands under magnetic fields, revealing different parity regimes linked to subgap states, including potential Majorana modes.

Contribution

It identifies and characterizes three distinct ground state parity evolutions in hybrid superconducting islands, highlighting the role of zero-energy states and Majorana modes.

Findings

Observation of robust 2e-periodic even-parity ground state.

Identification of a transition to 2e-periodic odd-parity ground state.

Detection of 1e-periodic ground states linked to zero-energy states.

Abstract

The number of electrons in small metallic or semiconducting islands is quantized. When tunnelling is enabled via opaque barriers this number can change by an integer. In superconductors the addition is in units of two electron charges (2e), reflecting that the Cooper pair condensate must have an even parity. This ground state (GS) is foundational for all superconducting qubit devices. Here, we study a hybrid superconducting-semiconducting island and find three typical GS evolutions in a parallel magnetic field: a robust 2e-periodic even-parity GS, a transition to a 2e-periodic odd-parity GS,and a transition from a 2e- to a 1e-periodic GS. The 2e-periodic odd-parity GS persistent in gate-voltage occurs when a spin-resolved subgap state crosses zero energy. For our 1e-periodic GSs we explicitly show the origin being a single zero-energy state gapped from the continuum, i.e. compatible with an Andreev bound states stabilized at zero energy or the presence of Majorana zero modes.