Gate- and flux-tunable sin(2φ) Josephson element with planar-Ge junctions

Hybrid superconductor-semiconductor Josephson field-effect transistors (JoFETs) function as Josephson junctions with gate-tunable critical current. Additionally, they can feature a non-sinusoidal current-phase relation (CPR) containing multiple harmonics of the superconducting phase difference, a so-far underutilized property. Here we exploit this multi-harmonicity to create a Josephson circuit element with an almost perfectly π-periodic CPR, indicative of a largely dominant charge-4e supercurrent transport. We realize such a Josephson element, recently proposed as building block of a protected superconducting qubit, using a superconducting quantum interference device (SQUID) with low-inductance aluminum arms and two nominally identical JoFETs. The latter are fabricated from a SiGe/Ge/SiGe quantum-well heterostructure embedding a high-mobility two-dimensional hole gas. By carefully adjusting the JoFET gate voltages and finely tuning the magnetic flux through the SQUID close to half a flux quantum, we achieve a regime where the $$\sin (2\varphi )$$ sin ( 2 φ ) component accounts for more than 95% of the total supercurrent. This result demonstrates a new promising route towards parity-protected superconducting qubits.