Measurement and simulation of half-integer Shapiro steps in graphene-based SQUIDs

Graphene-based superconducting quantum interference devices (SQUIDs) were measured in a current-biased regime with and without irradiation by a microwave (MW) signal. The charge carrier concentration in graphene can be varied with electrostatic gating, tuning the transparencies of the Josephson junctions (JJs) in the SQUIDs. The junctions in these devices are fabricated with graphene encapsulated in hexagonal boron nitride where the NbTi superconducting electrodes make highly transparent one-dimensional contacts with the graphene. They are expected to facilitate ballistic transport of charge carriers, implying a non-sinusoidal current-phase relation (CPR) similarly to superconductor-normal metal-superconductor (SNS) JJs. A characteristic feature of the non-sinusoidal CPR is the appearance of half-integer Shapiro steps when the CPR is highly skewed. Half-integer Shapiro steps should also be visible when an amount of magnetic flux equal to a half-integer multiple of the magnetic flux quantum is present in the SQUID loop. This sets this investigation apart from other work, which are focused on individual graphene-based JJs. As superconducting circuits become more complex, it will be important to understand the behaviour of circuit components beyond single junctions. These phenomena were explored both with the graphene SQUIDs and with a numerical simulation of the resistively and capacitively shunted junction (RCSJ) model. The simulation used a skewed CPR which could be varied based on the transparency of the JJs, applicable to ballistic SNS junctions. Simulation results confirmed the expected behaviours of devices with a skewed CPR and is a promising avenue for exploring further fractional Shapiro steps. The experimental measurements of the graphene SQUIDs found half-integer Shapiro steps, giving evidence of a ballistic tuneable CPR in these graphene-based devices and establishing a precedent for further investigation.