Half-integer shapiro steps in DC SQUIDs with graphene junctions

When the characteristic frequency of a Josephson junction (JJ) matches an applied ac field, Shapiro steps appear in the current-voltage characteristic at voltages corresponding to integer multiples of the magnetic flux quantum proportional to the frequency of the applied field. Half-integer steps are expected to appear in JJs with a non-sinusoidal current-phase-relation[1], such as graphene junctions with highly transparent modes. Here we explore these half-integer steps in a DC superconducting quantum interference device (SQUID) formed from two graphene JJs, where half-steps can be seen when the magnetic flux in the loop is equal to half a flux quantum, as expected[2], but also for integer flux when the CPR is non-sinusoidal. We find that the appearance of the half-integer steps can be controlled by changing the doping in the graphene and by changing the temperature, as both of these mechanisms change the skewness of the CPR[3,4]. We also confirm these results to simulations performed with a numerical resistively and capacitively shunted junction (RCSJ) model.

[1] Ueda K, et al. Physical Review Research. 2020;2(3).

[2] Vanneste C, et al. Journal of Applied Physics. 1988; 64(1):242-5.

[3] Nanda G, et al. Nano Letters. 2017; 17(6):3396-401.

[4] Thompson MD, et al. 2017; 110(16).