Integer and half-integer Shapiro steps in p-SQUIDs

We study the I-V characteristics of π-SQUID's in the presence of an rf radiation, adopting a perturbation approach to first order in the parameter β. We find that integer and half integer Shapiro steps appear in the I-V characteristics of these devices. In particular, half-integer Shapiro steps are seen to have amplitude proportional to β, while integer Shapiro steps are seen not to depend on β, except for applied magnetic fluxes being integer multiples of Φ 0