Shapiro steps in symmetric π-SQUID's

Integer and half-integer Shapiro steps amplitudes in the current-voltage characteristics of symmetric superconducting quantum interference devices containing one π-junction are calculated, in the absence of noise and for small values of the parameter β, by means of a reduced two-junction interferometer model. We find that, to first order in the parameter β, half-integer Shapiro steps are seen to have amplitude proportional to β, itself, while integer Shapiro steps are seen not to depend on β, except for applied fluxes being integer multiples of the elementary flux quantum Φ0.