Giant Shapiro steps in Josephson-junction arrays

Giant Shapiro steps have recently been observed in the I-V characteristics of Josephson-junction arrays, both with and without transverse magnetic fields. For magnetic fluxes per unit cell of the array {Φ}=(p/q)Φ₀, these steps occur at voltages per unit cell of {}{ω}/2eq, where {ω} is the frequency of the rf field. I present a calculation of this effect, restricted to certain values of f=p/q and certain current directions within the lattice. This calculation leads to results concerning the width of steps as a function of q and as a function of the amplitude of the driving field. It also leads to a prediction of subharmonic steps, at voltages of ({}{ω}/2e)(n/qm).