Defect motions and smearing of Shapiro steps in Josephson-junction ladders under magnetic frustration

We present simulation results on the dynamics of 1D Josephson ladder arrays at zero temperature in the presence of uniform magnetic fields when dc plus ac currents are applied. For a frustration f=p/q, the dynamics of the array can be described by the reduced equations for only q variables, if the initial configuration is assumed to be invariant under the q-lattice translation. When dc plus ac currents are injected, fractional Shapiro steps are found at time-averaged voltage 〈V〉=(n/q)(ħω/2e) with n an integer and ω the external driving frequency. If the ladder array is wound into an annular geometry, we can have defects in the vortex configuration depending on the initial random-phase configuration which cannot evolve into q-periodic states, and these defects are shown to smear the Shapiro steps. The dynamic resistance on the smeared Shapiro step is proportional to the number density of the defects.