Shapiro Step at Nonequilibrium Conditions
  Detailed numerical simulations of intrinsic Josephson junctions of high temperature superconductors under external electromagnetic radiation are performed taking into account a charge imbalance effect. We demonstrate that the charge imbalance is responsible for a slope in the Shapiro step the value of which increases with a nonequilibrium parameter. Coupling between junctions leads to the distribution of the slope's values along the stack. The nonperiodic boundary conditions shift the Shapiro step in IV-characteristics from the canonical position determined by $V_{ss}=\hbar f /(2e)$, where $f$ is a frequency of external radiation. This fact makes ambiguous the interpretation of the experimentally found Shapiro step shift by the charge imbalance effect. 
Yu. M. Shukrinov, M. Nashaat, K. V. Kulikov, R. Dawood, H. El Samman,   and Th. M. El Sherbini
cond-mat.supr-con