We theoretically demonstrate that in a nonhysteretic Josephson junction (JJ) with a $2\pi$ periodic supercurrent in the presence of radio-frequency (RF) radiation one or several low-lying Shapiro steps could be absent in the voltage-current $\left(VI\right)$ characteristic. The effect exists at low RF power and at frequencies $f$ approximately ten times smaller than $f_0=I_c{R}_N/{\mathrm{\Phi }}_0$ (where $I_c$ is the critical current, $R_N$ is the normal-state resistance of the Josephson junction, and ${\mathrm{\Phi }}_0$ is the magnetic flux quantum). The origin of the effect is related to the large differential resistance $R_{\mathrm{diff}}=dV/dI$ near $I\simeq I_c$, which is significantly greater than the value predicted by the resistively capacitance shunted junction (RCSJ) model in the overdamped limit. Our theoretical results are supported by experiments on Nb/NbSi/Nb Josephson junctions with nonhysteretic $VI$ curves, where we observe the absence of one or more low-lying Shapiro steps, depending on the frequency and power of the RF radiation.

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• Josephson effect
• Josephson junctions
• Superconducting devices
• Resistivity measurements