  Majorana zero modes are predicted in several solid state systems such as
hybrid superconductor-semiconductor structures and topological insulators
coupled to superconductors. One of the expected signatures of Majorana modes is
the fractional 4$\pi$ Josephson effect. Evidence in favor of this effect often
comes from a.c. Josephson effect measurements and focuses on the observation of
missing first or higher odd-numbered Shapiro steps. However, the disappearance
of the odd Shapiro steps has also been reported in conventional Josephson
junctions where no Majorana modes are expected. In this paper, we present a
phenomenological model that displays suppression of the odd Shapiro steps. We
perform resistively-shunted junction model calculations and introduce peaks in
differential resistance as function of the bias current. In the presence of
only the standard 2$\pi$ Josephson current, for chosen values of peak positions
and amplitudes, we can suppress the odd Shapiro steps, or any steps, thus
providing a possible explanation for the observation of missing Shapiro steps.

Mesoscale and Nanoscale Physics;Superconductivity