Model for missing Shapiro steps due to bias-dependent resistance and Shapiro steps experiments in topologically trivial planar Josephson junctions

In this talk, we introduce a new phenomenological model to explain the suppression of Shapiro steps, thus giving an alternative explanation for missing Shapiro steps. We introduce non-linearity in the RSJ model by introducing peaks in the differential resistance as a function of the dc current bias. We demonstrate that such peaks can suppress odd Shapiro steps in the presence of only a 2π periodic current and thus mimic the 4π Josephson effect which is considered a signature of topological superconductors hosting Majorana fermions. We also show that these resonance peaks can be used to suppress any Shapiro step. We finally discuss the limitations of our model and its applicability to recent experiments where such resonances have been observed.

We will also introduce our experiment on highly-transparent topologically-trivial Josephson junctions made of epitaxial Al/InAs quantum well system. Junctions are patterned by a new nanowire shadowing technique. We study Shapiro steps at a variety of frequencies and magnetic fluxes. Missing odd Shapiro steps up to index 5 is observed. Various explanations are discussed for missing odd Shapiro steps in our topologically-trivial system.