Shapiro steps in ballistic Josephson junction based on a single Bi₂Te_2.3Se_0.7 nanocrystal

Josephson junctions based on topological insulators are expected to host Majorana-type bound states that promote a 4π-periodic current-phase relationship. One experimental consequence of this periodicity is the absence of odd Shapiro steps in the current-voltage characteristics under microwave radiation. Here, we experimentally study the frequency-dependent amplitude of Shapiro steps in a ballistic Josephson junction involving a 23 nm-thick single nanocrystal of topological insulator Bi₂Te_2.3Se_0.7 connected to two planar Nb-electrodes. We observe a progressive suppression of the first step while decreasing the frequency below 2 GHz. Using the two-channel thermal resistively shunted junction (tRSJ) model, we show that despite a ballistic regime, the overheating phenomena are enough to account for the observed effect. Our results highlight the complex physics of Josephson junctions and underscore that the missing first Shapiro step alone is not a definitive signature of topological superconductivity.