Shapiro Steps in ballistic Josephson junction based on a single Bi2Te2.3Se0.7 nanocrystal

Communications Materials. 2026. Vol. 7. Article 91.

Stolyarov V. S., Kozlov S. N., Yakovlev D. S., Skryabina O. V., Lvov D. S., Vasenko A., Zhou J., Kupriyanov M. Y., Golubov A., Feuillet-Palma C., Ménard G., Bergeal N., Roditchev D.

Superconducting proximity junctions based on topological insulators are widely believed to harbor Majorana-like bound states. If so, the static current phase relationship (CPR) should have a 4π-periodic component. It is then usually assumed that the static CPR can be extended to treat dynamic, voltage-biased, experiments and can justify the suppression of the first phase-lock-in microwave resonance (the first ”Shapiro step” absence). A recent theory by Galaktionov and Zaikin asserts that the static CPR is not applicable in the dynamic regime and that the first step can disappear even if the CPR is strictly 2π-periodic, provided that the junction is ballistic. Here we study Shapiro steps on Nb/Bi2Te2.3Se0.7/Nb junctions, based on ultrasmall single crystals of a 3D topological insulator synthesized by a physical vapor deposition (PVD) technique. We present evidence that our junctions are ballistic. When subjected to microwave radiation the junctions exhibit Shapiro steps, but the first step is missing. Traditionally it is assumed that the missing first step (MFS) effect cannot be observe in the presence of quasiparticle poisoning, since the 4π-periodic component is suppressed if quasiparticles are present. Here we demonstrate that the MFS effect can occur even on the retrapping branch of the VI curve, which is associated with an intense generation of quasiparticles. In other words, the missing first step effect occurs in the dissipative regime, in which normal cores of phase slips move across the junction at a high rate. These results show that the 4π-periodic component is not a necessary condition for the disappearance of the first step

Keywords: сверхпроводники, топологические изоляторы, proximity effect, эффект близости, superconductors, topological insulators, Josephson junctions, Джозефсоновские контакты, Shapiro steps, ступеньки Шапиро