We develop theoretical model explaining these oscillations in terms of fine structure of low-energy Andreev bound states. We show that in the mK temperature range the investigated junctions exhibit a new type of oscillations of the Josephson current in magnetic field with an ultra-short period ∼ 1 Oe corresponding to energy spectrum with the level spacing of order of 1 µeV. In this work we report direct observation of the Josephson effect in the Nb/Bi2Te2Se/Nb structures which are characterized by ballistic electronic transport across the Bi2Te2Se nanocrystals. However, the phase-sensitive measurements of the Josephson currents that would serve as conclusive evidence of the p-wave symmetry are still lacking. There have been reports of the 4π-periodicity in such contacts, which are a hallmark of the p-wave superconductivity. The practical ways for its implementing are being extensively discussed in literature, and the contact of a superconductor with the topological insulator is expected to become the most promising candidate. The famed p-wave superconductivity harbors a variety of exotic topological states.
