We report transport measurements on Josephson junctions consisting of Bi2Te3 topological insulator (TI) thin films contacted by superconducting Nb electrodes. For a device with junction length L = 134 nm, the critical supercurrent I c can be modulated by an electrical gate which tunes the carrier type and density of the TI film. I c can reach a minimum when the TI is near the charge neutrality regime with the Fermi energy lying close to the Dirac point of the surface state. In the p-type regime the Josephson current can be well described by a short ballistic junction model. In the n-type regime the junction is ballistic at 0.7 K < T < 3.8 K while for T < 0.7 K the diffusive bulk modes emerge and contribute a larger I c than the ballistic model. We attribute the lack of diffusive bulk modes in the p-type regime to the formation of p–n junctions. Our work provides new clues for search of Majorana zero mode in TI-based superconducting devices.

New Dirac points may appear when periodic potentials are applied to graphene, and there are many interesting effects near them. Here we investigate the Zitterbewegung effect of fermions described by a Gaussian wave packet in graphene superlattice near these points. The Zitterbewegung near different Dirac points has similar characteristics, while fermions near new ones have different group velocities in both x- and y-direction, which causes the different properties of the Zitterbewegung near them. We also investigate the Zitterbewegung effect influenced by multi Dirac points, and get the evolution with changing potential. Our results suggest that graphene superlattice may provide an appropriate system to study the Zitterbewegung effect near new Dirac points experimentally.

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