coupled with niobium islands*

To study how the superconductivity works in topological insulator, we performed a transport experiment to measure the proximity effect in devices consisting of an array of many niobium islands on a Bi₂Se₃ film. We extract parameters describing the Berezinskii-Kosterlitz-Thouless (BKT) phase stiffening transition in the resistance-temperature dependence. We have also measured nonlinear transport in the array and find that the BKT relationship between these two measurements holds. ARPES measurements were also done on another set of Nb/Bi₂Se₃ samples to study how deep Cooper pair penetrate into Bi₂Se₃. This allows us to determine how surface state carriers and bulk carriers participate in proximity induced superconductivity in Bi₂Se₃.