Modelling the Superconducting Proximity Effect in Bi₂Se₃

We analyze data from two recent experiments we carried out, studying the superconducting proximity effect in B_i2Se₃, using the quasiclassical Green’s function formulation of the Usadel equations. One experiment studied the resistive transition on Bi2Se3 films covered with niobium islands, while the other used ARPES to measure E(k) at low temperatures in Bi₂Se₃ films of different thicknesses formed on niobium substrates to determine the dependence of the density of states on temperature and depth. We extract the pair amplitude as a function of energy and depth and use the Usadel equation to describe how this varies in space. This provides a prediction of the Berezinskii-Kosterlitz-Thouless transition temperature in the island arrays.