Josephson junctions made of closely-spaced conventional superconductors on the surface of 3D topological insulators have been proposed to host Andreev bound states (ABSs) which can include Majorana fermions. Here, we present an extensive study of the supercurrent carried by low energy ABSs in Nb/Bi$_2$Se$_3$/Nb Josephson junctions in various SQUIDs as we modulate the carrier density in the Bi$_2$Se$_3$ barriers through electrostatic top gates. As previously reported, we find a precipitous drop in the Josephson current at a critical value of the voltage applied to the top gate. This drop has been attributed to a transition where the topologically trivial 2DEG at the surface is nearly depleted, causing a shift in the spatial location and change in nature of the helical surface states. We present measurements that support this picture by revealing qualitative changes in the temperature and magnetic field dependence of the critical current across this transition. In particular, we observe pronounced fluctuations in the critical current near total depletion of the 2DEG that demonstrate the dynamical nature of the supercurrent transport through topological low energy ABSs.
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