  Using non-equilibrium Green's functions, we studied numerically the transport
properties of a Josephson junction, superconductor-topological
insulator-superconductor hybrid system. Our numerical calculation shows first
that proximity-induced superconductivity is indeed observed in the edge states
of a topological insulator adjoining two superconducting leads and second that
the special characteristics of topological insulators endow the edge states
with an enhanced proximity effect with a superconductor but do not forbid the
bulk states to do the same. In a size-dependent analysis of the local current,
it was found that a few residual bulk states can lead to measurable resistance,
whereas because these bulk states spread over the whole sample, their
contribution to the interference pattern is insignificant when the sample size
is in the micrometer range. Based on these numerical results, it is concluded
that the apparent disappearance of residual bulk states in the superconducting
interference process as described in Ref. [\onlinecite{HartNautrePhys2014f}] is
just due to the effects of size: the contribution of the topological edge
states outweighs that of the residual bulk states.
