  In this letter we study the effect of time-reversal symmetric impurities on
the Josephson supercurrent through two dimensional helical metals such as on
topological insulator surface state. We show that contrary to the usual
superconducting-normal metal-superconducting junctions, the suppression of
supercurrent in superconducting-helical metal-superconducting junction is
mainly due to fluctuations of impurities in the junctions. Our results, which
is a condensed matter realization of a part of the MSW effect for neutrinos,
shows that the relationship between normal state conductance and critical
current of Josephson junctions is significantly modified for Josephson
junctions on the surface of topological insulators. We also study the
temperature-dependence of supercurrent and present a two fluid model which can
explain some of recent experimental results in Josephson junctions on the edge
of topological insulators.
