Effect of Impurities on the Josephson Current through Helical Metals: Exploiting a Neutrino Paradigm.

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

Level quantization for the noncommutative Chern-Simons theory.

We show that the coefficient of the three-dimensional Chern-Simons action on the noncommutative plane must be quantized. Similar considerations apply in other dimensions as well.