Tunneling Gap as Evidence for Time-Reversal Symmetry Breaking at Surfaces of High-Temperature Superconductors

It is argued that recent Josephson junction and point-contact tunneling experiments, interpreted as intended by their authors, indicate that time-reversal symmetry breaking occurs at surfaces of cuprate superconductors. The variation among experiments and the failure of previous searches to find $T$-violation are ascribed to disorder and effects of 3-dimensionality. The ``anyon" approach to the $t$-$J$ model is shown to predict a conventional BCS order parameter of $d_{x^2-y^2} + i \epsilon \ d_{xy}$ symmetry, with $\epsilon $ roughly 3 times the doping fraction $\delta $, which is consistent with these experiments but not demonstrated by them.