  Broken time reversal symmetry (BTRS) in d wave superconductors is studied and
is shown to yield current carrying surface states. The corresponding
spontaneous magnetization is temperature independent near the critical
temperature Tc for weak BTRS, in accord with recent data. For strong BTRS and
thin films we expect a temperature dependent spontaneous magnetization with a
paramagnetic anomaly near Tc. The Hall conductance is found to vanish at zero
wavevector q and finite frequency w, however at finite q,w it has an unusual
structure.
