Spontaneous magnetization and Hall effect in superconductors with broken time-reversal symmetry

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