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 Φ 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 Φ with a paramagnetic anomaly near Tc. The Hall conductance is found to vanish at zero wave vector q and finite frequency ω, however at finite q, ω it has an unusual structure