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Broken time reversal symmetry (BTRS) in d+id' as well as in d+issuperconductors is studied and is shown to yield current carrying surfacestates. We evaluate the temperature and thickness dependence of the resultingspontaneous magnetization and show a marked difference between weak and strongBTRS. We also derive the Hall conductance which vanishes at zero wavevector qand finite frequency w, however at finite q,w it has an unusual structure. Thechirality of the surface states leads to quantum Hall effects for spin and heattransport in d+id' superconductors.Comment: 15 pages, 4 eps figure

Superconductors with broken time-reversal symmetry: Spontaneous magnetization and quantum Hall effects