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 is temperature independent near the critical temperature Tc for weak BTRS, in accord with recent data. The Hall conductance is found to vanish at zero wavevector q and finite frequency ω, however at finite q, ω it has an unusual structure. Recent data on the high Tc superconductor Y Ba2Cu3Ox (YBCO) has supported the presence of broken time reversal symmetry (BTRS) [1–3]. A d wave superconductor would show Andreev bound states at zero bias, however tunnelling data shows in some cases states away from zero bias [1,2], in particular in overdoped YBCO [2], consistent with BTRS. Spontaneous magnetization in the absence of an external field has been observed in YBCO [3], setting in abruptly at Tc and is almost temperature (T ) independent below Tc. The phenomenon has been attributed to either a dx2−y2 + idxy state or to formation of π junctions. No microscopic reason was given, however, for the spontaneous magnetization being independent of both T and of film thickness [3].