Time reversal symmetry breaking superconductors

The paper reviews recent work on time reversal symmetry (TRS) breaking superconductors. The family of TRS breaking superconductors is growing relatively fast, with many of its newly discovered members being non-centrosymmetric. However, many of the superconductors which possess center of inversion also break TRS. The TRS is often identified by means of the muon spin relaxation effect ($\mu$SR) or/and the Kerr effect. Both methods effectively measure the spontaneous appearance of the bulk magnetic field below superconducting transition temperature. One of the systems most carefully studied so far is Sr$_2$RuO$_4$ believed to be spin triplet chiral p-wave superconductor. This compound provides an example of the material whose many band, multi-condensate modelling has enjoyed a number of successes. We discuss in some details the properties of the material. Among them is the polar Kerr effect, which understanding has resulted in the discovery of the novel mechanism of the phenomenon. The mechanism is universal and thus applicable to all systems with multiorbital character of states at the Fermi energy.