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We show that multiband superconductors with broken time-reversal symmetry can produce spontaneous currents and magnetic fields in response to the local variations of pairing constants. Considering the iron pnictide superconductor Ba1−xKxFe2As2 as an example we demonstrate that both the point-group symmetric s + is state and the C4-symmetry breaking s + id states produce in general the same magnitudes of spontaneous magnetic fields. In the s + is state these fields are polarized mainly in ab crystal plane, while in the s + id state their ab-plane and c-axis components are of the same order. The same is true for the random magnetic fields which are produced by the order parameter fluctuations near the critical point of the time-reversal symmetry breaking phase transition. Our findings can be used as a direct test of the s+is/s+id dichotomy and the additional discrete symmetry breaking phase transitions with the help of muon spin relaxation experiments.

The problem of the skyrmion stability in the magnetic film with perpendicular anisotropy covered with a superconducting layer is considered. The expression of the magnetic skyrmion energy is derived analytically within the London model for the superconductor. It is shown that skyrmion can be stabilized by the superconducting dot or antidot even in the absence of Dzyaloshinskii–Moriya interaction. The corresponding stability conditions are obtained numerically. The wide range of the material and geometrical parameters of the system is analyzed.

We show that time reversal symmetry-breaking p(x)+ip(y) wave superconductors undergo several phase transitions subjected to an external magnetic field or supercurrent. In such a system, the discrete Z(2) symmetry can recover before a complete destruction of the order parameter. The domain walls associated with Z(2) symmetry can be created in a controllable way by a magnetic field or current sweep according to the Kibble-Zurek scenario. Such domain wall generation can take place in exotic superconductors like Sr(2)RuO(4), thin films of superfluid (3)He-A, and some heavy fermion compounds.