Superconductivity in Uranium Compounds

On the basis of microscopic theory it is demonstrated how the coupling between the electrons by means of magnetization fluctuations in ferromagnetic metal with orthorhombic symmetry gives rise equal spin pairing superconducting state with general form of the order parameter dictated by symmetry. The strong upturn of the upper critical field along $b$-direction above 5 Tesla in UCoGe is explained by the increase of pairing interaction caused by the suppression of the Curie temperature by magnetic field parallel to b-axis. It is proposed that similar phenomenon at much higher field must take place also for the field directed along the magnetically hardest a-direction.