Cooper pairs with broken time-reversal, parity, and spin-rotational symmetries in singlet type-II superconductors

We show that singlet superconductivity in the Abrikosov vortex phase is absolutely unstable with respect to the appearance of a chiral triplet component of a superconducting order parameter. This chiral component p_x+ip_y breaks time-reversal, parity, and spin-rotational symmetries of the internal order parameter responsible for a relative motion of two electrons in the Cooper pair. We demonstrate that the symmetry-breaking Pauli paramagnetic effects can be tuned by a magnetic-field strength and direction and can be made of the order of unity in organic and high-temperature layered superconductors.