Type-IV superconductivity: Cooper pairs with broken inversion and time-reversal symmetries in conventional superconductors

The vortex phase in a singlet superconductor in the absence of impurities is shown to be absolutely unstable with respect to the appearance of a triplet component that breaks both the inversion and time-reversal symmetries of Cooper pairs. The symmetry breaking paramagnetic effects are demonstrated to be of the order of unity if the orbital upper critical field, H_{c 2}(0), is of the order of the Clogston paramagnetic limiting field, H_p. We suggest a generic phase diagram of such a type-IV superconductor that is a singlet one at H = 0 and characterized by a mixed singlet-triplet order parameter with broken time-reversal symmetry in the vortex phase. The possibility to observe type-IV superconductivity in clean organic, high-T_c, MgB₂, and other superconductors is discussed.