Type-IV Superconductivity: Cooper Pairs with Broken Inversion and Time-Reversal Symmetries in Conventional Superconductors

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 which breaks both inversion and time-reversal symmetries of Cooper pairs. Symmetry breaking paramagnetic effects are demonstrated to be of the order of unity if the orbital upper critical field, $H_{c2}(0)$, is of the order of Clogston paramagnetic limiting field, $H_p$. We suggest a generic phase diagram of such type-IV superconductor, which is singlet one at $H=0$ and characterized by mixed singlet-triplet order parameter with broken time-reversal symmetry in vortex phase. A possibility to observe type-IV superconductivity in clean organic, high-$T_c$, $\mathrm{MgB_2}$, and other superconductors is discussed.