Hidden reentrant superconducting phase in a magnetic field in (TMTSF)$_{2}$ClO$_{4}$

We suggest explanation of the high upper critical magnetic field, perpendicular to conducting chains and parallel to conducting layers, $H^{b'}_{c2}\simeq 6$ T, experimentally observed in the organic superconductor (TMTSF)$_2$ClO$_4$. In particular, we show that $H^{b'}_{c2}$ can be higher than both the quasiclassical upper critical field and Clogston–Chandrasekhar paramagnetic limit in a singlet quasi-one-dimensional superconductor. We predict the coexistence of the hidden Reentrant and Larkin–Ovchinnikov–Fulde–Ferrell phases in a magnetic field. Our results are compared to the recent experimental data and shown to be in a good agreement with the experiments.