Hidden reentrant and Larkin-Ovchinnikov-Fulde-Ferrell superconducting phases in a magnetic field in a (TMTSF)₂ClO₄

We solve a long-standing problem about a theoretical description of the upper critical magnetic field, parallel to conducting layers and perpendicular to conducting chains, in a (TMTSF)₂ClO₄ superconductor. In particular, we explain why the experimental upper critical field, Hc2b ^′6T, is higher than both the quasiclassical upper critical field and the Clogston paramagnetic limit. We show that this property is due to the coexistence of the hidden reentrant and Larkin-Ovchinnikov-Fulde-Ferrell phases in a magnetic field in the form of three plane waves with nonzero momenta of the Cooper pairs. Our results are in good qualitative and quantitative agreement with the recent experimental measurements of Hc2b^′ and support a singlet d-wave-like scenario of superconductivity in (TMTSF) ₂ClO₄.