Microscopic theory of the superconducting gap in the quasi-one-dimensional organic conductor (TMTSF)2ClO4 : Model derivation and two-particle self-consistent analysis

We present a first-principles band calculation for the quasi-one-dimensional (Q1D) organic superconductor ${\left(\mathrm{TMTSF}\right)}_2{\mathrm{ClO}}_4$. An effective tight-binding model with the TMTSF molecule to be regarded as the site is derived from a calculation based on maximally localized Wannier orbitals. We apply a two-particle self-consistent (TPSC) analysis by using a four-site Hubbard model, which is composed of the tight-binding model and an onsite (intramolecular) repulsive interaction, which serves as a variable parameter. We assume that the pairing mechanism is mediated by the spin fluctuation, and the sign of the superconducting gap changes between the inner and outer Fermi surfaces, which correspond to a $d$-wave gap function in a simplified Q1D model. With the parameters we adopt, the critical temperature for superconductivity estimated by the TPSC approach is approximately 1 K, which is consistent with experiment.