Coexistent symmetries in a two-band organic superconductor

We have revisited the phase diagram of perchlorate Bechgaard salts under magnetic field at small temperature, using a spin ladder model with a Hubbard Hamiltonian. Using a non-perturbative Gor'kov method, we have calculated the free energies of all possible phases, including a phase with coexisting singlet and triplet superconducting pairs. With our choice of coupling parameters, this coexisting phase proved not favorable. Nevertheless, this study opens new fields of investigation, while the search of such a coexisting phase seems a realistic and promising goal. •We solve BCS equations with two superconducting order parameters in a magnetic field.•Using a ladder model including orbital effect we predict triplet superconductivity.•The solution of coupled gap equations corresponds to a coexistence phase.•We establish new theoretical developments to calculate properly free energies.•We also predict new triplet states with singlet pairing instabilities.