Abstract
One of the quasi-one-dimensional organic superconductors $$(\hbox {TMTSF})_2X$$ , called Bechgaard salts, has attracted a lot of interest since its discovery in 1980. These compounds have high critical magnetic field $$H_{\mathrm {c}2}$$ in the direction parallel to the layers, and their pairing symmetries seem to be different between low-field phase and high-field phase. In addition, recently, the possibility of the realization of odd-frequency superconductivity was pointed out. Therefore, we study pairing symmetries of Bechgaard salts under magnetic field with frequency-dependent pairing interaction due to spin and charge fluctuation. The model is given by the extended Hubbard model on a quasi-one-dimensional square lattice, and the spin susceptibility and charge susceptibility for the effective pairing interactions are derived by random-phase approximation under magnetic field. The odd-frequency s-wave and even-frequency f-wave regions expand as the magnetic field is increased.
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