Possible Pairing Symmetry of Superconductor Na_xCoO₂·yH₂O

Abstract

To discuss the possibility that the superconductivities in Na_xCoO₂·yH₂O are induced by electron correlation, we investigate the possible pairing symmetry based on the single-band Hubbard model whose dispersion of the bare energy band is obtained using the band structure calculation of Na_xCoO₂·yH₂O. The superconducting transition temperature is estimated by solving the Éliashberg equation. In this equation, both normal and anomalous self-energies are calculated up to the third-order terms with respect to the Coulomb repulsion. In the case of spin-singlet pairing, the candidate of pairing symmetry (the maximum eigen value λ_max^SS of Éliashberg’s equation) belongs to the d-wave (E₂ representation of D₆ group). In the case of spin-triplet pairing, the candidate of pairing symmetry (the maximum eigen value λ_max^ST of Éliashberg’s equation) belongs to the f_{y(y²−3x²)}-wave (B₁ representation of D₆ group). It is found that λ_max^SS\\simeqλ_max^ST and the transition temperatures of unconventional pairing state are estimated to be low compared with the observed temperature within our simple model.