Possible Pairing Symmetry of Superconductor Na_xCoO_2yH_2O

TL;DR

This study investigates the possible pairing symmetries in the superconductor Na_xCoO_2yH_2O using a Hubbard model and Eliashberg equations, identifying d-wave and f-wave as candidates but predicting lower transition temperatures than observed.

Contribution

It introduces a single-band Hubbard model based on LDA band structure calculations to analyze pairing symmetries in Na_xCoO_2yH_2O, considering both spin-singlet and triplet states.

Findings

Spin-singlet pairing likely has d-wave symmetry.

Spin-triplet pairing candidate is f-wave symmetry.

Estimated transition temperatures are lower than experimental observations.

Abstract

To discuss a possibility that the superconductivities in Na_xCoO_2yH_2O are induced by the electron correlation, we investigate the possible pairing symmetry based on the single-band Hubbard model whose dispersion of the bare energy band is obtained by using FLAPW-LDA band structure calculation of Na_xCoO_2yH_2O. The superconducting transition temperature is estimated by solving the Eliashberg 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 \lambda_max^SS of Eliashberg's equation) belongs to d-wave(E_2 representation of D_6 group). In the case of spin-triplet pairing, the candidate of pairing symmetry (the maximum eigen value \lambda_max^ST of Eliashberg's equation) belongs to f_{y(y^{2}-3x^{2})}-wave (B_1 representation of D_6 group). It is found that \lambda_max^SS\simeq\lambda_max^ST and the transition temperatures of unconventional pairing state are estimated to be low compared with observed temperature within our simple model.