On the Application of Bardeen–Cooper–Schrieffer Equations in Studies of the Pairing Mechanism in Iron Pnictides

The application of multiband Bardeen–Cooper–Schrieffer equations with semiempirical strong pairing corrections to determine the intraband and interband interaction constants of coupling in multiband superconductors from experimental data is considered. Using the example of the multiband superconductor MgB₂, it is shown that the inversion of such equations with the experimentally known ratios of the superconducting gaps in the σ and π bands of Δ_σ(0)/Δ_π(0) at temperatures of T → 0 and 2Δ_σ(0)/T_c (where T_c is the critical temperature of the transition to the superconducting state) as parameters makes it possible to reproduce the coupling constants in MgB₂ that are calculated ab initio with very good accuracy. Similar equations for two- and three-band iron pnictides with interband spin-fluctuation interaction are obtained and their features are considered. Such equations with experimental parameters represent a simple system of two (or three) algebraic equations. The solutions of the system of equations with experimentally found Δ_i(0)/Δ_j(0), 2Δ_j(0)/T_c, the electron-gap anisotropy coefficient η, and the density-of-state ratios γ_i/γ_j in the bands completely determine the coupling constants in the phonon and nonphonon channels and the degree of correlation of the spin and charge degrees of freedom of spin-fluctuation excitations. All the parameters necessary for calculating the intraband and interband interaction constants can be obtained, for example, from studies using tunneling spectroscopy.