Calculation of λ for the quasi-one-dimensional superconductor V₃Si

The band structure and the electron-phonon coupling are calculated for a σ-band hybridized with a δ₁-band using tight-binding parameters fit for V₃Si. The hybridization gives rise to a sharp peak in the electronic density of states near the state Γ₁₂ of the δ₁-band. The variation of the parameter N(0)I² (N(0) - the electronic density of states at the Fermi level, I² - the electron-phonon coupling constant) is studied at the vicinity of the Γ₁₂(δ₁) peak. It is found that there is some compensation between N(0) and I²; the narrow δ₁-band gives rise to a large value of N(0), but a small value of I²; while the σ-band gives rise to a large value of I², but a small value of N(0). As a result, the product N(0)I² does not follow the behavior of N(0) even qualitatively, and it possesses a maximum far from the peak in N(0). Following this calculation, and previous calculations for the δ₂ and σ-bands, an approximate relationship is developed for the contribution λ_ito λ, coming from the various sub-bands of the 3d band, depending on the individual width of the sub-band, and its contribution to the density of states.