Superconducting critical temperature and the isotope exponent versus total electron concentration for two-band superconductors: Effect of the band structure

Abstract

We consider the superconducting critical temperature Tc and the isotope exponent α versus carrier concentration ρ using the one-particle Green functions of the simplest coupled Hamiltonian for the two-band model with a single Tc [N. Kristoffel and P. Rubin, Physica C 356, 171 (2001)]. One of the bands, ɛ2(k→), is taken to be two dimensional, while the second band ɛ3(k→) is taken to be three dimensional. Taking only nearest-neighbor hopping for each one of the bands, we obtain that Tc versus ρ is symmetric around half filling in agreement with a general theorem of quantum mechanics. We also obtained the chemical potential μ versus ρ for several values of attractive interaction. We find that (1) the superconducting critical temperature Tc is maximum at ρ=1/2; (2) the chemical potential remains basically inside the smaller band, for the range of carrier concentration and Debye frequencies considered; (3) the isotope exponent has several symmetric minima around half filling depending on the anisotropy of the three-dimensional tight-binding band, namely, γ≡t3,x/t3,z≠1; (4) the chemical-potential curves, namely, μ versus ρ are completely independent of pairing interaction and Debye frequency; and (5) the number of symmetric minima and Tcmax goes down with increasing t3/t2 ratio. We have briefly discussed the possible relevance of our results with recent experimental data of the two-band compound MgB2.

Source-reported materials — not catalogue approval

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