Some Aspects of the Strong Coupling Theory of Superconductivity

Abstract

<p>The formulation of the strong coupling theory of superconductivity on the imaginary axis has been used to investigate a wide variety of problems. First, Jʀ, the ratio of the jump in the quasiparticle current at the gap voltage, in a superconducting tunneling junction has been calculated for many materials to good accuracy. Correlations of Jʀ with the strong coupling parameters λ-μ and Tc/ωℓn is confirmed, where λ is the electron-phonon mass enhancement factor, μ the Coulomb repulsion pseudopotential, Tc the critical temperature, and ωℓn a frequency characteristic of the electron-phonon spectral density, α²F(Ω). The functional derivative of Jʀ is calculated for a selection of materials using a new faster method.</p> <p>As well, the effect of the shape of α²F(Ω) on 2Δ₀/KʙTc and certain thermodynamic ratios is investigated. It is found that this ratio is largely determined by the parameters Tc and ωℓn for 2Δ₀/KʙTc and by Tc, ωℓn, and the area. A, under α²F(Ω) for the thermodynamics.</p> <p>The effects of pressure on α²F(Ω) are investigated using a simple model with a single adjustable parameter fitted to Tc. Model predictions of the behaviour of Δ₀ and the thermodynamics under pressure compare well with experiment.</p> <p>A simple model of alloying effects on α²F(Ω) with a single free parameter fitted to Tc is investigated. Comparison to Nb-Ta alloys is made with good results.</p> <p>Three procedures for extracting 2Δ₀/KʙTc from the electronic specific heat are examined for a selection of real and model spectra. One low temperature (T < ≈0.5Tc) method works well, but the other two high temperature (T > 0.5Tc) do not.</p> <p>A recent tunneling measurement of α²F(Ω) for NbN, displaying an unusually large value of μ*, has been studied. Computed results for thermodynamic and optical properties, using this spectra are consistent with experiment.</p> <p>Finally, inelastic scattering of electrons of paramagnetic impurities has been incorporated into strong coupling theory. Calculations show that this scattering can have measureable effect if the scattering potential is comparable to that of the host material.</p>