Optical Conductivity in a Two-Band Superconductor: Pb

Abstract

We demonstrate the effect of bandstructure on the superconducting properties of Pb by calculating the strong-coupling features in the optical conductivity, $\sigma (\omega )$, due to the electron-phonon interaction. The importance of momentum dependence in the calculation of the properties of superconductors has previously been raised for MgB${}_2$. Pb resembles MgB${}_2$ in that it is a two band superconductor in which the bands' contributions to the Fermi surface have very different topologies. We calculate $\sigma (\omega )$ by calculating a memory function which has been recently used to analyze $\sigma (\omega )$ of Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$. In our calculations the two components of the Fermi surface are described by parameterizations of de Haas--van Alphen data. We use a phonon spectrum which is a fit to neutron scattering data. By including the momentum dependence of the Fermi surface good agreement is found with the experimentally determined strong-coupling features which can be described by a broad peak at around 4.5 meV and a narrower higher peak around 8 meV of equal height. The calculated features are found to be dominated by scattering between states within the third band. By contrast scattering between states in the second band leads to strong-coupling features in which the height of the high energy peak is reduced by $\sim 50$ compared to that of the low energy peak. This result is similar to that in the conventional isotropic (momentum independent) treatment of superconductivity. Our results show that it is important to use realistic models of the bandstructure and phonons, and to avoid using momentum averaged quantities, in calculations in order to get quantitatively accurate results.

References in corpus (11)

• Superconductivity of metallic boron in MgB_2
• Beyond Eliashberg superconductivity in MgB2: anharmonicity, two-phonon scattering, and multiple gaps
• Boron Isotope Effect in Superconducting MgB${}_2$
• First-Principles Calculation of the Superconducting Transition in MgB2 within the Anisotropic Eliashberg Formalism
• Effect of magnetic and non-magnetic impurities on highly anisotropic superconductivity
• High-transition-temperature superconductivity in the absence of the magnetic-resonance mode
• Tunneling spectroscopy in small grains of superconducting MgB2
• Electronic structure of MgB${}_2$ from angle-resolved photoemission spectroscopy
• Energy Gap from Tunneling and Metallic Sharvin Contacts onto MgB2: Evidence for a Weakened Surface Layer
• Determination of the Fermi Surface of MgB${}_2$ by the de Haas-van Alphen effect
• Inversion techniques for optical conductivity data

Cited by in corpus (1)

• Optical spectroscopy of superconducting Ba{0.55}K{0.45}Fe2As2: evidence for strong coupling to low energy bosons