Anisotropic Eliashberg theory of MgB₂: T_c, isotope effects, superconducting energy gaps, quasiparticles, and specific heat

The anisotropic Eliashberg formalism, employing results from the ab initio pseudopotential density functional calculations, is applied to study the superconducting properties of MgB₂. It is shown that the relatively high transition temperature of MgB₂ originates from strong electron-phonon coupling of the hole states in the boron σ-bonds although the coupling strength averaged over the Fermi surface is moderate, and the reduction of the isotope effect arises from the large anharmonicity of the relevant phonons. The superconducting energy gap is nodeless but its value varies strongly on different pieces of the Fermi surface. The gap values Δ(k) cluster into two groups at low temperature, a small value of ∼2 meV and a large value of ∼7 meV, resulting in two thresholds in the quasiparticle density of states and an increase in the specific heat at low temperature due to quasiparticle excitations over the small gap. All of these results are in good agreement with corresponding experiments and support the view that MgB₂ is a phonon-mediated multiple-gap superconductor.