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.
Bibliographical noteFunding Information:
We would like to thank David Roundy and Hong Sun for collaborations of the work reviewed here. This work was supported by National Science Foundation grant no. DMR00-87088, and by the Director, Office of Science, Office of Basic Energy Sciences of the US Department of Energy under contract DE-AC03-76SF00098. Computational resources have been provided by the National Science Foundation at the National Center for Supercomputing Applications and by the National Energy Research Scientific Computing Center. H.J.C. acknowledges support from the Miller Institute for Basic Research in Science.
All Science Journal Classification (ASJC) codes
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics
- Energy Engineering and Power Technology
- Electrical and Electronic Engineering