Anisotropic Eliashberg theory for superconductivity in compressed and doped MgB2

We have studied superconducting properties of compressed and doped MgB2 by performing first-principles calculations of the normal material properties and by solving the fully anisotropic Eliashberg equations. At each pressure or doping, electronic structures, phonon spectra, and momentum-dependent electron-phonon coupling strengths are calculated. Then using the fully anisotropic Eliashberg equations, the superconducting transition temperatures (T-c), the superconducting energy gaps [Delta(k)], and the specific heats are obtained. Our results show that the multiple-gap nature of Delta(k) in MgB2 is robust with applied pressure although T-c and Delta(k) decrease substantially and that electron doping reduces T-c and degrades severely the superconducting energy gap in the pi bands.