First-principles calculation of the superconducting transition in MgB2 within the anisotropic Eliashberg formalism -: art. no. 020513

We present a study of the superconducting transition in MgB2 using the ab initio pseudopotential density-functional method, a fully anisotropic Eliashberg equation, and a conventional estimate for mu(*). Our study shows that the anisotropic Eliashberg equation, constructed with ab initio calculated momentum-dependent electron-phonon interaction and anharmonic phonon frequencies, yields an average electron-phonon coupling constant lambda=0.61, a transition temperature T-c=39 K, and a boron isotope-effect exponent alpha(B)=0.32. The calculated values for T-c, lambda, and alpha(B) are in excellent agreement with transport, specific-heat, and isotope-effect measurements, respectively. The individual values of the electron-phonon coupling lambda(k,k(')) on the various pieces of the Fermi surface, however, vary from 0.1 to 2.5. The observed T-c is a result of both the raising effect of anisotropy in the electron-phonon couplings and the lowering effect of anharmonicity in the relevant phonon modes.