A simple theory of 40 K superconductivity in MgB 2: first-principles calculations of Tc, its dependence on boron mass and pressure

Abstract

We have studied the superconducting properties of MgB 2 from first-principles under isotropic, uniaxial, and biaxial compressions. We find that the in-plane boron phonons near the zone-center are very anharmonic and strongly coupled to the planar B σ bands near the Fermi level. This mode is found to be the key to quantitatively explain the observed high T c, the total isotope effect and the pressure dependence of T c. We propose that a stringent test on the hole and phonon based theories of the superconductivity in MgB 2 would be a measurement of the biaxial ab-compression dependence of T c.