Phonon dispersion models for MgB2 with application of pressure

We evaluate, via the Local Density and the Generalised Gradient Approximations to the Density Functional Theory (DFT), the change in form and extent of the E2g phonon anomaly of MgB2 with increase in applied pressure up to 20 GPa. Ab initio DFT calculations on the phonon dispersion (PD) for MgB2 show a phonon anomaly symmetrically displaced around Γ, the reciprocal lattice origin. This anomaly is related to nesting between diametrically opposite sides of tubular elements of Fermi surfaces, which correspond to sigma bonding and run approximately parallel to the Γ-A reciprocal space direction. The anomaly is parallel to Γ-A and along Γ-M and Γ-K. The extent of the E2g phonon anomaly, δ, along Γ-M and Γ-K is a measure of the thermal energy, Tδ, that matches within error the experimental onset superconducting transition temperature, Tc. Ab initio DFT calculations with pressure for −5 GPa < P < 20 GPa show a linear reduction in Tδ that closely matches experimental Tc values for MgB2. For phonon-mediated superconductors with AlB2-type structures, the thermal energy of the phonon anomaly, Tδ, is a reliable predictor of Tc.