Electron Density Response to Phonon Dynamics in MgB2: An Indicator of Superconducting Properties

Abstract

Electron density differences resulting from atom displacement patterns aligned with phonon modes in MgB2 have been calculated using density functional theory (DFT). The extent of phonon anomalies, identified as indicators of the superconducting transition temperature, Tc, under a range of conditions in AlB2-type structures, reduce as boron atoms are displaced from their equilibrium positions along E2g mode directions. The Fermi energy for displacements along the directions of the E2g phonon mode accounts for changes in the covalent B-B bond electronic charge density. We applied differential atom displacements to show that the shifted σ band structure associated with the light effective mass became tangential to the Fermi level and that the Fermi surface undergoes a topological transition at a critical relative displacement of ~0.6% of the boron atoms from equilibrium. The difference in Fermi energies at this critical displacement and at the equilibrium position correspond to the superconducting energy gap. The net volume between tubular σ surfaces in reciprocal space correlated with the depth of the phonon anomaly and, by inference, it is a key to an understanding of superconductivity. This ab initioapproach offers a phenomenological understanding of the factors that determine Tc based on knowledge of the crystal structure.