First-Principles Calculation of the Real-Space Order Parameter and Condensation Energy Density in Phonon-Mediated Superconductors

We show that the superconducting order parameter and condensation energy density of phonon-mediated superconductors can be calculated in real space from first principles density functional theory for superconductors. This method highlights the connection between the chemical bonding structure and the superconducting condensation and reveals new and interesting properties of superconducting materials. Understanding this connection is essential to describe nanostructured superconducting systems where the usual reciprocal space analysis hides the basic physical mechanism. In a first application we present results for MgB₂, CaC₆ and hole-doped graphane.