Introducing electron correlation in solid-state calculations for superconducting states†

Analyzing the electronic localization of superconductors has been recently shown to be relevant for understanding their critical temperature [Nature Communications, 12, 5381, (2021)]. However, these relationships have only been shown at the Kohn–Sham density functional theory (DFT) level, where the onset of strong correlation linked to the superconducting state is missing. In this contribution, we approximate the superconducting gap in order to reconstruct the superconducting the one-reduced density matrix (1RDM) from a DFT calculation. This allows us to analyse the electron density and localization in the strong correlation regime. The method is applied to two well-known superconductors. Electron localization features along the electron–phonon coupling directions and hydrogen cluster formations are observed for different solids. However, in both cases we see that the overall localization channels are not affected by the onset of superconductivity, explaining the ability of DFT localization channels to characterize the superconducting ones.