Ab-initio theory of phonon-driven superconductivity

A prominent challenge of condensed-matter theory is to reliably predict material-specific properties of superconductors, such as the critical temperature. The superconducting version of density functional theory (SCDFT) meets this challenge for phonon-driven superconductors. The central quantity of SCDFT is a universal exchange-correlation functional which depends both on the electronic density and on the superconducting order parameter [1]. With the best available approximations for this functional, SCDFT is a genuine ab-initio theory with no adjustable parameters, allowing the prediction of the critical temperatures of phonon-driven superconductors within a few percent of experiment [2]. Examples of intermetallic compounds as well as hydrogen-rich materials under pressure will be presented. Apart from Tc, other quantities, such as the order parameter in real space, and the excitation gap are directly accessible in SCDFT. Highly complex materials such as NbSe2, featuring a competition between superconductivity and a charge density wave at low temperature, can be fully understood [3] with this approach. Furthermore, for a variety of materials, we analyze how the order parameter in real space is related to the chemical bonding structure [4]. Regions in the unit cell that provide an attractive coupling can be beautifully distinguished from those that contribute via Coulomb renormalization and those that are not coupled at all. By controlling the local bonding structure, SCDFT offers a route to locally tailor the order parameter in superconducting nanostructures [5].



[1] L.N. Oliveira, E.K.U. Gross, W. Kohn, Phys.Rev.Lett. 60, 2430 (1988).

[2] A. Sanna, C. Pellegrini, E.K.U. Gross, Phys. Rev. Lett. 125, 057001 (2020).

[3] A. Sanna, C. Pellegrini, E. Liebhaber, K. Rossnagel, K.J. Franke, E.K.U. Gross, npj Quantum Materials (2022)7:6.

[4] A. Linscheid, A. Sanna, A. Floris, E.K.U. Gross, Phys. Rev. Lett. 115, (2015).

[5] M.Schackert, T. Märkl, J. Jandke, M. Hölzer, S. Ostanin, E.K.U. Gross, A. Ernst, W. Wulfhekel, Phys. Rev. Lett. 114, 047002 (2015).