Regensburg 2019 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 22: Superconductivity: Theory

TT 22.3: Talk

Tuesday, April 2, 2019, 10:00–10:15, H7

Reduced Density Matrix Functional Theory for Superconductors — Jonathan Schmidt, •Carlos Benavides Riveros, and Miguel Marques — Martin-Luther Universität Halle Wittenberg

We present a new ab-initio theory for superconducting systems with nonlocal external potentials based on the one-particle reduced density matrix ρ(r,r′), the anomalous density χ(r,r′) and the nuclear density D(r,r′). We prove that all the system’s equilibrium properties are determined uniquely by these three quantities and deduce a variational principle for the grand canonical potential in terms of them. By replacing the local electronic density, which is used in density functional theory for superconductors (SC-DFT), with the non-local one-particle reduced density matrix, our theory is able to solve difficulties which arise in SC-DFT through the combination of local and non-local quantities.

Analogue to the Kohn-Sham system in DFT, we prove the existence of a Kohn-Sham system that is able to reproduce ρ, χ and D of an interacting system at finite temperature. On the basis of the Kohn-Sham system, we obtain a set of Bogoliubov-De Gennes-like single particle equations. Finally, we derive a first exchange-correlation functional through the Sham-Schlüter connection.