Generalized Coherent State Derivation of TDDFT Equations for Superconductors

TL;DR

This paper derives equations of motion for superconductors using a generalized coherent state approach, enabling analysis of Coulomb and pairing interactions, and calculates the transition temperature for 2D superfluidity.

Contribution

It introduces a novel variational method for deriving TDDFT equations for superconductors, incorporating both normal and anomalous density matrices.

Findings

Derived self-consistent equations for the superconducting order parameter Δ.

Analyzed the effects of Coulomb repulsion and pairing attraction.

Calculated the Kosterlitz-Thouless transition temperature for 2D superconductors.

Abstract

Equations of motion are derived for the normal and the anomalous single-electron density matrices of a Fermi liquid using a time dependent finite temperature generalized coherent state (GCS) variational ansatz for the many-body density matrix. Self-consistent equations for the order parameter $\Delta$ allow to investigate the interplay of Coulomb repulsion and pairing attraction in homogeneous and inhomogeneous Fermi-liquids with spontaneously broken symmetry such as high temperature superconductors. The temperature of the Kosterlitz-Thouless transition to the two-dimensional superfluidity is calculated.