Density Functional Theory of Fermion Condensation

Abstract

In this chapter, a density functional formulation of the fermion condensation is presented. It is demonstrated that the standard Kohn-Sham scheme is not valid beyond the topological FCQPT since the functional of the free energy F starts to depend on the quasiparticle density matrix. In the case of infinite homogeneous system, the ground state energy E becomes a functional of the quasiparticle occupation numbers $n(\mathbf{p})$, $E[n(\mathbf{p})]$. Thus, our consideration demonstrates that both the Landau Fermi liquid theory and the fermion-condensation theory are microscopic theories rather than phenomenological ones. We also present both the functional equation that defines the functional and a procedure to solve the equation. Our consideration also furnishes an opportunity to calculate the real single-particle excitation spectra of superconducting systems within the density functional theory. We show that the standard superconducting state, taking place in conventional metals, is strongly modified by the FC state, as it is shown in detail in Chap. 23.