Theory of fermion condensation as an analog of the liquid-drop theory of atomic nuclei

TL;DR

This paper explores the theory of fermion condensation, proposing it as a phase transition related to Fermi surface topology changes, using duality between momentum and density distributions.

Contribution

It introduces a novel perspective linking fermion condensation to Lifshitz topological phase transitions and Fermi surface topology changes.

Findings

Fermion condensation is associated with Lifshitz topological phase transition.

Duality between momentum and density distributions aids in understanding flat band systems.

Fermi surface topology changes precede fermion condensation.

Abstract

Employing the duality between the momentum distribution $n(p)$ and density distribution $\rho(r)$, problems of theory of systems with flat bands, pinned to the Fermi surface, are discussed. We propose that the Lifshitz topological phase transition associated with the formation of additional pockets of the Fermi surface is the precursor of fermion condensation.