Fermi surfaces and Luttinger's theorem in paired fermion systems

TL;DR

This paper explores the ground state properties of a two-fermion species mixture with molecular boson formation, analyzing Fermi surfaces, Luttinger's theorem constraints, and quantum phase transitions in Bose-Fermi mixtures.

Contribution

It provides a detailed analysis of Fermi surface constraints and phase transitions in unbalanced Bose-Fermi mixtures, extending understanding of Luttinger's theorem in these systems.

Findings

Fermi surfaces can appear in unbalanced fermion mixtures.

Luttinger's theorem constrains the Fermi surface volumes.

Quantum phase transitions involve changes in the number of Fermi surfaces.

Abstract

We discuss ground state properties of a mixture of two fermion species which can bind to form a molecular boson. When the densities of the fermions are unbalanced, one or more Fermi surfaces can appear: we describe the constraints placed by Luttinger's theorem on the volumes enclosed by these surfaces in such Bose-Fermi mixtures. We also discuss the nature of the quantum phase transitions involving changes in the number of Fermi surfaces.