Appearance of Fermion Condensation Quantum Phase Transition in Different Fermi Liquids

TL;DR

This paper demonstrates that fermion condensation quantum phase transition (FCQPT) causes the divergence of quasiparticle effective mass in Fermi liquids, and this behavior is universal across different dimensions and systems, supported by experimental data.

Contribution

The study reveals the universal appearance of FCQPT in Fermi liquids and describes how effective mass diverges near the critical point, with experimental validation across various systems.

Findings

Effective mass diverges as 1/(x - x_{FC}) near critical density.

Applying a magnetic field B tunes the system back to normal Fermi liquid behavior.

Kadowaki-Woods ratio remains constant near the critical point.

Abstract

We show that the quasiparticle effective mass $M^*$ diverges as a function of the system's density $x$, $M^*\propto 1/(x-x_{FC})$, when a system approaches the critical point $x_{FC}$ at which the fermion condensation quantum phase transition (FCQPT) occurs. Such behavior is of general form and takes place in both three dimensional systems and two dimensional ones. We demonstrate that a system which has undergone FCQPT and lies close to the critical point $x_{FC}$ can be driven back into the normal Fermi liquid by applying a small magnetic field $B$. As the field $B$ is reduced, the system is tuned back to the critical point and the effective mass diverges as $M^*\propto 1/\sqrt{B-B_{FC}}$ where $B_{FC}$ is the maximum field at which FCQPT takes place. We demonstrate the constancy of the Kadowaki-Woods ratio when approaching the critical point at the fields $B>B_{FC}$. Analyzing recent experimental data on the effective mass behavior in a strongly correlated two dimensional fluid $^3$He, in metallic two dimensional electron systems and in heavy-fermion systems, we show that the observed behavior is in agreement with our consideration. As a result, we may conclude that FCQPT can be conceived of as a universal cause of the strongly correlated regime in different Fermi liquids.