Two Types of the Effective Mass Divergence and the Gr\"uneisen Ratio in Heavy Fermion Metals

TL;DR

This paper analyzes two distinct divergence behaviors of the effective mass and Gr"uneisen ratio near fermion condensation quantum phase transitions in heavy fermion metals, revealing different regimes of non-Fermi liquid and Fermi liquid states.

Contribution

It identifies and characterizes two types of effective mass divergence and Gr"uneisen ratio behavior near FCQPT, providing a detailed theoretical framework for heavy fermion systems.

Findings

Near FCQPT, specific heat c_p ∝ √T and effective mass M* ∝ 1/√T.

At the transition, the Gr"uneisen ratio diverges as 1/√T.

In the Fermi liquid phase, the ratio diverges as 1/r with r being the distance from the critical point.

Abstract

The behavior of the specific heat $c_p$, effective mass $M^*$, and the thermal expansion coefficient $\alpha$ of a Fermi system located near the fermion condensation quantum phase transition (FCQPT) is considered. We observe the first type behavior if the system is close to FCQPT: the specific heat $c_p\propto \sqrt{T}$, $M^*\propto1/\sqrt{T}$, while the thermal expansion coefficient $\alpha\propto \sqrt{T}$. Thus, the Gr\"uneisen ratio ${\rm \Gamma}(T)=\alpha/c_p$ does not diverges. At the transition region, where the system passes over from the non-Fermi liquid to the Landau Fermi liquid, the ratio diverges as ${\rm \Gamma}(T)\propto 1/\sqrt{T}$. When the system becomes the Landau Fermi liquid, ${\rm \Gamma}(T,r)\propto 1/r$, with $r$ being a distance from the quantum critical point. Provided the system has undergone FCQPT, the second type takes place: the specific heat behaves as $c_p\propto \sqrt{T}$, $M^*\propto 1/T$, and $\alpha=a+bT$ with $a,b$ being constants. Again, the Gr\"uneisen ratio diverges as ${\rm \Gamma}(T)\propto 1/\sqrt{T}$.