Two Types of the Effective Mass Divergence and the Grüneisen Ratio in Heavy Fermion Metals

Abstract

The behavior of the specific heat $c_p$, effective mass $M^{\ast }$, 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 $c_p\propto \sqrt{T}$, $M^{\ast }\propto 1/\sqrt{T}$, while the thermal expansion coefficient $\alpha \propto \sqrt{T}$. Thus, the Grüneisen ratio $\mathrm{\Gamma }(T)=\alpha /c_p$ 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 $\mathrm{\Gamma }(T)\propto 1/\sqrt{T}$. When the system becomes the Landau Fermi liquid, $\mathrm{\Gamma }(T,r)\propto 1/r$, 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 $c_p\propto \sqrt{T}$, $M^{\ast }\propto 1/T$, and $\alpha =a+bT$ with $a,b$ being constants. Again, the Grüneisen ratio diverges as $\mathrm{\Gamma }(T)\propto 1/\sqrt{T}$.

8 pages, LaTex format

References in corpus (2)

• Divergence of the Grueneisen Ratio at Quantum Critical Points in Heavy Fermion Metals
• Physics of the Insulating Phase in the Dilute Two-Dimensional Electron Gas

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