Hall coefficient in heavy fermion metals

TL;DR

This paper models the jump in the Hall coefficient observed in heavy fermion metal YbRh2Si2 at a quantum critical point, explaining it through a fermion condensate model that links the transition to entropy behavior and critical fluctuations.

Contribution

It introduces a fermion condensate model to explain the Hall coefficient jump and the nature of the quantum phase transition in heavy fermion metals.

Findings

The Hall coefficient exhibits a jump at the quantum critical point.

The transition changes from second to first order at zero temperature.

The divergence of the Grüneisen ratio is linked to entropy behavior.

Abstract

Experimental studies of the antiferromagnetic (AF) heavy fermion metal $\rm YbRh_2Si_2$ in a magnetic field $B$ indicate the presence of a jump in the Hall coefficient at a magnetic-field tuned quantum state in the zero temperature limit. This quantum state occurs at $B\geq B_{c0}$ and induces the jump even though the change of the magnetic field at $B=B_{c0}$ is infinitesimal. We investigate this by using the model of heavy electron liquid with the fermion condensate. Within this model the jump takes place when the magnetic field reaches the critical value $B_{c0}$ at which the ordering temperature $T_N(B=B_{c0})$ of the AF transition vanishes. We show that at $B\to B_{c0}$, this second order AF phase transition becomes the first order one, making the corresponding quantum and thermal critical fluctuations vanish at the jump. At $T\to0$ and $B=B_{c0}$, the Gr\"uneisen ratio as a function of temperature $T$ diverges. We demonstrate that both the divergence and the jump are determined by the specific low temperature behavior of the entropy $S(T)\propto S_0+a\sqrt{T}+bT$ with $S_0$, $a$ and $b$ are temperature independent constants.