Quantum Critical End Point for the Kondo Volume Collapse Model

The Kondo volume collapse describes valence transitions in $f$-electron metals and is characterized by a line of first order transitions in the pressure-temperature phase plane terminated at critical end points. We analyze the quantum critical end point, when the lower end point is tuned to $T=0$, and determine the specific heat, thermal expansion, and compressibility. We find that the inclusion of quantum critical fluctuations leads to a novel bifurcation of the first order phase line. Finally, we show that critical strain fluctuations can cause both, superconductivity and non-Fermi liquid behavior near the critical point.

Figure 1

Pressure-temperature phase diagram for the KVC model for different values of the bare bulk modulus $B$ from the slave boson theory (see text). The main figure includes critical fluctuations; the inset is the mean field result. Solid ($B=B^{*}$) and dashed ($B\ne B^{*}$) lines represent first order transitions from a low $T_K$ phase, to the left of the line, to a high $T_K$ phase, to the right of the line (this is for Ce alloys; the reverse would be true for Yb ones). The open and solid circles indicate critical end points for $T>0$ and $T=0$, respectively. The inclusion of fluctuations causes the first order line to “bifurcate.” The lower line then terminates at a quantum critical end point for $B=B^{*}$. We show results for increasing $B$ from left to right: $B/B^{*}=0.96$, 0.9683, 0.98, 0.99, 1, and 1.015 (main figure); $B/B^{*}=0.96$, 1, and 1.015 (inset).

Figure 2

Slave boson mean field results for the strain dependence of the Gibbs free energy. A double minima indicates the presence of a first order transition. For $B=B^{*}$ and $T=0$, the double minima collapse to a single one, indicating the presence of a quantum critical end point. For $B<B^{*}$ (inset), the transition is always first order.