Search for quantum critical behavior in the specific heat of HTS cuprates*

Much evidence has been accumulated suggesting the presence of a quantum critical point in the lightly overdoped regime for high-$T_{c}$ superconductors, around $p$=0.19 holes per Cu. It is however not decisive. In the neighborhood of a quantum critical point the normal-state electronic specific heat should contain a $T$ln($T)$ term. While this would be concealed by the onset of superconductivity it is in principle recoverable using the entropy balance that exists in a second-order phase transition. This paper reviews the data for Y$_{0.8}$Ca$_{0.2}$Ba$_{2}$Cu$_{3}$O$_{7-d}$ and Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+d}$ and places limits on the magnitude and doping evolution of a $T$ln($T)$ term in the specific heat across the phase diagram.