Thermodynamics and the pairon model for cuprates

Abstract

Two recent papers explore the idea of ``pairons'' (incoherent bound pairs above ${T}_{c}$) as a model for the pseudogap in cuprate high-${T}_{c}$ superconductors. From this model the authors calculate the resultant electronic specific heat and static magnetic susceptibility. At elevated temperature the pairons thermally unbind causing a broad peak in the specific heat, additional to the second-order peak at ${T}_{c}$ where the pairons coherently condense. With this unbinding the electronic entropy recovers to its bare quasiparticle linear-in-$T$ value. We show that this is inconsistent with the measured specific heat which reveals an entropy which never recovers to the highest temperature investigated (about 400 K). In the case of ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8}$ and ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$ there is a broad peak above ${T}_{c}$ in the specific heat coefficient, $\ensuremath{\gamma}$, but this arises from the nearby van Hove singularity (vHs) which is more distant in the case of ${\mathrm{Y}}_{0.8}{\mathrm{Ca}}_{0.2}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{y}$ and therefore not discernible. We propose a number of further critical tests. In the pairon model the BCS ratios are not satisfied until vanishingly near where superconductivity disappears in the heavily overdoped region whereas, experimentally, these mean-field ratios are sustained across the overdoped regime once the pseudogap has closed at critical doping.