Universal limiting transition temperature for the high $T_\mathrm{c}$ superconductors

Since their discovery three decades ago it has emerged that the physics of high-$T_\mathrm{c}$ cuprate superconductors is characterised by multiple temperature scales, and a phenomenology that deviates significantly from the conventional paradigm of superconductivity. Below the "pseudogap" temperature, $T^*$, a range of experiments indicate a reduction in the density of states. Lower in temperature, $T_\mathrm{c}$ marks the onset of a bulk zero-resistance state. Intermediate between these, numerous other temperature boundaries and cross-overs have been identified, often postulated to be associated with fluctuations of some kind. However, for the most part there is little consensus either over their definitions or the physical mechanisms at play. One of these temperature scales is the Nernst onset temperature, $T_\mathrm{onset}$, below which thermoelectric phenomena characteristic of superconductivity are observed. Depending on the material, the difference between $T_\mathrm{onset}$ and $T_\mathrm{c}$ ranges from almost nothing to over 100K. In this paper, we identify $T_\mathrm{onset}$ from published experimental data according to a consistent definition; this reveals a remarkable consistency of behaviour across the whole high-$T_\mathrm{c}$ family, despite the appreciable variations in other parameters. Our analysis suggests that in the cuprates there is an inherent limit to $T_\mathrm{c} \sim 135$K. We compare this behaviour with other strongly-correlated superconductors and propose a unified picture of superconducting fluctuations close to the Mott state.