Thermodynamics of the pseudogap in cuprates - Tallon, Jeffery L.; Storey, James G. (Frontiers in Physics, 2022)
The key thermodynamic characteristics of the pseudogap state in cuprate superconductors are reviewed. These include YBa$_2$Cu$_3$O$_{7-δ}$, Y$_{0.8}$Ca$_{0.2}$Ba$_2$Cu$_3$O$_{7-δ}$, YBa$_2$Cu$_4$O$_{8}$, Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$, La$_{2-x}$Sr$_x$CuO$_4$ and Tl$_2$Ba$_2$CuO$_4$. The electronic specific heat was extracted using a differential technique and the evolution of the specific heat coefficient $γ$ and electronic entropy, $S$, as a function of temperature, doping and magnetic field reveals a canonical behaviour summarised by the following. The normal-state gap which opens in the pseudogap domain apparently remains open to the highest temperatures investigated. The gap decreases in magnitude with increasing doping and closes abruptly at a critical doping of $p ≈ 0.19$ holes/Cu, independent of temperature. In this picture $T^*(p)$, above which the pseudogap opens, is a vertical line similar to the vertical line separating incoherent and coherent antinodal quasiparticle states found in ARPES. The important role of fluctuations is evident by a diverging enhancement of $γ(T)$ either side of $T_{c}$ and this enables extraction of the mean-field transition temperature $T_{c}^{mf} > T_{c}$, defining a crescent of parapairing above $T_{c}(p)$ which extends across the entire superconducting phase diagram and which is quite distinct from pseudogap phenomenology. The data is consistent with $d$-wave pairing and the BCS ratios are extracted, revealing canonical near-weak-coupling behaviour across the overdoped region with a sudden suppression occurring at $p ≈ 0.19$ when the pseudogap sets in.