AUTHOR=Tallon Jeffery L. , Storey James G. 

TITLE=Thermodynamics of the pseudogap in cuprates

JOURNAL=Frontiers in Physics

VOLUME=Volume 10 - 2022

YEAR=2022

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2022.1030616

DOI=10.3389/fphy.2022.1030616

ISSN=2296-424X

ABSTRACT=The key thermodynamic characteristics of the pseudogap state in cuprate superconductors are reviewed. These include YBa$_2$Cu$_3$O$_{7-\delta}$, Y$_{0.8}$Ca$_{0.2}$Ba$_2$Cu$_3$O$_{7-\delta}$, YBa$_2$Cu$_4$O$_{8}$, Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$, 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 $\gamma$ 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 $p \approx 0.19$ 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 $\gamma(T)$ either side of $T_{\textrm{c}}$ and this enables extraction of the mean-field transition temperature $T_{\textrm{c}}^{\textrm{mf}} > T_{\textrm{c}}$, defining a crescent of parapairing above $T_{\textrm{c}}(p)$ 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 $p \approx 0.19$ when the pseudogap sets in.