AUTHOR=Tallon Jeffery L. , Storey James G. 

TITLE=Thermodynamics of the pseudogap in cuprates

JOURNAL=Frontiers in Physics

VOLUME=10

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=<p>The key thermodynamic characteristics of the pseudogap state in cuprate superconductors are reviewed. These include YBa<sub>2</sub>Cu<sub>3</sub>O<sub>7−<italic>δ</italic></sub>, Y<sub>0.8</sub>Ca<sub>0.2</sub>Ba<sub>2</sub>Cu<sub>3</sub>O<sub>7−<italic>δ</italic></sub>, YBa<sub>2</sub>Cu<sub>4</sub>O<sub>8</sub>, Bi<sub>2</sub>Sr<sub>2</sub>CaCu<sub>2</sub>O<sub>8+<italic>δ</italic></sub>, La<sub>2−<italic>x</italic></sub>Sr<sub><italic>x</italic></sub>CuO<sub>4</sub>, and Tl<sub>2</sub>Ba<sub>2</sub>CuO<sub>4</sub>. The electronic specific heat was extracted using a differential technique, and the evolution of the specific-heat coefficient <italic>γ</italic> and electronic entropy <italic>S</italic> as a function of temperature, doping, and magnetic field reveals a canonical behavior summarized 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 <italic>p</italic> ≈ 0.19 holes/Cu, independent of temperature. In this picture, the pseudogap is separated from the pseudogap-free region of the phase diagram by a vertical line similar to the vertical line separating the incoherent and coherent antinodal quasiparticle states found in ARPES. The important role of fluctuations is evident by a diverging enhancement of <italic>γ</italic>(<italic>T</italic>) on either side of <italic>T</italic><sub>c</sub>, and this enables extraction of the mean-field transition temperature <inline-formula id="inf1"><mml:math id="m1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mtext>c</mml:mtext></mml:mrow><mml:mrow><mml:mtext>mf</mml:mtext></mml:mrow></mml:msubsup><mml:mo>&gt;</mml:mo><mml:msub><mml:mrow><mml:mi>T</mml:mi></mml:mrow><mml:mrow><mml:mtext>c</mml:mtext></mml:mrow></mml:msub></mml:math></inline-formula>, defining a crescent of parapairing above <italic>T</italic><sub>c</sub>(<italic>p</italic>) which extends across the entire superconducting phase diagram and which is quite distinct from pseudogap phenomenology. The data are consistent with <italic>d</italic>-wave pairing and the BCS ratios are extracted, revealing canonical near-weak-coupling behavior across the over-doped region with a sudden suppression occurring at <italic>p</italic> ≈ 0.19 when the pseudogap sets in.</p>