Many current descriptions of the pseudogap in underdoped cuprates envision a doping-dependent transition line $T^{*}\left(p\right)$ which descends monotonically toward zero just beyond optimal doping. There is much debate as to the location of the terminal point $p^{*}$ where $T^{*}\left(p\right)$ vanishes, whether or not there is a phase transition at $T^{*}$ and exactly how $T^{*}\left(p\right)$ behaves below $T_{\mathrm{c}}$ within the superconducting dome. One perspective sees $T^{*}\left(p\right)$ cutting the dome and continuing to descend monotonically to zero at $p^{*}\approx 0.19$ holes/Cu—referred to here as entrant behavior. Another perspective derived from photoemission studies is that $T^{*}\left(p\right)$ intersects the dome near $p\approx 0.23$ holes/Cu then turns back below $T_{\mathrm{c}}$, falling to zero again around $p^{*}\approx 0.19$—referred to here as reentrant behavior. By examining field-dependent thermodynamic data for ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ we show that neither entrant nor reentrant behavior is supported. Rather, $p^{*}$ sharply delimits the pseudogap regime: For $p<0.19$ the pseudogap is always present, independent of $T$. Similar results are found for ${\mathrm{Y}}_{0.8}{\mathrm{Ca}}_{0.2}{\mathrm{Ba}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$. For both materials, $T^{*}\left(p\right)$ is not a temperature but a crossover scale, $\approx E^{*}\left(p\right)/2k_B$, reflecting instead the underlying pseudogap energy $E^{*}\left(p\right)$ which vanishes as $p\to p^{*}\approx 0.19$.

• Received 30 July 2019
• Revised 20 April 2020
• Accepted 28 April 2020

DOI:https://doi.org/10.1103/PhysRevB.101.174512