Locating the pseudogap closing point in cuprate superconductors: Absence of entrant or reentrant behavior

Many current descriptions of the pseudogap in underdoped cuprates envision a doping-dependent transition line T*(p) which descends monotonically toward zero just beyond optimal doping. There is much debate as to the location of the terminal point p* where T*(p) vanishes, whether or not there is a phase transition at T* and exactly how T*(p) behaves below Tc within the superconducting dome. One perspective sees T*(p) cutting the dome and continuing to descend monotonically to zero at p*≈0.19 holes/Cu---referred to here as entrant behavior. Another perspective derived from photoemission studies is that T*(p) intersects the dome near p≈0.23 holes/Cu then turns back below Tc, falling to zero again around p*≈0.19---referred to here as reentrant behavior. By examining field-dependent thermodynamic data for Bi₂Sr₂CaCu₂O_8+δ 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 Y0.8Ca0.2Ba₂Cu₃O_7-δ. For both materials, T*(p) is not a temperature but a crossover scale, ≈E*(p)/2kB, reflecting instead the underlying pseudogap energy E*(p) which vanishes as p→p*≈0.19.