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 Bi2Sr2CaCu2O8+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 Y0.8Ca0.2Ba2Cu3O7-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.