Effect of the pseudogap on the transition temperature in the cuprates and implications for its origin

Cuprates possess a large pseudogap that spans much of their phase diagram(1,2). The origin of this pseudogap is as debated as the mechanism for high-temperature superconductivity. In one class of theories, the pseudogap arises from some instability not related to pairing, typically charge, spin or orbital current ordering. Evidence of this has come from a variety of measurements indicating symmetry breaking(3-6). On the other side are theories where the pseudogap is associated with pairing. This ranges from preformed pairs(7) to resonating valence bond theories where spin singlets become charge coherent(8). Here, we study pairing in the cuprates by constructing the pair vertex using spectral functions derived from angle-resolved photoemission data. Assuming that the pseudogap is not due to pairing, we find that the superconducting instability is strongly suppressed, in stark contrast to what is actually observed. We trace this suppression to the destruction of the BCS logarithmic singularity from a combination of the pseudogap and lifetime broadening. Our findings strongly support those theories of the cuprates where the pseudogap is instead due to pairing.