  The unclear relationship between cuprate superconductivity and the pseudogap
state remains an impediment to understanding the high transition temperature
(Tc) superconducting mechanism. Here we employ magnetic-field-dependent
scanning tunneling microscopy to provide phase-sensitive proof that d-wave
superconductivity coexists with the pseudogap on the antinodal Fermi surface of
an overdoped cuprate. Furthermore, by tracking the hole doping (p) dependence
of the quasiparticle interference pattern within a single Bi-based cuprate
family, we observe a Fermi surface reconstruction slightly below optimal
doping, indicating a zero-field quantum phase transition in notable proximity
to the maximum superconducting Tc. Surprisingly, this major reorganization of
the system's underlying electronic structure has no effect on the smoothly
evolving pseudogap.
