The microscopic mechanism for the disappearance of superconductivity in
overdoped cuprates is still under heated debate. Here we use scanning tunneling
spectroscopy to investigate the evolution of quasiparticle interference
phenomenon in Bi2​Sr2​CuO6+δ​ over a wide range of hole densities.
We find that when the system enters the overdoped regime, a peculiar
quasiparticle interference wavevector with quarter-circle pattern starts to
emerge even at zero bias, and its intensity grows with increasing doping level.
Its energy dispersion is incompatible with the octet model for d-wave
superconductivity, but is highly consistent with the scattering interference of
gapless normal carriers. The weight of the gapless quasiparticle interference
is mainly located at the antinodes and is independent of temperature. We
propose that the normal fluid emerges from the pair-breaking scattering between
flat antinodal bands in the quantum ground state, which is the primary cause
for the reduction of superfluid density and suppression of superconductivity in
overdoped cuprates