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The superconducting state is achieved by the condensation of Cooper pairs andis protected by the superconducting gap. The pairing interaction between thetwo electrons of a Cooper pair determines the superconducting gap function.Thus, it is very pivotal to detect the gap structure for understanding themechanism of superconductivity. In cuprate superconductors, it has been wellestablished that the superconducting gap may have a d-wave function {\Delta} ={\Delta}_0cos2{\theta}. This gap function has an alternative sign change byevery pi/2 in the momentum space when the in-plane azimuthal angle theta isscanned. It is very hard to visualize this sign change. Early experiments forrecommending or proving this d-wave gap function were accomplished by thespecially designed phase sensitive measurements based on the Josephson effect.Here we report the measurements of scanning tunneling spectroscopy in one ofthe model cuprate system Bi2Sr2CaCu2O8+{\delta} and conduct the analysis ofphase-referenced quasiparticle interference (QPI). Due to the uniquequasiparticle excitations in the superconducting state of cuprate, we have seenthe seven basic scattering vectors that connect each pair of the terminals ofthe banana-shaped contour of constant quasiparticle energy (CCE). Thephase-referenced QPI clearly visualizes the sign change of the d-wave gap. Ourresults illustrate a very effective way for determining the sign change ofunconventional superconductors.

Directly visualizing the sign change of d-wave superconducting gap in Bi2Sr2CaCu2O8+{\delta} by phase-referenced quasiparticle interference