High-$T_{c}$ Superconductivity meets a 3+3-Dimensional Spectroscopic Tool

Using a novel high-precision variable-temperature Fourier-transform scanning tunneling spectroscopy (FTSTS) technique, we observed for the first time (Science 325, 1099 (2009)) the complete set of dispersive octet peaks in the pseudogap phase (up to 1.5 $T_{c})$ as well as in the superconducting phase (down to 0.1 $T_{c})$ of the underdoped (UD37K) Bi2212. Looking further into the fine structures of the 3D FTSTS data by a novel cross-sectional analysis technique, we could resolve additional signal components that are key to truly quantitative analyses based on the full many-body Green's function. The high-precision measurement of 3D [2D position(nm), energy(mV)] FTSTS over the entire accessible 3D [T(Kelvin) vs p(doping {\%}) vs B(Tesla)] phase diagram, accompanied by the novel cross-sectional FTSTS analysis based on the full many-body Green's function, will provide one of the most stringent tests for a ``complete'' many-body theoretical understanding of the high-$T_{c}$ cuprate superconductivity.