Pre-pairing and the "Filling" Gap in the Cuprates From the Tomographic Density of States

We use the tomographic density of states (TDoS), which is a measure of the density of states for a single slice through the band structure of a solid, to study the temperature evolution of the superconducting gap in the cuprates. The TDoS provides unprecedented accuracy in determining both the superconducting pair-forming strength, $\Delta$, and the pair-breaking rate, $\Gamma$. In both optimally- and under-doped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$, we find the near-nodal $\Delta$ smoothly evolves through the superconducting transition temperature - clear evidence for the existence of pre-formed pairs. Additionally, we find the long observed `filling' of the superconducting gap in the cuprates is due to the strongly temperature dependent $\Gamma$.