Anisotropic electron damping and energy gap in Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$

The many body electron-electron interaction in cuprates causes the broadening of the electronic bands in $\mathit{\text{k}}$-space, leading to a deviation from the standard Fermi liquid. While a $\mathit{\text{k}}$-dependent anisotropic electronic scattering ($\mathit{\text{k}}$-DAES) has been assessed by photoemission, its fingerprint in $\mathit{\text{Q}}$-space has been scarcely considered. Here, we explore the $\mathit{\text{Q}}$-dependent electron dynamics in optimally doped Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$ through the evolution of low-energy charge excitations as measured by resonant inelastic x ray scattering (RIXS). In the normal state, the RIXS spectra display a continuum of excitations down to 0~meV, while the superconducting state features a spectral weight suppression below 80 meV without any enhancement at higher energies. To interpret the energy and $\mathit{\text{Q}}$-evolution of our data, we introduce a phenomenological expression of the charge susceptibility by including the $\mathit{\text{k}}$-DAES. We show that only the charge susceptibility with $\mathit{\text{k}}$-DAES captures the RIXS data, highlighting the importance of $\mathit{\text{k}}$-DAES when describing the $\mathit{\text{Q}}$-dependence of charge excitations from 0 to few eV scale. Furthermore, we also find that the inclusion of $\mathit{\text{k}}$-DAES is essential when quantitative parameters such as the electronic energy gap are extracted from RIXS data.