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

Abstract

The many body electron-electron interaction in cuprates causes the broadening of the electronic bands in \textit{\textbf{k}}-space, leading to a deviation from the standard Fermi liquid. While a \textit{\textbf{k}}-dependent anisotropic electronic scattering (\textit{\textbf{k}}-DAES) has been assessed by photoemission, its fingerprint in \textit{\textbf{Q}}-space has been scarcely considered. Here, we explore the \textit{\textbf{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 \textit{\textbf{Q}}-evolution of our data, we introduce a phenomenological expression of the charge susceptibility by including the \textit{\textbf{k}}-DAES. We show that only the charge susceptibility with \textit{\textbf{k}}-DAES captures the RIXS data, highlighting the importance of \textit{\textbf{k}}-DAES when describing the \textit{\textbf{Q}}-dependence of charge excitations from 0 to few eV scale. Furthermore, we also find that the inclusion of \textit{\textbf{k}}-DAES is essential when quantitative parameters such as the electronic energy gap are extracted from RIXS data.