Influence of incommensurate dynamic charge-density-wave scattering on the photoemission line shape of superconducting high-$T_c$ cuprates

We show that the spectral line shape of superconducting ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ (LSCO) and ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ (Bi2212) can be well described by the coupling of the charge carriers to collective incommensurate charge-density-wave (CDW) excitations. Our results imply that besides antiferromagnetic fluctuations also low-energy CDW modes can contribute to the observed dip-hump structure in the Bi2212 photoemission spectra. In case of underdoped LSCO we propose a possible interpretation of angle resolved photoemission spectroscopy data in terms of a grid pattern of fluctuating stripes where the charge and spin scattering directions deviate by $\alpha =\pi /4.\mathrm{}$ Within this scenario we find that the spectral intensity along $\mathrm{}(0,0)\mathrm{}\to (\pi ,\pi )$ is strongly suppressed, consistent with recent photoemission experiments. In addition, the incommensurate charge-density-wave scattering leads to a significant broadening of the quasiparticle peak around $(\pi ,0).\mathrm{}$