Fig. 2: Strange-metal self-energy.

a Sketch of the charge density fluctuation (CDF) and charge density wave (CDW) mediated quasiparticle scattering on the Fermi surfaces. Points on the Fermi surface are identified by the angle ϕ. Owing to the broadness of CDFs in momentum space, all the states along the Fermi surface (thick black line) can be scattered by low-energy CDFs over other portions of the Fermi surface, and no particular nesting condition is needed. The involvement of only one branch of the Fermi surface in the Brillouin zone is displayed for clarity: The scattered portions of the Fermi surface (broad reddish areas) essentially cover the whole branch. Therefore the whole Fermi surface is affected in a nearly isotropic way. On the contrary, the CDWs are peaked in momentum space and scatter the Fermi surface states in rather restricted regions of other Fermi surface branches (hot spots). These occur where the bluish lines cross the thick black line. b Scattering rate [i.e. the imaginary part of the self-energy at zero frequency \({{\Gamma }}(\phi )=-{\rm{Im}}\ {{\Sigma }}(\phi ,T,\omega =0)\)] at a given temperature T = 80 K, as a function of the position on the Fermi surface, as identified by the angle ϕ defined in panel a. The nearly isotropic red line corresponds to the case when all the scattering would be due to CDFs, while the blue dashed line represents the scattering due to CDWs only. c Imaginary part of the electron self-energy as a function of the (negative) electron binding energy, at different temperatures above T_CDW, below which the CDWs emerge to produce the narrow peak in resonant X-ray scattering. The coupling between fermion quasiparticles and CDFs is g = 0.166 eV. d Same as c, but with both frequency and self-energy axes rescaled by the temperature (k_B is the Boltzmann constant), to highlight the approximate scaling behaviour at low frequency.