Planckian behavior of cuprates at the pseudogap critical point simulated via flat electron-boson spectral density

Planckian behavior has been recently observed in La₁Sr₀CuO₄ at the pseudogap critical point. The Planckian behavior takes place in an intriguing quantum metallic state at a quantum critical point. Here, the Planckian behavior was simulated with an energy-independent (or flat) and weakly temperature-dependent electron-boson spectral density (EBSD) function by using a generalized Allen's (Shulga's) formula. We obtained various optical quantities from the flat EBSD function, such as the optical scattering rate, the optical effective mass, and the optical conductivity. These quantities are well fitted with the recently observed Planckian behavior. Fermi-liquid behavior was also simulated with an energy-linear and temperature-independent EBSD function. The EBSD functions agree well with the overall doping- and temperature-dependent trends of the EBSD function obtained from the optically measured spectra of cuprate systems, which can be crucial for understanding the microscopic electron-pairing mechanism for high-T superconductivity in cuprates.