Fit-Free Optical Determination of Electronic Thermalization Time in Nematic Iron-Based Superconductors

We present a nematic response function model (NRFM) for fit-free direct extraction of the characteristic time of ultrafast electronic thermalization in iron-based superconductors, materials with electronic nematicity. By combining the NRFM for polarization-dependent pump--probe measurements of electronic nematic response with the two-temperature model (TTM) for sub-picosecond quasiparticle relaxation, we quantify the electronic thermalization timescales and their anisotropy. The nematic response function is modeled as the difference of normalized reflectivity signals, revealing a pronounced sub-picosecond extremum in signal evolution that directly yields the characteristic electronic thermalization time. This method demonstrates that the NRFM is consistent with TTM fits of transient optical response, yielding electronic thermalization time constants on the order of 110--230~fs for the FeSe$_{1-x}$Te$_x$ and Ba(Fe$_{0.92}$Co$_{0.08}$)$_2$As$_2$ thin films. The proposed approach can be applied to any material that exhibits electronic nematicity, providing a powerful tool for direct mapping of the relaxation time in nematic materials, avoiding complex experimental data-fitting procedures.