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

TL;DR

The paper tackles the challenge of quantifying ultrafast electronic thermalization in electronic-nematic iron-based superconductors by introducing the Nematic Response Function Model (NRFM), which extracts the electronic thermalization time directly from polarization-resolved pump–probe signals. NRFM leverages the nematic channel, with the signal defined as $\eta(t)=({\Delta R}/{R})_{\\parallel}-({\Delta R}/{R})_{\\perp}$, to obtain a time marker $t_{min}$ that maps to the average relaxation time $\\tau_{avg}=(\\tau_{\\parallel}+\\tau_{\\perp})/2$, including corrections for finite instrument response function (IRF). The extracted times $\\tau_{avg}$ and anisotropic components $\\tau_{\\parallel}$ and $\\tau_{\\perp}$ (e.g., yielding $\\tau_e$ in the range $110$–$230$ fs for FeSe0.8Te0.2 and Ba(Fe0.92Co0.08)2As2) align with independent two-temperature model (TTM) fits, validating NRFM as a robust, fit-free approach. The method is inherently suited to high-throughput studies of nematic relaxation dynamics and can be extended to other electronically nematic materials beyond these iron-based superconductors.

Abstract

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.

Figures (4)

• Figure 1: Nematic response function model. (a) Modeling of transient nematicity signal $\eta$ as a difference of normalized exponential decay functions $\exp(-{t/\tau_{\parallel, \perp}} )$ with characteristic relaxation times $\tau_{\parallel} = 95$ fs and $\tau_{\perp} =$ 105, 115, and 125 fs for the infinitesimally short optical excitation ($\tau_{\mathrm{IRF}}=0$ fs). (b) Minimum position $t_{\min}$ versus $\Delta_{\tau}$, compared to $\tau_{\perp}$, $\tau_{\parallel}$ and their average $\tau_{\mathrm{avg}}$ for $\tau_{\mathrm{IRF}}=0$ fs. (c) Divergence of $t_{\min}$ at small $\Delta_{\tau}$ when $\ln(r) \neq 0$ ($r=1.01, 1.02, 1.05$), and $\tau_{\mathrm{IRF}}=0$ fs. (d) Modeling of $\eta$ for finite-pulse excitation with $\tau_{\mathrm{IRF}}=0 - 60$ fs: difference of exponentials $\exp(-t/\tau_{\parallel,\perp})$ convolved with a Gaussian IRF ($\tau_{\parallel}=95$ fs, $\tau_{\perp}=125$ fs). (e) $t_{\min}$ versus $\Delta_{\tau}$ with a Gaussian IRF, compared to $\tau_{\perp}$, $\tau_{\parallel}$, and $\tau_{\mathrm{avg}}$ ($\tau_{\mathrm{IRF}}=50$ fs). (f) Comparison between the modeled $\tau_{\mathrm{avg}}$ (solid line), the minimum position $t_{\min}$, and the $\tau_{\mathrm{avg}}$ (dashed line) calculated from Eq. \ref{['eq:tauavg_IRF']}.
• Figure 2: Schematic of the experimental setup for polarization-resolved pump--probe measurements. AT is pump intensity attenuator, $\lambda/4$ is quarter-wavelength plate, W is a Wollaston prism, and PD are photodetectors.
• Figure 3: (a) Subpicosecond transient reflectivity of FeSe$_{0.8}$Te$_{0.2}$ at 8 K. Top panel: normalized transient reflectivity with superimposed TTM fits. Middle panel: nematic response function $\eta$ for transient reflectivity traces, shown in the top panel. Bottom panel: 2D map of the nematic response function $\eta$ versus photoexcitation fluence and time delay. Solid line near the minimum $\eta_{\mathrm{min}}(F,t_{\mathrm{min}})$ corresponds to $\tau_{\mathrm{avg}}$ from Eq. \ref{['eq:tauavg_IRF']}. (b) Electronic thermalization time constants, obtained from TTM (solid) and from NRFM (hollow). Solid and dashed lines show $t_{\min}$ and $\tau_{\mathrm{avg}}$ from Eq. \ref{['eq:tauavg_IRF']}, respectively. (c) Differences $\Delta_{\tau}$, obtained from (b).
• Figure 4: Subpicosecond transient dynamics of FeSe and Ba(Fe$_{0.92}$Co$_{0.08}$)$_2$As$_2$. (a) Top panel: normalized transient reflectivity of FeSe thin film at 3 K with superimposed TTM fits. Bottom panel: nematic response function $\eta$ for transient reflectivity traces, shown in the top panel. (b) Electronic thermalization time constants, obtained from TTM (solid) and from NRFM (hollow), for FeSe thin film. Solid and dashed lines show $t_{\min}$ and the $\tau_{\mathrm{avg}}$ obtained from Eq. \ref{['eq:tauavg_IRF']}, respectively. (c) Differences $\Delta_{\tau}$, obtained from (b). (d) Top panel: normalized transient reflectivity of Ba(Fe$_{0.92}$Co$_{0.08}$)$_2$As$_2$ thin film at 8 K with superimposed TTM fits. Bottom panel: nematic response function $\eta$ for transient reflectivity traces, shown in the top panel. (e) Electronic thermalization time constants, obtained from TTM (solid) and from NRFM (hollow), for Ba(Fe$_{0.92}$Co$_{0.08}$)$_2$As$_2$ thin film. Solid and dashed lines show $t_{\min}$ and $\tau_{\mathrm{avg}}$ from Eq. \ref{['eq:tauavg_IRF']}, respectively. (f) Differences $\Delta_{\tau}$, obtained from (e).