Ultrafast Gap Dynamics and Electronic Interactions in a Photoexcited Cuprate Superconductor

We perform time- and angle-resolved photoemission spectroscopy (trARPES) on optimally doped ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ (BSCCO-2212) using sufficient energy resolution (9 meV) to resolve the $k$-dependent near-nodal gap structure on time scales where the concept of an electronic pseudotemperature is a useful quantity, i.e., after electronic thermalization has occurred. We study the ultrafast evolution of this gap structure, uncovering a very rich landscape of decay rates as a function of angle, temperature, and energy. We explicitly focus on the quasiparticle states at the gap edge as well as on the spectral weight inside the gap that “fills” the gap—understood as an interaction, or self-energy effect—and we also make high resolution measurements of the nodal states, enabling a direct and accurate measurement of the electronic temperature (or pseudotemperature) of the electrons in the system. Rather than the standard method of interpreting these results using individual quasiparticle scattering rates that vary significantly as a function of angle, temperature, and energy, we show that the entire landscape of relaxations can be understood by modeling the system as following a nonequilibrium, electronic pseudotemperature that controls all electrons in the zone. Furthermore, this model has zero free parameters, as we obtain the crucial information of the SC gap $\mathrm{\Delta }$ and the gap-filling strength ${\mathrm{\Gamma }}_{\text{TDoS}}$ by connecting to static ARPES measurements. The quantitative and qualitative agreement between data and model suggests that the critical parameters and interactions of the system, including the pairing interactions, follow parametrically from the electronic pseudotemperature. We expect that this concept will be relevant for understanding the ultrafast response of a great variety of electronic materials, even though the electronic pseudotemperature may not be directly measurable.

Popular Summary

High-temperature superconductivity, in which electricity flows through a substance without resistance at temperatures well above absolute zero, has inspired decades of experimental advances in the quest to understand the exotic physics. One of the most valuable tools to emerge in recent years is “time- and angle-resolved photoemission spectroscopy” (trARPES), which uses ultrashort pulses of laser light to reveal how electrons move and interact in a solid. While trARPES investigations on superconductors have revealed rich behavior, physicists disagree on the interpretation, leaving open several questions. Specifically, researchers would like to understand how photoexcitation (in which an electron gains energy by absorbing a photon) affects a superconductor and what that can reveal about superconductivity itself. Using trARPES to study a type of superconductor, we find that the photoexcited electrons rapidly redistribute their energy among the whole population, i.e., rapidly thermalize, and the rich behavior observed is a consequence of the interplay between these “hot” electrons and the underlying superconductivity.

Our work uses significantly improved energy resolution over previous research, which allows for a clearer picture of the superconducting physics. Furthermore, by drawing on results from previous high-resolution ARPES experiments, we are able to show how the quantities important to superconductivity in a photoexcited system, such as electron pairing and self-energies, compare and connect to their equilibrium values. Overall, our investigation ties together previous results under a straightforward interpretation and gives a clear picture of how superconductivity responds to photoexcitation.

Under sufficiently intense photoexcitation, or at sufficiently short times, we expect this thermalized electron approximation to break down. Therefore, our results provide a natural reference point for future studies exploring photoexcited superconductors in these new regimes.

Figure 1

Nodal response to ultrafast $4\text{−}\mu \mathrm{m}$ pump from an optimally doped, $T_C=91\mathrm{K}$ Bi-2212 sample. Data are taken at the nodal position, shown in the inset to panel (b), at an equilibrium temperature of $T=25\mathrm{K}$, and a $4\text{−}\mu \mathrm{m}$ pump fluence of $60\mu \mathrm{J}/{\mathrm{cm}}^2$. Panel (a) shows raw ARPES spectra at various time delays. Panel (b) shows the transient spectra, defined by subtracting the equilibrium spectrum from each delay. Panel (c) shows a map of SW vs delay obtained by integrating the ARPES spectrum along the momentum cut, shown by the yellow arrow in panel (a). Panel (d) is the analogous map for the transient data, referred to as a $\mathrm{\Delta }\mathrm{SW}$ map, produced similarly to panel (c).

Figure 2

Off-node [inset to panel (b)] gapped spectra at various pump-probe delays from the same $T_C=91\mathrm{K}$ sample as Fig. 1, with all panels the same as in Fig. 1. The equilibrium temperature is 20 K, and the pump fluence is $80\mu \mathrm{J}/{\mathrm{cm}}^2$. Note in panel (d) how the region inside the gap recovers (returns to white) faster than the region at the gap edge.

Figure 3

Extracting electronic temperature from nodal Fermi edges. Panel (a) shows the $k$-integrated spectral weight for several delays along with Fermi-Dirac fits as solid lines (see Supplemental [39] for details). The momentum integration window is shown by the yellow line in Fig. 1. The electronic temperature $T_{el}$ is extracted from the Fermi fit (see Ref. [39]). This $T_{el}$ is plotted vs delay in panel (b) using a $4\text{−}\mu \mathrm{m}$ fluence of $45\mu \mathrm{J}/{\mathrm{cm}}^2$, which brings the maximum $T_{el}$ to approximately $T_C$. The temperature decay is fit to a single exponential, shown by the solid red line in panel (b), and the fit returns a decay time of $3.7\pm 0.3\mathrm{ps}$. The dashed red line in panel (b) is a guide to the eye.

Figure 4

Ultrafast off-nodal gap and quasiparticle response—data and thermal model. Panel (a) shows the $\mathrm{\Delta }\mathrm{SW}$ map for the cut shown in the inset. Temporal line cuts for different energy regions are shown in panel (b) along with single exponential fits and their returned lifetimes. The energy regions, chosen to improve the counting statistics while still separating the qualitatively different spectral regions, are defined as $-40\mathrm{meV}<{\omega }_3<-12\mathrm{meV}$, $-12\mathrm{meV}<{\omega }_2<0\mathrm{meV}$, and $0\mathrm{meV}<{\omega }_1<30\mathrm{meV}$. For clarity, we normalize the temporal line cuts to their maximum values. Panel (c) shows a simulated $\mathrm{\Delta }\mathrm{SW}$ map using our zero-parameter thermal model, discussed in the text. This model, with no free parameters, captures both the qualitative and quantitative features of the experimental data, as shown by the model line cuts in panel (d) (integrated over the same $\omega$ ranges) and their associated fitted lifetimes, which match the experimental data well. Panel (e) shows the gap and pair-breaking rate extracted from high-resolution equilibrium ARPES [40] that serve as the input to the thermal model. Panel (f) shows some representative TDoS curves, simulated from the inputs in (e), for which the key effect is the gap principally filling with increasing $T$.

Figure 5

Off-nodal momentum dependence of $\mathrm{\Delta }\mathrm{SW}$ maps. Panels (a1)–(a3) show $\mathrm{\Delta }\mathrm{SW}$ maps for three different cuts, with $k$-space locations shown by the inset in panel (a2). Panel (a1) has the same data as Fig. 4, reproduced for ease of comparison. Panels (a1)–(a3) have gap sizes of $\mathrm{\Delta }=12$, 15, and 22 meV, respectively. Panels (b1)–(b3) show the temporal line cuts corresponding to each $\mathrm{\Delta }\mathrm{SW}$ map. The integration windows used to generate the line cuts in panel (b) are shown with red and green bars to the right of each $\mathrm{\Delta }\mathrm{SW}$ map. Panels (b1)–(b3) also show single exponential fits in black dashed lines, with extracted $\tau$’s indicated in the panels.

Figure 6

The $k$-space crossover of gap dynamics. Both experimentally (circles and triangles) and theoretically (solid lines), we find that the near-nodal region is characterized by a faster recovery of in-gap states compared to those above $E_{\mathrm{F}}$, while the antinodal region shows the reverse. This physics is driven by the interplay of different momentum and temperature-dependent pairing ($\mathrm{\Delta }$) and self-energy ($\mathrm{\Gamma }$) scales. The Fermi surface locations of these regimes are shown in the right panel. The simulated decays (solid lines) represent a model of fully thermalized electrons, with a temperature decay measured via the node (black dashed line), which agrees well with the data.