Clustering-Enhanced Time- and Angle-Resolved Photoemission Study of LaTe$_3$: Absence of a Photoinduced Secondary CDW in the Electronic Structure

TL;DR

This work addresses whether a light-induced transient $a$-CDW can leave electronic signatures in LaTe$_3$'s electronic structure. It combines TR-ARPES with a full-Fermi-contour FeSuMa approach and conventional hemispherical-analyzer data, analyzed via unsupervised $k$-means clustering to map dynamics across the Fermi contour and test for signatures of an orthogonal CDW with wave vectors such as $q_c$ and $q_a$. The results show region-specific dynamics tied to the melting and re-formation of the equilibrium $c$-CDW, including coherent amplitude-mode oscillations at $f \approx 2.8$~THz, but no robust evidence for a transient $a$-CDW in the electronic structure. Tight-binding modeling incorporating bilayer splitting accounts for the observations without requiring an $a$-CDW, suggesting ultrafast structural changes do not translate into a detectable electronic second CDW in LaTe$_3$. The study demonstrates the value of full-FC TR-ARPES combined with clustering for disentangling complex order-parameter dynamics and clarifies the electronic consequences of photoinduced phase transitions in quasi-one-dimensional CDW systems.

Abstract

Optical control offers a compelling route for tailoring material properties on an ultrafast time scale. Ordered states such as charge density waves (CDWs) can be transiently melted by an ultrafast light excitation. This is also the case for the rare-earth tritelluride LaTe$_3$, a prototypical CDW compound. For this material it has recently been reported that the suppression of the primary CDW allows the transient formation of a second CDW, whose wave vector is orthogonal to the primary one. This creates the intriguing scenario where light enables switching between two distinct ordered phases of the material. While the second CDW has so far been observed by structural techniques, it remains an open question how the interplay of the two CDW phases is reflected in the material's electronic structure. We investigate this via time- and angle-resolved photoemission measurements of LaTe$_3$. The complex Fermi contour is probed using a FeSuMa analyzer, which records the photoemission intensity of the entire Fermi contour at once. The dynamics revealed by the FeSuMa analyzer are complemented by measurements using a conventional hemispherical electron analyzer. We combine conventional data analysis with $k$-means clustering, an unsupervised machine learning technique, demonstrating its strong potential for disentangling large datasets. While we do not find any features that cannot be explained by the melting and re-establishment of the primary CDW, distinct dynamics and coherent oscillations are observed in the different branches of the Fermi contour.

Figures (8)

• Figure 1: (a) Illustration of CDW gap formation via Fermi-contour replicas generated by the periodic lattice distortion with wave vector $q_c$. A gap opens where the original Fermi contour overlaps with a replica. (b) Sketch of the LaTe$_3$ Fermi contour in the absence of a CDW. The dashed square marks the surface-projected Brillouin zone. (c) Equilibrium Fermi contour measured with the FeSuMa analyzer. The red arrows mark the so called butterfly structure. (d) Fermi contour near peak excitation ($t - t_0 = 170$ fs). (e) Difference between the data in (c) and (d). Red indicates a positive and blue a negative difference. (f) Photoemission intensity as a function of time delay, integrated over the two regions marked in panels (b)–(e) by the purple and yellow squares.
• Figure 2: $k$-means clustering ($k = 5$) of the time distribution curves at each point of the Fermi contour, using the data from Fig. \ref{['fig:fig1']}(e). (a) Spatial distribution of the five clusters. (b) Corresponding cluster centroids. (c) Tight-binding calculation corresponding to Fig. \ref{['fig:fig1']}(e), i.e., the difference between a model without a CDW and one with a fully established $c$-CDW. The color scale is chosen to match that used in the experimental data in Fig. \ref{['fig:fig1']}(e).
• Figure 3: Time-resolved photoemission intensity along the $\Gamma$–X direction. (a) Equilibrium dispersion measured before $t_0$. The inset indicates the orientation of the momentum cut. (b) Zoomed-in difference plots for a selection of pump–probe delays, corresponding to the area enclosed by the dashed rectangular in (a).
• Figure 4: Tight-binding model calculations for varying gap sizes $2\Delta$ along the $k_x$ direction. The gap is indicated by the green arrow. (top) Electronic structure in the fully developed $c$-CDW phase. (middle) Intermediate stage with a reduced gap. (bottom) Normal phase with no CDW gap. Only the spectral weight of the original $p_x$ and $p_z$ orbitals is shown.
• Figure 5: Clustering analysis of the normalized time distribution curves extracted from the data in Fig. \ref{['fig:hemi']} using $k = 4$ clusters. (a) Cluster distribution for the states below $E_\mathrm{F}$. (b) Corresponding cluster centroids, i.e., the mean time distribution curve of each cluster after subtraction of a constant background. (c), (d) Same analysis for the states above $E_\mathrm{F}$.