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