Bragg glass signatures in Pd$_x$ErTe$_3$ with X-ray diffraction Temperature Clustering (X-TEC)

The Bragg glass phase is a nearly perfect crystal with glassy features predicted to occur in vortex lattices and charge density wave systems in the presence of disorder. Detecting it has been challenging despite its sharp theoretical definition in terms of diverging correlation lengths. Here, we present evidence supporting a Bragg glass phase in the systematically disordered charge density wave material PdxErTe3. We do this using comprehensive x-ray data and a machine learning analysis tool called X-ray temperature clustering, or X-TEC. We establish a diverging correlation length in samples with moderate intercalation over a wide temperature range. To enable this analysis, we introduced a high-throughput measure of inverse correlation length that we call peak spread. The detection of Bragg glass order and the resulting phase diagram advance our understanding of the complex interplay between disorder and fluctuations significantly. Moreover, the use of our analysis technique to target fluctuations through a high-throughput measure of peak spread can revolutionize the study of fluctuations in scattering experiments.