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Moir\'e materials such as magic angle twisted bilayer graphene (MATBG)exhibit remarkable phenomenology, but present significant challenges forcertain experimental methods, particularly scanning probes such as scanningtunneling microscopy (STM). Typical STM studies that can image tens ofthousands of atomic unit cells can image roughly ten moir\'e cells, making dataanalysis statistically fraught. Here, we propose a method to mitigate thisproblem by aggregating STM conductance data from several bias voltages, andthen using the unsupervised machine learning method of gaussian mixture modelclustering to draw maximal insight from the resulting dataset. We apply thismethod, using as input coarse-grained bond variables respecting the point groupsymmetry, to investigate nematic ordering tendencies in MATBG for both chargeneutral and hole-doped samples. For the charge-neutral dataset, the clusteringreveals the surprising coexistence of multiple types of nematicity that areunrelated by symmetry, and therefore generically nondegenerate. By contrast,the clustering in the hole doped data is consistent with long range order of asingle type. Beyond its value in analyzing nematicity in MATBG, our method hasthe potential to enhance understanding of symmetry breaking and its spatialvariation in a variety of moir\'e materials.

Unsupervised learning of two-component nematicity from STM data on magic angle bilayer graphene