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

Moiré materials such as magic angle twisted bilayer graphene (MATBG) provide an exciting platform for the study of novel states of matter, but their large unit cells present significant difficulties for atomic resolution probes such as scanning tunneling microscopy (STM). Motivated by STM measurements on MATBG that visually suggest the breaking of rotational symmetry (i.e. nematic order), we develop an unsupervised machine learning method to identify and characterize nematicity from STM conductance images in an unbiased fashion. The method consists of two steps: feature selection, in which a two-component nematic order parameter respecting point group symmetry is formed from suitable averages of the conductance surrounding each moiré site; and clustering, in which values of this order parameter are suitably aggregated, and the unsupervised machine learning technique of Gaussian mixture modeling is applied in order to divide the dataset into groups, or clusters, that should represent the same phenomenology. Applying the technique to STM conductance data on MATBG yields clusters corresponding to two symmetry-inequivalent types of nematicity in both hole-doped and charge neutral samples. The comparable, but highly voltage-dependent prevalence of these non-degenerate forms of nematicity in the same field of view suggests that nematicity arises from electronic interactions rather than explicit local symmetry breaking (such as strain). Beyond this particular study, we expect our technique will be of great value in exploiting the power of STM in the burgeoning field of moiré materials.