Unsupervised learning of nematic order from scanning tunneling spectroscopy on twisted bilayer graphene*

Moiré materials such as magic angle twisted bilayer graphene (TBG) 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). We therefore develop an automated method to extract salient physical quantities from STM data on moiré materials, and apply it to measurements on TBG that visually suggest the breaking of rotational symmetry (i.e. nematic order). We apply the machine learning technique of Gaussian mixture modeling to this data to classify the STM images at different bias voltages into several categories in an unbiased fashion. This classification yields evidence for a nematic order that manifests itself in a manner strongly dependent on bias voltage. In addition to providing evidence for spatial symmetry breaking in TBG, our techniques can be applied in the future to overcome the intrinsic challenges of exploiting STM in the burgeoning field of moiré materials.