Machine Learning Correlates CDW Properties with Local Gap in Cuprates*

With the advent of atomic resolution imaging techniques comes the challenge of disentangling the intrinsic electronic properties of materials from their stochastic atomic-scale disorder. In the past decade, machine learning (ML) image analysis techniques have rapidly evolved, and their applications in physics are just emerging. Here, we use ML to test correlation hypotheses between spatially resolved measurements of disordered materials to overcome the limitations of standard Fourier analysis techniques. We apply artificial neural networks to uncover the doping-dependence of the density wave (DW) structure in the cuprate superconductor (Pb,Bi)₂(Sr,La)₂CuO_6+δ (Bi-2201) imaged via scanning tunneling microscopy. In Bi-based cuprates, the electronic inhomogeneity, caused by local variations in doping, limits the precision of DW wavevector measurements. Our ML algorithm overcomes this limitation and allows clear differentiation between commensurate and incommensurate DW instabilities with physically distinct mechanisms. More broadly, our work lays the foundation for a ML approach to quantify intrinsic periodic order and correlations from datasets where these trends are masked by disorder.