Nature 570, 484–490 (2019)

We as humans are fairly good at recognizing faces, even in fuzzy images, but would likely fail to detect correlation and order in images of complex, noisy data. While Fourier analysis often helps, it also fails if the disorder is too strong. Zhang et al. now demonstrate how machine learning using artificial neural networks (ANNs) can identify hidden order in experimental data of electronic quantum matter, such as high-temperature superconductors or quantum spin liquids, which cannot be unveiled with traditional methods.

The researchers analyse sets of differential conductance maps obtained by scanning tunnelling microscopy experiments on carrier-doped copper oxide Mott insulator samples. The strong atomic-scale disorder in such samples commonly prohibits recognition of periodic electron density variations and the determination of the quantum state. Zhang et al. first train the ANNs with synthetic images representing different order, commensurate or not with the atomic lattice of the crystal, but including disorder and defects. Then, the researchers run them on sets of experimental images of several samples with different doping levels. The machine learning algorithm recognizes a lattice-commensurate, symmetry-breaking order, which provides experimental evidence to distinguish between competing theoretical models to describe this Mott insulator.