Credit: Adapted from Y. Zhang and E.A. Kim, Phys. Rev. Lett. (2017) by APS/Alan Stonebraker.
An exotic topological phase of matter was identified with a machine-learning approach. The left schematic illustrates a snapshot of the electronic density of the system. Using a quantum loop topography (QLT) technique, the neighboring triangular regions in the electronic density profile are translated to multidimensional images of the material’s structure. These images show different insulating phases that are then fed into a neural network. (The four vertical circles are a hidden layer in the neural network.) The machine learns by example if the phase is topological or not. For future applications, the “educated” machine can detect topological phases on its own.