Exploration of Topological Metamaterial Band Structures and Chern numbers using Deep Learning

Band structures are ubiquitous in physics as they describe natural as well as engineered materials. Even for systems for which the numerical calculation of the band structure for a single configuration is in itself not proibitevely expensive, efficient numerical methods are highly valuable as they allow the systematic investigation of large sets of configurations. This is particularly important for engineered materials whose unit cell geometry can be arbitrarily designed.
Recently, we have introduced a numerical method for band structure calculations based on deep neural networks (NNs). In our approach, the NN does not predict the band structure directly but rather makes it easily accessible via the parameters of a tight-binding model. Our tight-binding model gives then access not only to the band structure but also, potentially, to the topological properties of the Bloch waves.
Among other interesting applications, we present the case study of a metamaterials realized alternating a trivial and a topological material according to an arbitrary pattern. We show that a NN trained with minimal information about the symmetry of the Bloch waves can predict the (spin) Chern numbers for arbitrary unit cell geometry. This is remarkable because the Chern numbers are not symmetry enforced.