Rapid Exploration of Topological Band Structures using Deep Learning

TL;DR

This paper presents a deep learning approach that rapidly explores and classifies topological band structures in nanostructures, significantly accelerating design and optimization processes for topological materials.

Contribution

A novel neural network method that maps geometries to tight-binding models, enabling fast classification and optimization of topological band structures across various geometries.

Findings

Accelerated classification of topological band structures.

Effective identification of fragile topologies.

Rapid optimization of domain wall designs.

Abstract

The design of periodic nanostructures allows to tailor the transport of photons, phonons, and matter waves for specific applications. Recent years have seen a further expansion of this field by engineering topological properties. However, what is missing currently are efficient ways to rapidly explore and optimize band structures and to classify their topological characteristics, for arbitrary unit cell geometries. In this work, we show how deep learning can address this challenge. We introduce an approach where a neural network first maps the geometry to a tight-binding model. This allows us to exploit any underlying space group and predict the symmetries of Bloch waves. We demonstrate how that helps to rapidly categorize a large set of geometries in terms of their band representations, identifying designs for fragile topologies. Engineering of domain walls and optimization are also accelerated by orders of magnitude. The approach is general enough to permit future applications to the geometry discovery in other classes of materials (e.g. active and nonlinear metamaterials).