Identifying topological states in matter

Abstract

The rise of topological insulators, semimetals and superconductors established the topology of the electronic band structure as a fundamental material property. Topological materials can realize exotic novel quantum states such as an integer quantum Hall state in the absence of an external magnetic field, quasiparticle states needed for topological quantum computing, and many more. The topological nature of these states makes them insensitive to small perturbations, which has profound practical consequences. Consequently, the ability to reliably identify topological states is crucial in understanding and predicting many physical effects. In this work, we propose a general approach for calculating any topological invariant, based on the charge centers of hybrid Wannier functions. The method is illustrated in the context of Chern insulators, Z 2 topological insulators and Weyl semi- metals. Most importantly, we present Z2Pack, an easy-to-use software implementing this technique. It can be used as a post-processing tool for first-principles calculations or as a standalone package for tight-binding or k.p models. The fully automated calculation of topological invariants makes Z2Pack ideally suited for both the search for topological states of matter in existing materials and the design of materials or heterostructures with desirable topology.