Engineering Topological Materials

TL;DR

This paper introduces a systematic method for designing topological materials by embedding defects or textures to control symmetry and dimension, enabling targeted topological phase transitions.

Contribution

It presents a novel approach to engineer topological phases by manipulating defects and textures, facilitating transitions between classes in the tenfold classification.

Findings

Defects can induce topological phase transitions.

Controlled navigation across topological classes is possible.

Examples demonstrate generation of phases with different invariants.

Abstract

The tenfold classification provides a powerful framework for organizing topological phases of matter based on symmetry and spatial dimension. However, it does not offer a systematic method for transitioning between classes or engineering materials to realize desired topological properties. In this work, we introduce a general method for designing topological materials by embedding defects or spatial textures, which alter symmetry or dimension. This enables controlled navigation across the tenfold table, allowing one to induce topological phase transitions on demand. We illustrate this approach through several nontrivial examples, demonstrating how local defects can generate phases with different symmetries and topological invariants.