Structure-driven phase transitions in paracrystalline topological insulators

TL;DR

This paper investigates how structural disorder influences phase transitions in noncrystalline topological insulators, revealing a sequence of topological changes driven by disorder and demonstrating topological protection in extreme conditions.

Contribution

The study introduces a novel procedural generation method using Perlin noise to model disorder in 2D lattices and explores resulting topological phase transitions.

Findings

Topological phase transitions occur with disorder-induced gap closing.

Structural disorder can be continuously tuned from crystalline to amorphous phases.

Topological protection persists even under extreme disorder.

Abstract

We study phase transitions driven by structural disorder in noncrystalline topological insulators. We introduce a procedural generation algorithm, the Perlin noise, typically used in computer graphics, to incorporate disorder to a two-dimensional lattice, allowing a continuous interpolation between a pristine and a random gas system, going through all different intermediate structural regimes, such as the paracrystalline and the amorphous phases. We define a two-band model, including intraorbital and interorbital mixings, on the structures generated by the algorithm and we find a sequence of structure-driven topological phase transitions characterized by changes in the topological Bott index, at which the insulating gap dynamically closes while evolving from the Bragg planes of the Brillouin zone towards the center. We interpret our results within the framework of Hosemann's paracrystal theory, in which distortion is included in the lattice structure factor and renormalizes the band-splitting parameter. Based on these results, we ultimately demonstrate the phenomenon of topological protection at its extreme.