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Fluctuations and correlations of local topological order parameters in disordered two-dimensional topological insulators

Roberta Favata1*, Nicolas Baù1*, Antimo Marrazzo2*

1 Dipartimento di Fisica, Università di Trieste, Strada Costiera 11, I-34151 Trieste, Italy

2 Scuola Internazionale Superiore di Studi Avanzati (SISSA), I-34136 Trieste, Italy

* Corresponding authors emails: roberta.favata@phd.units.it, nicolas.bau@phd.units.it, amarrazz@sissa.it
DOI10.24435/materialscloud:3w-0e [version v1]

Publication date: Mar 31, 2025

How to cite this record

Roberta Favata, Nicolas Baù, Antimo Marrazzo, Fluctuations and correlations of local topological order parameters in disordered two-dimensional topological insulators, Materials Cloud Archive 2025.49 (2025), https://doi.org/10.24435/materialscloud:3w-0e

Description

Two-dimensional topological insulators are characterized by an insulating bulk and conductive edge states protected by the nontrivial topology of the bulk electronic structure. They remain robust against moderate disorder until Anderson localization occurs and destroys the topological phase. Interestingly, disorder can also induce a topological phase—known as a topological Anderson insulator—starting from an otherwise pristine trivial phase. While topological invariants are generally regarded as global quantities, we argue that space-resolved topological markers can act as local order parameters, revealing the role of fluctuations and correlations in the local topology under Anderson disorder and vacancies. With this perspective, we perform numerical simulations of disorder-driven topological phase transitions in the Haldane and Kane-Mele models, using supercells with both open and periodic boundary conditions. We find that short-scale fluctuations of topological markers vanish upon coarse-graining, except at the topological phase transition, where their correlation length peaks and large-scale fluctuations remain.

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File name Size Description
data.zip
MD5md5:3faf0dcef69e34c2bbba0ecaa92a94a6
4.3 MiB Results for single-point (spin) Chern number, local (spin) Chern markers and Chern-Chern correlation functions
README.txt
MD5md5:061c6ab8b5c99c775d6cea0096a0f68e
3.3 KiB README

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External references

Preprint
R. Favata, N. Baù, A. Marrazzo, Fluctuations and correlations of local topological order parameters in disordered two-dimensional topological insulators

Keywords

Topological order parameters Local topology Fluctuations and correlations Haldane model Kane-Mele model Anderson disorder Vacancies

Version history:

2025.49 (version v1) [This version] Mar 31, 2025 DOI10.24435/materialscloud:3w-0e