Probing Topological Stability with Nonlocal Quantum Geometric Markers

TL;DR

This paper investigates nonlocal quantum geometric markers as correlation functions that can diagnose and distinguish topological phase transitions, providing a versatile tool for understanding topological stability even in amorphous systems.

Contribution

It reveals the nonlocal behavior of quantum geometric markers and their distinct spatial signatures at topological transitions, enhancing the understanding of topological phase stability.

Findings

Markers behave as correlation functions independent of structure

Markers show sharp variations near topological transitions

Distinct signatures differentiate topological transitions within the same class

Abstract

Spatially resolved local quantum geometric markers play a crucial role in the diagnosis of topological phases without long-range translational symmetry, including amorphous systems. Here, we focus on the nonlocality of such markers. We demonstrate that they behave as correlation functions independently of the material's structure, showing sharp variations in the vicinity of topological transitions and exhibiting a unique pattern in real space for each transition. Notably, we find that, even within the same Altland-Zirnbauer class, distinct topological transitions generate qualitatively different spatial signatures, enabling a refined, class-internal probe of topological stability. As such, nonlocal quantum geometric indicators provide a more efficient and versatile tool to understand and predict the stability of topological phase transitions.