Classification of fragile topology enabled by matrix homotopy
Name
5rqd-bp11.pdf
Size
3.09 MB
Format
Adobe PDF
Checksum (MD5)
9b032076f38edd1d96734881be7a5c63
Author(s)
Lee, Ki Young
Wong, Stephan
Vaidya, Sachin
Loring, Terry A.
Cerjan, Alexander
Date Issued
September 10, 2025
Journal
Physical Review Research
Publisher
American Physical Society (APS)
Citation
Lee, Ki Young, Wong, Stephan, Vaidya, Sachin, Loring, Terry A. and Cerjan, Alexander. 2025. "Classification of fragile topology enabled by matrix homotopy." Physical Review Research, 7 (3).
Version
Final published version
Abstract
Flat bands in twisted materials have attracted considerable attention due to the emergence of correlated phases
that can be associated with the non-Wannier-representable nature of its single-particle states. Specifically, these
bands can exhibit a class of topology that can be nullified by the addition of trivial bands, termed fragile topology,
which has required an expansion of prior classification schemes. However, existing approaches for predicting
fragile topology rely on momentum-space methods, e.g., Wilson loops, presenting a fundamental challenge
for using fragile topology as a predictor of correlated phases in aperiodic systems, such as incommensurate
twist angles in moiré materials. Here, we develop a Z2 energy-resolved topological marker for classifying
fragile phases using a system’s position-space description, enabling the direct classification of finite, disordered,
and aperiodic materials. By translating the physical symmetries protecting the system’s fragile topological
phase into matrix symmetries of the system’s Hamiltonian and position operators, we use matrix homotopy to
construct our topological marker while simultaneously yielding a quantitative measure of topological robustness.
We demonstrate our framework’s effectiveness in both a low-energy tight-binding model and a continuum
photonic crystal model of C2T -symmetric systems, and find that fragile topology can both persist under
strong disorder and even exhibit disorder-induced reentrant phase transitions. Our photonic crystal results
also demonstrate the robustness of fragile topology, and the applicability of our approach, to heterostructures
lacking a bulk spectral gap. Overall, our framework serves as an efficient tool for elucidating fragile topology,
offering guidance for the prediction and discovery of correlated phases in both crystalline and aperiodic
materials.
MIT Department
Massachusetts Institute of Technology. Department of Physics
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1103/5rqd-bp11
