TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.17.3.086
TI  - Real-space approach for the Euler class and fragile topology in quasicrystals and amorphous lattices
PY  - 2024/09/20
UR  - https://scipost.org/SciPostPhys.17.3.086
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 17
IS  - 3
SP  - 086
A1  - Li, Dexin
AU  - Wang, Citian
AU  - Huang, Huaqing
AB  - We propose a real-space formalism of the topological Euler class, which characterizes the fragile topology of two-dimensional systems with real wave functions. This real-space description is characterized by local Euler markers whose macroscopic average coincides with the Euler number, and it applies equally well to periodic and open boundary conditions for both crystals and noncrystalline systems. We validate this by diagnosing topological phase transitions in clean and disordered crystalline systems with the reality endowed by the space-time inversion symmetry $\mathcal{I}_{ST}$. Furthermore, we demonstrated the topological Euler phases in quasicrystals and even in amorphous lattices lacking any spatial symmetries. Our work not only provides a local characterization of the fragile topology but also significantly extends its territory beyond $\mathcal{I}_{ST}$-symmetric crystalline materials.
ER  -

@Article{10.21468/SciPostPhys.17.3.086,
	title={{Real-space approach for the Euler class and fragile topology in quasicrystals and amorphous lattices}},
	author={Dexin Li and Citian Wang and Huaqing Huang},
	journal={SciPost Phys.},
	volume={17},
	pages={086},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.17.3.086},
	url={https://scipost.org/10.21468/SciPostPhys.17.3.086},
}