Real-space Formalism for the Euler Class and Fragile Topology in Quasicrystals and Amorphous Lattices

Autor:	Li, Dexin, Wang, Citian, Huang, Huaqing
Rok vydání:	2023
Předmět:	Condensed Matter - Mesoscale and Nanoscale Physics Condensed Matter - Disordered Systems and Neural Networks
Druh dokumentu:	Working Paper
Popis:	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. Comment: 41 pages,8 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2311.01557 Zobrazit plný text záznamu View this record from Arxiv