2024/05/25 by Jin Dai, Y. X. Zhao, Dai, J. X. +1
Engineering · #FOS: Physical sciences #Hydrocarbon exploration and reservoir analysis #Mesoscale and Nanoscale Physics (cond-mat.mes-hall)
paper · pdf · doi:10.48550/arxiv.2405.16001
openalex publication_date 2024/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Chiral symmetry on bipartite lattices with different numbers of A-sites and B-sites is exceptional in condensed matter, as it gives rise to zero-energy flat bands. Crystalline systems featuring chiral symmetry with non-equal sublattices include Lieb lattices, dice lattices, and particularly Moiré systems, where interaction converts the flat bands into fascinating many-body phases. In this work, we present a comprehensive classification theory for chiral symmetry with non-equal sublattices. First, we identify the classifying spaces as Stiefel manifolds and derive the topological classification table. Then, we extend the symmetry by taking PT symmetry into account, and ultimately obtain three symmetry classes corresponding to complex, real, and quaternionic Stiefel manifolds, respectively. Finally, we apply our theory to clarify the topological invariant for PT-invariant Moiré systems and construct physical models with Lieb and dice lattice structures to demonstrate our theory. Our work establishes the theoretical foundation of topological phases protected by chiral symmetries with non-equal sublattices.