Experimental observation of boundary flat bands with topological spin textures

Flat bands, particularly the class possessing nontrivial quantum geometry, attract wide interest in multidisciplinary fields as a fertile playground for exotic transport phenomena and correlated phases. The chiral symmetry provides a generic principle for realizing ideal flat bands at the boundary of a topological phase. However, boundary flat bands enforced by traditional chiral symmetry are trivial in quantum geometry as the symmetry operator is a constant unitary matrix. Recently, we generalized the chiral symmetry by allowing dependence on partial momentum components and introduced the concept termed subchiral symmetry. Notably, systems lacking chiral symmetry but possessing subchiral symmetry can have boundary flat bands with intriguing properties, such as topological spin textures and quantized π Berry phases. This Letter reports an experimental realization and observation of such topological boundary flat bands and the concomitant topological spin textures in a two-dimensional circuit system. Our study provides a scheme for topologically nontrivial flat bands and a forward-looking experimental platform for the exploration of novel physics emerging in flat bands.