Boundary Flat Bands with Topological Spin Textures Protected by Sub-chiral Symmetry

TL;DR

This paper introduces sub-chiral symmetry, a momentum-dependent generalization of chiral symmetry, which enables topological flat bands with spin textures and quantized Berry phases in systems lacking conventional chiral symmetry.

Contribution

It generalizes chiral symmetry to sub-chiral symmetry, revealing new topological boundary flat bands with spin textures in systems without traditional chiral symmetry.

Findings

Boundary flat bands with topological spin textures are supported by sub-chiral symmetry.

Quantized Berry phases are associated with these boundary flat bands.

Such bands could lead to novel physics with interactions or disorder.

Abstract

Chiral symmetry plays an indispensable role in topological classifications as well as in the understanding of the origin of bulk or boundary flat bands. The conventional definition of chiral symmetry refers to the existence of a constant unitary matrix anticommuting with the Hamiltonian. As a constant unitary matrix has constant eigenvectors, boundary flat bands enforced by chiral symmetry, which share the same eigenvectors with the chiral symmetry operator, are dictated to carry fixed (pseudo)spin polarizations and be featureless in quantum geometry. In this work, we generalize the chiral symmetry and introduce a concept termed sub-chiral symmetry. Unlike the conventional chiral symmetry operator defined as constant matrix, the sub-chiral symmetry operator depends on partial components of the momentum vector, so as its eigenvectors. We show that topological gapped or gapless systems without chiral symmetry but with sub-chiral symmetry can support boundary flat bands, which exhibit topological spin textures and quantized Berry phases. We expect that such intriguing boundary flat bands could give rise to a variety of exotic physics in the presence of interactions or disorders.