Higher-order topology and fractional charge in monolayer graphene

Abstract

Typical higher-order topological systems require the fine-tuning of hopping textures and external fields, which considerably hinders their practical realization. Based on a simple picture that corners are "edges"of edges, we determine that in the already-thoroughly-studied monolayer graphene, higher-order topological corner states appear without introducing any additional effects. Unlike quadrupole insulators, owing to degenerate Dirac points in graphene, the emergence of topological corner states depends on the corner angle and edge geometries. We provide a useful expression for the indication of corner states in graphene by the product of Zak phases. We also discuss the methods for experimental detection of the nontrivial higher-order topology in graphene such as the fractional corner anomaly and the disparity of local density of states between trivial and nontrivial corners.