Emerging network model in a twisted monolayer-rhombohedral graphene

Abstract

We investigate the coexistence of localized states and propagating one-dimensional (1D) modes in graphene moir\'e systems. We first show within a minimal model that a spatially varying scalar potential can confine localized states, while sign changes of a staggered potential generate 1D modes along the resulting domain walls. These two types of states can coexist within the same finite energy window and form a hybrid network. We then demonstrate a microscopic realization of this mechanism in twisted monolayer-rhombohedral N-layer graphene. Band structures, energy contours, and Bloch wave functions obtained in a realistic parameter regime reveal the coexistence of localized nearly flat-band states and propagating quasi-1D modes. Our results establish twisted monolayer-rhombohedral graphene as a promising platform for realizing hybrid electronic networks with coexisting states of distinct effective dimensionalities.