Topological end states and Zak phase of rectangular armchair ribbon

摘要

AbstractWe consider the end states of a half-filled rectangular armchair graphene ribbon (RAGR) in a staggered potential. Taking electron–electron interactions into account we find that, as the strength of the staggered potential varies, three types of couplings between the end states can occur: antiferromagnetic without or with spin splitting, and paramagnetic without spin-splitting. We find that a spin-splitting is present only in the staggered potential region0/mml:mo>Δ/mml:mo>Δc. The transition from the antiferromagnetic state atΔ=0to the paramagnetic state goes through an intermediate spin-split antiferromagnetic state, and this spin-splitting disappears suddenly atΔc. For small and large values ofΔthe end charge of a RAGR can be connected to the Zak phase of the periodic armchair graphene ribbon (PARG) with the same width, and it varies continuously as the strength of the potential changes.Highlights?End charge is connected to the topological Zak phase.?Absence of inversion symmetry breaks quantization of the Zak phase.?Boundary states have a rich magnetic structure.]]>