Second-order topological corner states in zigzag graphene nanoflake with different types of edge magnetic configurations

Abstract

We study the energy spectrum and energy levels of the extended Kane-Mele model with magnetic atoms on their zigzag edges. It is demonstrated that the edges of ferromagnetism or antiferromagnetism are enough to break the time-reversal symmetry and host one-dimensional gapped edge states. Thus a second-order topological phase transition could happen, which leads to the emergence of topological in-gap zero-dimensional corner states. We also prove that the in-gap corner states are robust against corner defects and magnetic disorder. Our proposal based on the edge antiferromagnetism represents that the high-order topological states can be realized although the net magnetization of the material is zero. In addition, we discuss the influence of spin magnetization orientation on the degeneracy and energy of in-gap corner states.

Electronic structures, transport properties, and optical absorption of bilayer blue phosphorene nanoribbons

“…31 Especially, in the z-GNRs a pair of almost flat bands is found to correspond to edge states. [32][33][34] On the other hand, the bilayer a-GNRs of different widths 35 are always semiconducting and the bilayer z-GNRs show a gapless band structure with a flat band shifted away from the Fermi level based on the LDA. Moreover, the bilayer z-GNRs are found to be semiconducting based on the GGA if the magnetic orders of the atoms at two edges are considered.…”