Edge states of zigzag bilayer graphite nanoribbons

TL;DR

This paper investigates the electronic and magnetic properties of zigzag bilayer graphite nanoribbons using tight binding and Hubbard models, revealing fixed Fermi points, edge states influenced by trigonal warping, and ferromagnetic edge spins.

Contribution

It provides a detailed analysis of edge states, Fermi point behavior, and edge magnetism in Z-BGNR, including effects of inter-layer hopping parameters and ribbon width, which were not comprehensively studied before.

Findings

Existence of two fixed Fermi points in idealized model.

Edge states reflect trigonal warping effects.

Edge spins are ferromagnetically aligned within the same edge.

Abstract

Electronic structures of the zigzag bilayer graphite nanoribbons(Z-BGNR) with various ribbon width $N$ are studied within the tight binding approximation. Neglecting the inter-layer hopping amplitude $\gamma_4$, which is an order of magnitude smaller than the other inter-layer hopping parameters $\gamma_1$ and $\gamma_3$, there exist two fixed Fermi points $\pm k^*$ independent of the ribbon width with the peculiar energy dispersion near $k^*$ as $\ve (k) \sim \pm (k-k^*)^N$. By investigating the edge states of the Z-BGNR, we notice that the trigonal warping of the bilayer graphene sheets are reflected on in the edge state structure. With the inclusion of $\gamma_4$, the above two Fermi points are not fixed, but drift toward the vicinity of the Dirac point with the increase of the width $N$ as shown by the finite scaling method and the peculiar dispersions change to the parabolic ones. The edge magnetism of the Z-BGNR is also examined by solving the half-filled Hubbard Hamiltonian for the ribbon using the Hartree-Fock approximation. We have shown that within the same side of the edges, the edge spins are aligned ferromagnetically for the experimentally relevant set of parameters.