Edge states of zigzag bilayer graphite nanoribbons

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 $\pm k^{\ast }$ independent of the ribbon width with the peculiar energy dispersion near $k^{\ast }$ 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.

22 pages, 7 figures; Corrections are added concerning the edge magnetism

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