The electronic structures of zigzag bilayer graphite nanoribbons (Z-BGNRs) with various ribbon widths 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, there exist two fixed Fermi points +/- k* independent of the ribbon width with a peculiar energy dispersion near k* as epsilon(k) similar to +/-(k-k*)(N). By investigating the edge states of Z-BGNRs, we notice that the trigonal warping of the bilayer graphene sheets is reflected 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 increasing width N, as shown by the finite scaling method, and the peculiar dispersions change to parabolic ones. The edge magnetism of Z-BGNRs 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.
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机译：在紧密结合近似范围内，研究了具有各种带宽度N的曲折双层石墨纳米带（Z-BGNR）的电子结构。忽略比其他层间跳变参数小一个数量级的层间跳变幅度gamma（4），存在两个固定的费米点+/- k *，与碳带宽度无关，附近存在特殊的能量色散k *为epsilon（k），类似于+/-（kk *）（N）。通过研究Z-BGNRs的边缘状态，我们注意到双层石墨烯片的三角翘曲反映在边缘状态结构中。包含伽马（4）时，上述两个费米点不是固定的，而是随着宽度N的增加而向狄拉克点附近漂移，如有限缩放方法所示，奇异色散变为抛物线色散。还通过使用Hartree-Fock近似求解带的半填充的Hubbard哈密顿量来检查Z-BGNR的边缘磁性。我们已经表明，在边缘的同一侧，对于实验相关的参数集，边缘自旋铁磁对齐。
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