The influences of an external electric field with uniform or modulated potential on the electronic and optical properties of armchair graphene nanoribbons (GNRs) are explored using the multi-orbital tight-binding Hamiltonian. The interplay between an electric field and interaction between (s, $p_x$, $p_y$, $p_z$) orbitals remarkably enriches the main features of band structures and absorption spectra. The applied electric field can notably alter the energy dispersions of $\pi$ and $\sigma$ bands, leading to the deformation of band-edge states, open and close of a band gap, and modification of the Fermi energy. The vertical optical excitations happen among the $\pi$ bands, while their available channels depend on the Fermi level which is controlled by the $\sigma$-edge bands and a finite potential. With the rich and unique properties, GNRs are suitable candidates for applications in the fields of photodetectors, nanoelectronics, and spintronics. The calculated results are expected to be examined by the angle-resolved photoemission spectroscopies (ARPES) and optical spectroscopies.

中文翻译：

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存在周期性电位下扶手椅石墨烯纳米带电子和光学特性的多轨道紧束缚模型

使用多轨道紧束缚哈密顿量探讨了具有均匀或调制电位的外部电场对扶手椅石墨烯纳米带 (GNR) 的电子和光学性质的影响。电场和（s，$p_x$，$p_y$，$p_z$）轨道之间的相互作用显着丰富了能带结构和吸收光谱的主要特征。施加的电场可以显着改变$\pi$和$\sigma$能带的能量色散，导致带边状态的变形、带隙的打开和关闭以及费米能量的改变。垂直光学激发发生在$\pi$ 带之间，而它们的可用通道取决于由$\sigma$-边缘带和有限势控制的费米能级。凭借丰富而独特的属性，GNR 是光电探测器、纳米电子学和自旋电子学领域应用的合适候选者。预计计算结果将通过角分辨光电发射光谱 (ARPES) 和光学光谱进行检查。