The theoretical analysis of topological insulators (TIs) has been traditionally focused on infinite homogeneous crystals with band gap in the bulk and nontrivial topology of their wave functions, or infinite wires whose boundaries host surface or edge metallic states. Such infinite-length edge states exhibit quantized conductance which is insensitive to edge disorder, as long as it does not break the underlying symmetry or introduce energy scale larger than the bulk gap. However, experimental devices contain finite-size topological region attached to normal metal (NM) leads, which poses a question about how precise is quantization of longitudinal conductance and how electrons transition from topologically trivial NM leads into the edge states. This particularly pressing issue for recently conjectured two-dimensional (2D) Floquet TI where electrons flow from time-independent NM leads into time-dependent edge states, the very recent experimental realization [J. W. McIver et al., Nat. Phys. 16, 38 (2020)] of Floquet TI using graphene irradiated by circularly polarized light did not exhibit either quantized longitudinal or Hall conductance. Here, we employ a charge-conserving solution for Floquet-nonequilibrium Green functions of irradiated graphene nanoribbon to compute longitudinal two-terminal conductance, as well as spatial profiles of local current density as electrons propagate from NM leads into the Floquet TI. For comparison, we also compute conductance of graphene-based realization of 2D quantum Hall, quantum anomalous Hall, and quantum spin Hall insulators. Although zero-temperature conductance within the gap of these three conventional time-independent 2D TIs of finite length exhibits small oscillations due to reflections at the NM-lead/2D-TI interface, it remains very close to perfectly quantized plateau at $2e^2/h$ and completely insensitive to edge disorder. This is due to the fact that inside conventional TIs there is only edge local current density which circumvents any disorder. In contrast, in the case of Floquet TI both bulk and edge local current densities contribute equally to total current, which leads to longitudinal conductance below the expected quantized plateau that is further reduced by edge vacancies. We propose two experimental schemes to detect coexistence of bulk and edge current densities within Floquet TI: (i) drilling a nanopore in the interior of irradiated region of graphene will induce backscattering of bulk current density, thereby reducing longitudinal conductance by $\sim 28\%$; (ii) imaging of magnetic field produced by local current density using diamond nitrogen-vacancy centers.

中文翻译：

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通过有限长度的边缘状态进行的定量传输的鲁棒性：Floquet拓扑与量子自旋和异常霍尔绝缘子的成像电流密度

拓扑绝缘体（TI）的理论分析一直以来都集中在无限均匀的晶体上，这些均匀的晶体在其波函数的整体和非平凡拓扑中具有带隙，或者其边界承载表面或边缘金属态的无限导线。这种无限长的边缘状态表现出对边缘无序不敏感的量化电导，只要它不破坏下面的对称性或引入大于体隙的能级即可。然而，实验装置包含附着在普通金属（NM）引线上的有限尺寸的拓扑区域，这就提出了一个问题，即纵向电导的量化精度如何，以及电子如何从拓扑上琐碎的NM引线过渡到边缘态。等。，Nat。物理 16，38（2020）]使用圆偏振光辐照的石墨烯的Floquet TI没有显示出量化的纵向电导或霍尔电导。在这里，我们采用受辐照的石墨烯纳米带的Floquet非平衡Green函数的电荷守恒解决方案，以计算纵向两端电导率，以及当电子从NM引线传播到Floquet TI中时局部电流密度的空间分布。为了进行比较，我们还计算了基于石墨烯的二维量子霍尔，量子反常霍尔和量子自旋霍尔绝缘体的电导。尽管在这三个传统的与时间无关的有限长度的常规2D TI的间隙内的零温度电导由于NM-lead / 2D-TI界面处的反射而表现出较小的振荡，但它仍然非常接近于完美量化的平台$2{Ë}^2/H$对边缘疾病完全不敏感 这是由于以下事实：在传统的TI内部，只有边缘局部电流密度可以避免任何混乱。相反，在弗洛凯TI的情况下二者的体积和边缘局部电流密度同样有助于总电流，这导致期望的量化高原由边缘空位进一步减小到低于纵向电导。我们提出了两种实验方案来检测Floquet TI内部体积和边缘电流密度的共存：（i）在石墨烯辐照区域内部钻纳米孔会引起体积电流密度的反向散射，从而降低纵向电导率。$〜28％$; （ii）使用金刚石氮空位中心对局部电流密度产生的磁场成像。