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石墨烯是具有蜂窝结构的特殊二维材料，在电子器件应用方面具有潜力．拓扑安德森绝缘体现象是一种在无序诱导下系统从金属转变为拓扑绝缘体即拓扑安德森绝缘体的新奇现象．本文基于Haldane模型，利用非平衡格林函数理论，分别计算了不同状态下ZigZag边界准一维石墨烯条带的输运性质随无序的变化．研究发现拓扑平庸和拓扑非平庸状态下的系统都具有鲁棒的边缘态．当费米能处于导带中，两种状态的系统在较弱和较强无序作用下电导快速下降，而在中等无序强度下，前者电导下降减缓，后者出现电导为一的平台，表明系统出现拓扑安德森绝缘体相．对边缘态与体态的传输系数的分析表明Haldane模型中上述现象的形成基础是体态与鲁棒边缘态的共存，随着无序的增强体态被局域化，拓扑平庸的边缘态能一定程度下抵抗中等强度的无序，有拓扑保护的边缘态鲁棒性更强几乎不受影响，使得系统输运稳定性增强并产生电导平台．Graphene, a two-dimensional material characterized by its honeycomb lattice structure, has demonstrated significant potential for applications in electronic devices. The topological Anderson insulator (TAI) represents a novel phenomenon where a system transitions into a topological phase induced by disorder. In past studies, TAI is widely found in theoretical models such as the BHZ model and the Kane-Mele model. One common feature is that these models can open topological non-trivial gaps by changing their topological mass term, but the rise of TAI is unconcerned with the gaps’ topological status. In order to investigate if the disorder-induced phase has any difference in the two situations where the clean-limit Haldane model is topological trivial or non-trivial, the Haldane model is considered in an infinitely long quasi-one-dimensional ZigZag-edged graphene ribbon in this study. The Hamiltonian and band structure of it are analyzed, and the non-equilibrium Green's function theory is employed to calculate the transport properties of ribbons under both topologically trivial and non-trivial states vs. disorder. Conductance, current density, transport coefficient and localisation length are calculated as parameters characterising the transmission properties. It is found that the system in both topological trivial or topological non-trivial state has edge states by analyzing the band structure. When the Fermi energy lies in the conduction band, the conductance of the system decreases rapidly at both weak and strong disorder strengths, regardless of whether the system is topological non-trivial or not. At moderate disorder strengths, the conductance of topological non-trivial systems keeps stable with value one, indicating that a topological Anderson insulator phase rises in the system. Meanwhile, the decrease of conductance noticeably slows down for topological trivial systems. Calculations of local current density show that both systems exhibit robust edge states, with topologically protected edge states showing greater robustness. An analysis of the transmission coefficients of edge and bulk states reveals that the coexistence of bulk states and robust edge states is fundamental to the observed phenomena in the Haldane model. Under weak disorder, bulk states are localized, and the transmission coefficient of edge states decreases due to scattering into the bulk states. Under strong disorder, edge states are localized as well, resulting in zero conductance. However, at moderate disorder strength, bulk states are annihilated while robust edge states persist, thereby reducing scattering from edge states to bulk states. This enhances the transport stability of the system. The fluctuation of conduction and localisation length reveal that the metal-TAI-normal insulator transition occurs in the Haldane model with topological non-trivial gap and if the system is cylinder shape so that there are no edge states, the TAI will not occur. For the topological trivial gap case, only metal-normal insulator transition can be clearly identified. As thus, topologically protected edge states are so robust that generate a conductance plateau and it is proved that topologically trivial edge states are robust in a certain degree to resist this strength of disorder. The robustness of edge states is a crucial factor for the occurrence of the TAI phenomenon in the Haldane model.
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Keywords:
- quantum anomalous Hall effect /
- disorder /
- topological Anderson insulator /
- quantum transport
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