本研究利用緊束縛模型（tight-binding model）與 KWANT 量子傳輸模擬方法，探討石墨烯奈米卷軸（graphene nanoscrolls, GNSs）中幾何結構與雜質分佈對量子傳輸特性的影響。石墨烯奈米卷軸為由石墨烯奈米帶螺旋捲曲形成之開放式奈米結構，其兼具石墨烯奈米帶與碳奈米管之特性，並同時具有曲率效應、層間耦合與開放邊界等特殊幾何條件，因此展現出不同於傳統二維材料之電子結構與量子傳輸行為。

本研究首先建立石墨烯奈米卷軸之理論模型，並分析不同邊界結構（Type1 至 Type4）對能帶結構之影響。研究結果顯示，在 Type1 的 1.0 圈石墨烯奈米卷軸中，原本石墨烯奈米帶之邊界平帶（flat band）會因層間耦合而轉變為具有線性色散之交叉能帶，形成類似狄拉克錐（Dirac-cone-like）之電子態。進一步改變層間耦合強度 γ1 後，可觀察到交叉能帶之斜率與費米速度隨之改變，顯示層間交互作用為主導低能量電子結構的重要因素。此外，不同邊界排列方式亦會造成能帶交叉與平帶之轉換，顯示邊界幾何對量子態分佈具有高度敏感性。

在量子傳輸分析方面，本研究利用 Landauer-Büttiker formalism 計算系統之量子電導，並探討不同卷曲圈數與磁場條件下之電子傳輸特性。結果發現，相較於平面石墨烯奈米帶，石墨烯奈米卷軸之縱向量子電導可提升超過一個數量級，特別在 1.0 ∼ 1.2 圈附近具有顯著之導電增強現象。此結果顯示幾何捲曲與層間耦合將造成能帶重建（band reconstruction）與傳輸通道增加，進而提升系統之電子傳輸效率。此外，在外加磁場作用下，石墨烯奈米卷軸亦展現出明顯之正磁電導（positive magnetoconductance）現象，反映其幾何結構與量子相位干涉間之耦合效應。

除了幾何效應外，本研究亦系統性分析不同空間相關雜質對量子傳輸之影響，包括高斯分佈（Gaussian distribution）、沃洛諾伊分佈（Voronoi distribution）以及軸向與徑向延伸之平滑雜質模型。為建立更複雜之空間相關雜質分佈，本研究進一步提出幽靈晶格（ghost lattice）概念，以控制雜質種子點之空間排列，進而模擬不同空間相關雜質對石墨烯奈米卷軸電導穩定性之影響。研究結果指出，空間相關雜質會改變局域電子態與散射行為，並進一步影響系統之量子電導與載子分佈。

綜合上述結果，本研究證明石墨烯奈米卷軸之幾何結構、層間耦合與雜質分佈皆會顯著影響其電子結構與量子傳輸特性。其中，螺旋幾何所造成之能帶重建與多通道導電效應，顯示石墨烯奈米卷軸具有成為幾何導向量子電子元件之潛力。本研究之結果可作為未來拓樸奈米材料、量子傳輸系統與新型石墨烯電子元件設計之理論基礎。

This study employs the tight-binding model and the KWANT quantum transport simulation framework to investigate the effects of geometric structures and disorder distributions on the quantum transport properties of graphene nanoscrolls (GNSs). Graphene nanoscrolls are open-ended nanostructures formed by spirally rolling graphene nanoribbons. They possess characteristics of both graphene nanoribbons and carbon nanotubes, while simultaneously exhibiting spiral curvature effects, interlayer coupling, and open boundary conditions. These unique geometric features give rise to electronic structures and quantum transport behaviors that are distinct from those of conventional two-dimensional materials and planar graphene systems.

First, a theoretical model of graphene nanoscrolls was established, and the influence of different boundary structures (Type1 to Type4) on the band structures was analyzed. The results demonstrate that, in a Type1 1.0-turn graphene nanoscroll, the original flat edge band of the graphene nanoribbon transforms into a linearly dispersive crossing band due to interlayer coupling, forming Dirac-cone-like electronic states. By further varying the interlayer coupling strength γ1, the slope of the crossing bands and the corresponding Fermi velocity were found to change accordingly, indicating that interlayer interaction plays a dominant role in determining the low-energy electronic structure. In addition, different boundary arrangements lead to transitions between band crossings and flat bands, revealing the strong sensitivity of quantum state distributions to boundary geometry.

For quantum transport analysis, the Landauer-Büttiker formalism was employed to calculate the quantum conductance of the system, and the electronic transport properties under different winding numbers and magnetic field conditions were investigated. The results reveal that the longitudinal quantum conductance of graphene nanoscrolls can increase by more than one order of magnitude compared with planar graphene nanoribbons, particularly within the winding range of 1.0 ∼ 1.2 turns, where significant conductance enhancement is observed. These findings indicate that geometric curling and interlayer coupling induce band reconstruction and increase the number of transport channels, thereby enhancing electron transport efficiency. Furthermore, under external magnetic fields, graphene nanoscrolls exhibit pronounced positive magnetoconductance, reflecting the coupling between geometric structures and quantum phase interference effects.

In addition to geometric effects, this study systematically investigates the influence of spatially correlated disorders on quantum transport, including Gaussian-distributed disorders, Voronoi-distributed disorders, and axially or radially extended smooth disorder models. To construct more complex spatially correlated disorder, a ghost lattice concept was further proposed to control the spatial arrangement of disorder seed points, thereby simulating the influence of different spatially correlated disorders on the conductance stability of graphene nanoscrolls. The results indicate that spatially correlated disorders modify local electronic states and scattering behavior, further affecting the quantum conductance and carrier distributions of the system.

Overall, this study demonstrates that the geometric structure, interlayer coupling, and disorder distributions of graphene nanoscrolls significantly influence their electronic structures and quantum transport properties. In particular, the band reconstruction and multi-channel conduction induced by spiral geometry suggest that graphene nanoscrolls possess strong potential for applications in geometry-driven quantum electronic devices. The results of this work provide a theoretical foundation for future studies of topological nanomaterials, quantum transport systems, and novel graphene-based electronic devices.

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