二維材料，如石墨烯、過渡金屬二硫化物(TMDCs)等，因在第一個布里淵區具有兩個簡併的狄拉克點所以引起許多的關注。能谷電子學使用此二元的「能谷類自旋」於資訊處理與計算上面。值得注意的是，這個新穎的角動量自由度，因其所擁有的能谷軌道耦合(類似於自旋軌道耦合)的機制，可以用電場調控。也因此當電子行經具有電位能或材料能隙改變之物理系統時，不同能谷電子在物理上的表現特性會不同。
此論文的第一部分將上述的原理與構想應用到能谷篩選器的實現上面。我們提出了一個多能帶理論用以計算在石墨烯為主體的側向量子結構中，電子之傳輸特性與能谷的相依性。我們所採取的第一步驟是考慮僅有一個介面的結構，也就是電位能或能隙在空間中的分布會有一個不連續的改變。我們用這個理論模型來研究電子在介面處的傳輸與反射；我們發現這兩個物理特性都受電子能谷類自旋的影響—不同的類自旋呈現出不同的傳輸與反射係數。因此這個性質可被用來產生具有「能谷極化」的電子源。我們發現隨著不同的介面類型與石墨烯層數(單層或雙層)，其結果都會有所差異。我們的數值結果非常清楚的指出雙層石墨烯結構在能谷電子學上所具備有利的特色。基於此結果，我們更一進步研究在AB-堆疊的雙層石墨烯中側向穿隧的表現與其能谷相依性。我們考慮由多個量子井或能障所構成的側向結構。我們研究穿隧電流的能谷相依性在源極(source)與汲極(drain)之間存在電壓差或不對稱的能障結構。對於單一能障的結構而言，我們發現能谷混成(intervalley mixing)的影響微乎其微，而能谷極化效果的程度則是與能障高度與寬度有著正相關的關聯。對於雙能障結構而言，能谷混成的效應因著電子在能障之間共振行為有著顯著的提升；並且這些共振發生所對應的能階也具有能谷相依性，可用來來產生可觀的穿隧能谷極化電流。我們也研究斜向入射電子的穿隧能谷電流的極化程度與溫度之相依性，發現此相依性看出隨著溫度的提升，能谷極化的主要機制從「能谷軌道耦合」漸漸轉變為「能帶變曲」。
此論文的第二部分旨在論述在過渡金屬二硫化物中的一個新穎的自旋(spin)、能谷(valley)與原子軌道(orbital)三者合併構成的類自旋(SVO pseudospin)。先驅性的研究已經指出在此材料的能帶價帶中共存著多種類型的角動量—自旋 (1/2 sz = ±1/2)、能谷 (τ = K, K' or ±1)與原子軌道 (lz = ±2)。因此三者有著強耦合的關係(interlocking)，使其所組成的SVO類自旋對於環境中的干擾有很強韌的耐受力；這樣的特性非常有助於此類自旋在電子學方面的應用。另一方面，對於物理研究與應用而言，施加外場是一個非常普遍與強而有力的方式以達到對物理系統的調控。此論文的第二部分從TMDCs中複雜的能帶結構簡化出一個可被廣泛應用的有效理論，用以描述場控下的SVO類自旋物理，包含其在能谷內與能谷間的動態表現；此有效理論足以預測與討論此類自旋在任意方向的電場與磁場下之線性反應。我們提供了典範型的外場配置用來達成SVO類自旋控制，包含其翻轉。作為一個有實際應用價值的範例，這個理論提出其在量子電腦方面的應用，藉由全電控方式同時操控sz, τ, 與lz，藉此控制量子位元。我們展示了這個方案在具有靜態外場與動態電場的設置上的可達成單次計算約耗時奈秒的計算速度。

Two-dimensional (2D) materials, such as graphene and transition metal dichalcogenides (TMDCs), stand out due to the presence of two distinctive Dirac cones (energy valleys) in the first Brillouin zone. Valleytronics exploits this “valley pseudospin” for information processing and computing. Notably, this exotic angular momentum degree of freedom could be tailored by electrical means using the valley-orbit interaction, in analogy to the spin-orbit interaction. Therefore, modulation of the potential energy or band gap profile in real space makes electrons of opposite valleys behave contrastingly.
The first part of the thesis applies this idea into the realization of valley-based filters. We present a multi-band theory to calculate the valley-dependent electron transport in graphene-based lateral quantum structures. As a first step, we consider structures with a single interface that exhibits an energy gap or potential discontinuity. Both reflection off and transmission through an interface are found to exhibit valley-contrasting behavior that can be used to generate valley-polarized electron sources. The result varies with the type of interfaces, as well as between monolayer and bilayer graphene based structures. Our numerical results clearly demonstrate the advantage of bilayer graphene structures. Based on these facts, we further study the valley aspect of lateral tunneling transport in AB-stacked bilayer graphene. Lateral structure with multiple well/barrier interfaces are considered. We study the degree of tunneling current valley contrast under the condition of a source-drain bias or barrier asymmetry. For a single-barrier structure, it is found that the intervalley mixing is negligible, and the valley contrast is positively correlated with the barrier width and height. For a double-barrier structure, the intervalley mixing is shown to be significantly enhanced at resonant tunneling, with the resonant levels being found valley split, enabling the generation of a sizable tunneling current valley polarization. The temperature dependence of tunneling current valley polarization is also examined. An interesting crossover from the valley-orbit interaction-dominant polarization to the warping-dominant polarization is found to occur as the temperature is raised.
The second part of the thesis deals with exotic spin-valley-orbital pseudospins in TMDCs. Pioneering studies have demonstrated convincingly the co-existence of multiple angular momentum degrees of freedom – of spin (1/2 sz = ±1/2), valley (τ = K, K' or ±1), and atomic orbital (lz = ±2) origins – in the valence band with strong interlocking among them, which results in noise-resilient pseudospin states ideal for spintronic type applications. With field modulation a powerful, universal means in physics studies and applications, this part of thesis develops, from bare models in the context of complicated band structure, a general effective theory of field-modulated spin-valley-orbital pseudospin physics that is able to describe both intra- and inter- valley dynamics. Based on the theory, it predicts and discusses the linear response of a pseudospin to external electric and magnetic fields of arbitrary orientations. Paradigm field configurations are identified for pseudospin control including pseudospin flipping. For a nontrivial example, it presents a spin-valley-orbital quantum computing proposal, where the theory is applied to address all-electrical, simultaneous control of sz, τ, and lz for qubit manipulation. It demonstrates the viability of such control with static field effects and an additional dynamic electric field. An optimized qubit manipulation time ~ O(ns) is given.

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