The non-charge degree of freedom (DOF) of a quantum mechanical system, which is called “isospin” in this thesis, provides chances for designing new functional or even novel devices. Chapter 1 gives the preparation for the following discussions. In Chapter 2, we study spin-filtering of a magnetic impurity in quasi-one-dimensional electron liquids with Rashba spin-orbit interaction. The study is within the framework of Tomonaga-Luttinger theory, and the spin-charge separation is not valid due to this Rashba interaction. The weak magnetic impurity provides the scattering mechanism and breaks the time-reversal symmetry. Combing all these elements, it is found that the spin polarization or net spin current will be generated. In Chapter 3, a physical implementation of the valley-pair quantum bits (qubits) on gapped graphene double quantum dot is proposed. Graphene is a two-dimensional material with the unique electron dispersion - it has two degenerate, independent energy valleys, a novel degree of freedom, and the graphene with energy gaps at these valleys are assumed in our study. Similar to the spin-pair qubits which use spin-singlet/triplet, we use “valley-singlet/triplet” to form the valley-pair qubits. We further provide practical procedures to manipulate the qubits based on electrical tuning of the valley moment. Valley pair qubits are characterized by a) scalability and fault-tolerance, b) all-electric manipulation via electric gates, and c) long coherence time, all being rather useful assets in qubit implementation.

電子除了基本電荷量以外還帶有自旋。本文把基本電荷量以外，像電子自旋這樣的，其他用來描述電子狀態的量子數或自由度，稱為“同位旋”。而同位旋電子學探討的是，利用這些額外的自由度來設計新功能的元件的可能性。本文第一章提供對後面討論的相關的準備，第二章開始，便討論在准一維電子系統中，磁性雜質伴隨Rashba效應產生的自旋過濾。整個討論使用Tomonaga-Luttinger的理論，而Luttinger理論中常出現的電荷-自旋分離，在我們加入的Rashba效應影響下會被破壞。弱磁性雜質是一個破壞時間反演對稱的散射源。一起考慮這些機制的系統，將會有自旋極化的效果(即產生自旋電流)。本文的第三章提出基於石墨烯其色散關係的valley(能谷)這個新穎自由度而設計出的雙量子點量子位元。石墨烯的色散關係中，包含兩個簡併的能谷。我們的討論還假定了石墨烯在能谷處已經打開了能隙。類似用自旋的singlet和triplet形成自旋對量子位元的想法，我們的設想是利用能谷的singlet和triplet。此外，我們也提出了基於以電壓調變能谷磁矩，來操作此量子位元的方法。基於能谷的量子位元的特性或優點，乃是：a) 容錯的與可以規模化集成的能力，b) 可用電極來進行全電性的操控 和 c) 很長的相干時間，以上皆是建構量子位元時的重要考慮。

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