電閘極對二維拓樸材料(HgTe/CdTe)之邊緣 態和量子傳輸的影響

Abstract

此論文包含三部分：HgTe/CdTe 量子井的拓樸特徵、有或無分裂閘極之柱狀量子自旋霍爾井的電子能譜以及在柱狀HgTe/CdTe 量子自旋霍爾井中經過由有限長的分裂閘極所構成之量子接點的量子傳輸。

於第一部分，吾做出及展示出HgTe/CdTe 系統的 2 Z 拓樸不變性。於第二部分，吾證明若邊於態存在則其維持於柱狀量子自旋霍爾井的邊界而非由分裂閘極所定義出的邊界。最後，第三部分，在量子接點組態下，電導中有著值得關注的結構被發現。此結構與邊緣態的關係將會被探討。

This work covers three parts: the topological features of the HgTe/CdTe quantum well, the electronic spectrum of quantum Hall bar with or without a split-gated configuration, and the quantum transport through a quantum point contact formed by a finite-length split-gate on a HgTe/CdTe quantum Hall bar. In the first part, we work out and demonstrate the Z2 topological invariant of HgTe/CdTe system. In the second part, we show that the edge states, when exist, will remain locating to the vicinity of the boundaries of the quantum spin Hall bar and not to the boundaries defined by the split gates. Finally, in the third part, interesting structures the the conductance are found in the quantum point contact configuration. Relation of these structures to the edge states will be explored.