在多種拓樸系統中以全電性的方式產生與調控邊緣態

Abstract

此提案目標在多種拓樸系統中，探究以全電性的方式生產與調控邊緣態的可能性。計畫中有三種不同感到有趣的拓樸系統，名為扶手型開放邊界、帶狀HgTe量子井以及人工拓樸系統。 A) 扶手型開放邊界的石墨烯: 吾計畫去探究施加邊緣電位於扶手型帶狀石墨烯的效應，此延續著我們施加邊緣電位於扶手型石墨烯的開放邊界，此處原子被施予on-site energy，能形成非Tamm類型的邊緣態的發現。其中特別感興趣的是在扶手型帶狀石墨烯中產生垂直於平面的贗自旋的研究以及利用邊緣電位進行邊緣態的抽運研究。於後者，邊緣電位同時具有靜態與時間週期分量。 B) 帶狀HgTe量子井: 吾計畫去探究分裂式閘極(split-gate)量子接點對於帶狀HgTe量子井傳輸特性的效應，吾將聚焦在分裂式閘極(split-gate)對於邊於態的效應，亦即閘極對於邊緣態能有多少程度的橫向位移。進而仔細地研究邊緣態、體態與其導致的量子傳輸特性其間的交互作用。可預期地邊緣態與體態對於閘極量子接點的不同反應能提供我們額外的著力點去探究系中的拓樸性質並且能再進一步研究電荷與自旋的量子抽運。於後者，邊緣電位同時具有靜態與時間週期分量。 C) 人工拓樸系統: 人工拓樸系統中，吾將聚焦在能以背閘調變的偏壓，其空間分佈為台階狀，對於延著階狀方向邊緣態形成的效應。此人工拓樸系統由垂直於奈米圖樣化的二維電子氣所形成。延著階狀邊緣態的物理特性改變將會被研究。二維電子氣平面的奈米圖像包括金屬閘晶格，其基本拓樸自然特性已在上一個計畫有所研究，以及在磁場中由被磁通量管所通過的二維電子氣平面，此二維電子氣被平放在 type-II型的超導體平面上。

This proposal aims at exploring possible ways of all-electric generation and modulations of edge states in various topological systems. Three different topological systems are of interest in this project, namely, graphene with armchair open boundaries, HgTe quantum well stripes, and artificial topological systems. A) Graphene with armchair open boundaries: We plan to explore the effects of structured edge-potential on armchair graphene nanoribbon (AGNR), following on our finding that an edge-potential, where edge atoms are biased with on-site energy, can cause the formation of edge state (which is not Tamm-type) at a graphene armchair open boundary. Of particular interest are the possible out-of-plane pseudospin polarizations generated in the AGNR and the use of the structured edge-potential for the study of quantum pumping of the edge states. The edge-potential in the latter case will have both a static and a time-periodic components. B) HgTe quantum well stripes: We plan to explore the effects of a split-gate quantum point contact (QPC) on the quantum transport characteristics of the HgTe quantum well stripe. Our focus will be upon the effects of the split-gate biasing on the edge state, namely, to what extent will the edge state transverse position be shifted by the split-gate bias. Moreover, the interplay between the edge states and the bulk-like states and their resulting effects on the quantum transport characteristics will be studied in detail. The expected different responses of the edge states and the bulk-like states to the split-gate potential (QPC) should provide us an extra knob for the probing of the topological physics in the system, and, furthermore, for the quantum charge or spin pumping in the system. For the latter case, the split-gate bias will have both a static and a time-periodic components. C) Artificial topological systems: Our focus will be upon the effects of a step-like spatially varying back-gate biasing on the formation of edge states in the artificial topological systems along the step. The artificial topological systems are formed out of nano-patterning two dimensional electron gas (2DEG). The change in the physical nature of the edge states with the step-size of the back-gate bias will be studied. The nano-patterning of the 2DEG include the case of a metal-gate lattice on it, which basic topological nature we have studied in our previous project, and a flux-tube lattice penetrating the 2DEG, when the 2DEG, being put in close vicinity to a layer of type-II superconductor, is subjected to an external magnetic field.