二維系統中量子霍爾平臺間遷移和絕緣體-量子霍爾導體相變之標度分析與鋁-氧化鋁垂直約瑟夫森結電性傳輸之研究

Abstract

超導電路的實現和臨界量子相變的研究是當代凝聚態物理實驗研究的兩大支柱。我們在這兩個學科中分別選擇一個主題來研究：一個是關於約瑟夫森結的傳輸特性研究，另一個是關於絕緣體-量子霍爾（I-QH）躍遷的討論。在單層外延石墨烯中。 首先，我們可能觀察到主要由分子束外延（MBE）製造的垂直Al / AlOx / Al 約瑟夫森結中的多次安德烈夫反射（MAR）。雖然用於構建超導電極和穿隧能障的材料並不新穎，但論文中所提及之用以製造Al/AlOx/Al約瑟夫森結之製程複雜度相較於普遍使用之遮蔽式蒸渡製程已大幅降低。Al超導電極的沉積和AlOx氧化層的形成均在MBE系統中完成，而微影製程則只需對其中一個超導電極進行。電性量測方面，從標準的四端測量所獲得的電流-電壓特性曲線中觀察到兩階段轉變行為和 多次安德烈夫反射。然而，臨界電流對溫度和磁場的相依性則並沒有和理論模型之預測有很好的一致性，這歸因於約瑟夫森勢壘中短路通道的顯著貢獻。這一結果說明本篇論文中用以簡化Al/AlOx/Al 約瑟夫森結製程複雜度之方法仍需要修改，特別是在提供打線接合之金屬電極和 AlOx 氧化層的大面積重疊。 其次，我們在 SiC 上生長，以Cr(CO)3作為覆蓋層的單層外延石墨烯測量到電子的傳輸特性由原先之絕緣態(ν=0)轉變至佔據高朗道能階(ν=6>2)的量子霍爾態的現象。這類型的相變是所謂的直接絕緣態-量子霍爾態 (I-QH) 相變，其特徵為在臨界磁場 B_c 處測得的縱向電阻率ρ_xx，其數值將不隨溫度溫度改變而發生變化。通過進行直接絕緣態-量子霍爾態相變的標準標度分析，描述此一現象的臨界指數κ被發現為 0.15±0.02，此數值接近於文獻中從ν=6到 ν=2的量子霍爾平台間躍遷中提取的κ值( κ_(plateau-plateau)=0.14)。從這個發現，我們認為這兩種相變可能屬於同一個普適性。

The realization of superconducting circuits and the investigation of the critical quantum phase transition are two backbones of contemporary experimental research in condensed matter physics. We chose one topic from each of these two disciplines to study in this thesis: one is contributed to the electrical and magneto-transport properties of Josephson junctions, and the other focuses on the discussion of insulator-quantum Hall (I-QH) transition in monolayer epitaxial graphene. Firstly, we observe possibly the multiple Andreev reflection (MAR) in the vertical Al/AlOx/Al Josephson junction mainly fabricated by the molecular beam epitaxy (MBE). Although the materials used to construct the superconducting electrodes and the tunneling barrier are not novel, the complexity of the fabrication of the Josephson junction is considerably reduced. The deposition of the Al superconducting electrodes and the formation of the AlOx oxide layer are all completed in the MBE system, and the photolithography only needs to be performed with respect to one of the superconducting electrodes. In the current-voltage characteristics obtained from the standard four-terminal measurement, two-stage transition behaviors and MAR are perceived. However, the dependence of the critical current on the temperature and magnetic field does not show great agreement with the typical behaviors of tunneling junction, which are attributed to the appreciable contribution of the non-Josephson barrier shorts. This result demonstrates the development of the simpler fabrication process for the Al/AlOx/Al Josephson junction in this work needs to be modified, especially on the large-area overlap of the bonding pad and the AlOx oxide layer. Secondly, we detected a transition from an insulating state (ν=0), in which ρ_xx decreases with increasing temperature, to a high Landau-level-filling-factor >2 (ν=6) QH state in monolayer epitaxial graphene grown on SiC with additional multilayer Cr(CO)3 capping on the graphene. This transition is the so-called direct I-QH transition, which is characterized by an approximately temperature-independent point in the measured longitudinal resistivity ρ_xx at a critical magnetic field, B_c. Through the standard scaling analysis for the direct I-QH transition, the critical exponent κ is determined to be 0.15, which is close to the value of κextracted from the ν=6 to ν=2 plateau-plateau transition, 0.14, in the literature. With this finding, we suggest that these two phase transitions may belong to the same universality.