強關聯電子及量子摻雜系統中之新穎量子現象

Abstract

近20年來電子在固態材料中的強關聯交互作用(strong electron-electron correlations)已產生許多不能用獨立電子來解釋的新的量子集體現象，這些新現象發生在量子力學效應顯得十分重要的零溫或低溫系統中。最著名的例子包括金屬氧化物中之高溫超導體以及於摻雜質之金屬中之Kondo 效應。這些穩定的量子基態或稱”量子相”(quantum phase)。隨著電子強關聯交互作用之改變, 這些系統中如果存在相互競爭的兩種不同的量子相, 在零溫下便會產生連續的”量子相變”(quantum phase transitions)--即系統之基態從量子相A連續轉變為量子相B。這些系統在兩種量子相的臨界點--量子臨界點 (quantum critical point）上，會展現非常特殊的非費米液體(non Fermi-liquid)行為，即其熱力學性質具有統一的Power-law的臨界行為。 雖然許多這些現象已被深入的研究過，但至今仍有不少未被解決的問題以及有更多新的量子態及量子相變已經或有待被發現。因此，研究此一問題在基礎科學上非常具有重要性。有賴於最近快速發展的奈米科技，其高度可調性(tunability)已使半導體奈米結構(semiconductor nano-structures)之量子摻雜系統(quantum impurity systems)(特別是量子點（quantum dot))已成為研究新量子態與量子相變極有前景的材料。此外, 強關聯中之新潁材料(如拓樸絕緣體(topological insulator))亦預期產生新的量子態及量子相變。因此，我的研究目標為:在理論上發現，理解並預測在不同物質材料中新的量子態和量子相變,並期能解釋新的實驗現象。未來三年我將集中於以下在凝態物理中十分基礎而重要的研究課題 1. 新穎材料量子點中因Kondo效應之消失所產生之非平衡量子相變 (nonequilibrium quantum phase transitions) 與其臨界行為, 如:在加偏壓之量子點與耗散環境(dissipation),或二維石墨烯(graphene),或磁性金屬,或強關聯奈米線(strongly correlated nano-wires)等偶合系統中之非平衡量子臨界行為。當上述Kondo量子點系統因外加偏壓而處於非平衡狀態時，其所產生之｢非平衡量子相變與臨界現象｣並未被廣泛地研究,因此成為一新穎而具基礎物理研究性之課題。近年來我在此領域已有突破性進展,並居國際領先群中. 2. 研究新穎之量子態, 如: 量子點（quantum dot）與二維拓樸絕緣體偶合系統中具非費 米液體行為之二渠道(two-channel) Kondo效應, 及於二維拓樸絕緣模型中尋找具拓樸性 質之超導態(topological superconductivity).此兩者亦為凝態物理中有趣行為而重要之課題. 在研究方法上，我將採用不同的理論及數值方法，包括標準量子多體理論(Quantum Many-body Theory)，玻色子化(Bosonization), 量子場論(Quantum Field Theory)與重整化群理論(Renormalization Group),及自洽平均場理論 (self-consistent Mean-Field Theories)。在上述方法交互運用之下，非常有希望得到新而有趣的結果。在過去五年中，我在相關領域的研究已獲得相當的成果，相信我的研究在未來會有具體的成果

Over the recent decades, many fascinating novel collective quantum many-body phenomena have emerged in strongly correlated electron systems where electron-electron correlations are important, such as: unconventional superconductivity in cuprates and iron pnictides, exotic Kondo states in quantum dots and in heavy fermions, and topological insulators. These fascinating new quantum collective phenomena occur at very low temperatures when quantum mechanics plays an important role, and they cannot be explained in terms of independent electrons. With the change of electron correlations, these materials at zero temperature can undergo the continuous “quantum phase transitions” when there are competing quantum ground state phases. At the quantum critical point separating two different phases, the thermodynamic properties of the system exhibit unique universal power-law behaviors– the hallmark of quantum phase transitions. Though some of these phenomena have been intensively studied, many outstanding puzzles still remain unsolved and new quantum phases are yet to be discovered, in particular in strongly correlated quantum impurity systems. It is therefore of great importance in fundamental physics research to study these newly emergent phenomena. Fortunately, due to recent progress in nano-technology , semiconductor nano-structures have become the promising better source of materials to address these issues. Newly discovered correlated electron systems, such as: heavy fermion compounds and topological insulators, also offer a route to new quantum phases and phase transitions. The main goals of my research therefore are to discover, understand, explain, and predict theoretically these new quantum phases and phase transitions in various materials. We hope to offer theoretical foundations to these new quantum many-body phenomena. In the coming years I will focus my research on (1). Kondo breakdown and quantum criticality out of equilibrium in quantum impurity systems, such as: quantum dot coupled to unconventional electron baths (graphene, ferromagnetic metals, Luttinger liquid) or a dissipative environment (charge and spin fluctuations). (2). Exotic quantum phase and phase transitions in systems involving impurity in topological insulators (TI), such as: quantum phase transition between 1-channel and 2-channel Kondo ground states in quantum dot coupled to 2D TIs, search for topological superconducting phase in doped 2D TIs. Various analytical and numerical approaches are used, including: quantum field theory of many-body systems, standard bosonization approach, self-consistent (Keldysh) Green’s function combined with the large-N approach, perturbative Renormalization Group (RG) techniques. By combining them appropriately, it is promising to succeed in solving the problems. My recent research on quantum phase transitions in coupled double-quantum-dot setup associated with the Kondo effect not only successfully explained the experiments but also provided a comprehensive understanding in gaining the local spin control in spintronic devices. In my very recent work, we pioneerly investigated the nonequilibrium quantum transport near the quantum phase transition of a dissipative quantum dot and the pseudogap Kondo model, which has significant impact on this new research field. Moreover, my theoretical works along these lines have attracted significant attention to the experimentalists. Some of my predictions on the side-coupled double Kondo dots have been observed already in recent experiment. With this experience at hand, it is promising in my research to obtain fruitful results in the next 3 years.