強關聯電子及介觀系統中之新量子態與量子相變

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(high Tc superconductivity)以及無序的量子基態(quantum disordered ground state)。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獨特的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有待發現。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)及冷原子氣體(cold atomic gases)等介觀(mesoscopic)物理系統 已成為研究新量子態與量子相變更有前景的材料。此外, 新量子態及量子相變之研究對 奈米科技本身也有可觀的?在應用價值。因此，我的研究目標為以下兩點: 1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。 2應用上述物質的物理特性於奈米結構中以期對長久未解決問題提出新的洞見，並有助 於發展新的奈米科技。 未來三年我將集中於以下的研究課題: 1在與Kondo 效應相關的奈米半導體量子點（quantum dot）系統中，研究量子相變及其 中電子平衡和非平衡傳輸理論。 2在強關聯及介觀物理系統中，特別是冷原子光學晶格(cold atoms in optical lattices)系統 中，於理論上發現新的量子態及量子相變。 在研究方法上，我將採用不同的理論及數值方法，包括量子多體理論，重整化群理 論(Renormalization Group)，數值重整化群(Numerical Renormalization Group)。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，重要成果包括: 1成功的解釋在二維磁性材料中發現新的量子態--量子自旋無序液體（quantum spin?liquid）。 2預測在有摻雜質的挫折反鐵磁材料(doped frustrated antiferromagnets)中出現奇特新穎的 超導態，此一發現有助於瞭解高溫超導尚未解決的難題。 3在耦合雙量子點(coupled quantum dots)的研究中，我和合作者成功的解釋實驗上量測到 的奇特的電子導電行為--即Kondo 和Spin?singlet 兩種量子態的競爭所造成的現象。此 一成果也具應用價值--即提供自旋電子學（spintronics）系統中控制區域自旋（local spin） 的理論基礎。此一理論基礎有助於量子計算(quantum computation)研究之發展。 有著上述研究經驗，我相信我的研究在未來會有具體的成果

Over the past 20 years, strong electron-electron correlation (interaction) in solid-state materials has given rise to many fascinating new collective phenomena which can not be explained in terms of independent electrons. These new many-body phenomena occur at zero or very low temperatures where quantum mechanics plays an essential role. The well-known examples include high-temperature superconductivity and disordered quantum ground states in transition-metal-oxides. 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 criti- cal point separating two different phases, the thermaldynamic properties of the system exhibit unique universal power-law behaviors– the hallmark of quantum phase transitions. Though these phenomena have been heavily studied, some outstanding puzzles still remain unsolved and new quantum states are yet to be discovered. It is therefore of great importance in fundamental physics research to study these new emergent phenomena. Fortunately, due to recent progress in nano-technology , semiconductor nano-structures and ultra-cold atomic gases have become the promising better source of materials to address these issues. In addition to great academic importance, this research field also has potential impact on the current nanotechnology. The main goals of my research therefore are (1). to discover, understand, explain, and predict theoretically these new quantum phases and phase transitions in various materials. (2). to apply this physics to electronic transport through nano-structures with anticipation of new phenomena , more insight on the puzzles and technological progress to arise. In the coming years I will focus my research on (1). quantum phase transitions and charge transport associated with the Kondo effect in nano-structures, especially in semiconductor quantum dots. (2). novel and exotic quantum phases in various new correlated and mesoscopic systems, especially in cold atomic gases with Bose-Einstein Condensation. Various analytical and numerical approaches are used, including: quantum field theory of many-body systems, perturbative Renormalization Group (RG) and Numerical Renormalization Group (NRG) techniques. By combining them appropriately, it is promising to succeed in solving the problems. With much flexibility and tunability in current mesoscopic and nano devices, we anticipate new quantum states and new type of phase transitions to be realized. One highlight of my past research is successfully explain the novel 「spin-liquid」 phase– a spin disordered quantum state, which was recently realized experimentally for the first time in magnetic materials. Various new superconducting states with exotic quantum orders were also predicted in doped magnetic insulators, giving insight to the long-standing puzzle– the mechanism of high temperature superconductivity. In a recent study of quantum phase transitions in coupled quantum dots associated with the Kondo effect, I not only successfully explained the experiments but also provided a comprehensive understanding in gaining the local spin control in spintronic devices, one of the most active research areas in nanotechnology. With this experience, it is promising in my research to obtain fruitful results.