2014-01-012024-05-18https://scholars.lib.ntu.edu.tw/handle/123456789/697913摘要：找尋新的物質態是凝聚態物理中最重要的題目之一。在強相關電子系統的新穎物質態尤其是近三十年來物理學家關注的問題。 其中最著名的是高溫超導體與量子霍爾效應的發現。高溫超導體中奇特難理解的正常態產生高臨界溫度的問題至今仍然是自然界最大的一個謎。另一方面,量子霍爾效應中帶有分數電荷的激發態開&#21843;了新的認知。去年, 在自旋冰的材料中更發現古典的自由磁單極。這些有趣的系統的基本特性是激發態的性質往往與組成物質無關。本計畫將研究幾個強相關電子系統中重要的問題, 以下將對研究的方向做概述: 分數電荷激發態: 我們將推廣過去在高維度量子霍爾效應的工作, 探討模型中分數電荷激發態的問題,並且嘗試建立在任何維度分數電荷存在的定理。 非阿貝爾量子霍爾效應: 我們將把非阿貝爾量子霍爾效應推廣到高維度的空間,並且研究模型中奇異的邊界態。 石墨烯：2010年的諾貝爾獎頒給石墨烯的發現者。近年來，石墨烯的分數量子霍爾效應也被發現。 本計劃將研究石墨烯中異於傳統分數量子霍爾效應的新穎物質態。 <br> Abstract: New states of matter in the strongly correlated electronic systems (SCES) always give us surprises. The most famous examples are the high temperature superconductors and the fractional quantum Hall effect. The first one has an exotic normal state that leads to high transition temperature; the second one hosts deconfined fractional charge excitations. Nevertheless, the deconfined magnetic monopoles are recently found in the spin ice materials. A generic feature in those systems is that the elementary excitation is very distinct to the constituent particles. Therefore, the SCES provides a perfect playground for physicists to place their orders for the particles that cannot be observed in the high-energy accelerators. In this project, we will attack some important questions in the SCES. In the following, we outline the directions that we are pursuing. Fractional excitation. Recently, the fractional quantum Hall effect has been generalized to higher dimension by our group [1,2]. Using this new effect, a lattice hopping model can be constructed in any dimension. In this project, we shall explore the possibility of the existence of the fractional excitation in our model. We shall further work out the general principle to discuss its deconfinement in any dimension. Non-abelian quantum Hall effect. After the fractional quantum Hall effect is generalized to higher dimension, the next difficult but interesting direction is to generalize the non-abelian quantum Hall effect (NAQHE) to higher dimension. In the NAQHE, the majorana fermion emerges in the edge state, which is considered as an active candidate for the tolerant-fault quantum computing. Therefore, it is urgent to its higher dimensional sisters and to study the edge states. Graphene: Nobel prize in 2010 was issued to the discovery of graphene. Albeit its tremendous applications, its nature of 2D Dirac fermion leads to exotic quantum states of fractional quantum Hall effect discovered in the recent years. In this project, we will try to investigate those new states of matter in graphene.分數電荷量子霍爾效應超導體等效場論拓撲場論fractional excitationquantum Hall effectsuperconductoreffective field theorytopological field theory