2015-01-012024-05-17https://scholars.lib.ntu.edu.tw/handle/123456789/672849摘要：由於物理基礎研究地進步與電腦計算速度的快速成長，現在科技有機會利用量子方法來設計與製作新穎材料並進而合成後來使用奇特的物理特性‧要能了解這些新穎材料的機制，發展理論方法來研究這些系統中的多體效應是非常重要。本研究選擇目前凝態理論最有挑戰性的幾個課題進行前沿研究。 凝態物理中的多尺度模擬 電腦的計算能力快速進步使得複雜系統的分析成為可能，而第一原理的計算幾乎已不需任何可調參數。本子項目主要在利用泛函密度理(DFT)論與量子蒙地卡羅(QMC)來研究奈米尺寸的物性， 如何解決在空間與時間的多尺度現象，而能有一個整體理論成為凝聚理論中重要的挑戰。本項目的重要目標是結合能帶理論，格林函數與Boltzmann方程式來了解奈米系統的多尺度響應，而研究的範圍會集中在團簇，單分子與二維電子氣。我們也會發展有效數值方法來處理強關聯系統內的問題。計畫參與的同仁都具有多年經驗且有互補的專長，相信此計畫必可讓台灣在此方面有更多國際參與與影響。 新穎材料中奇異量子態及量子傳輸 奈米結構下的電子傳輸中的物理，是非常的豐富，低溫下，量子力學的行為變得重要。我們的研究將側重於理解和控制的量子特性，在自旋極化結構中的電子傳輸。我們利用非平衡格林函數來了解奈米尺寸的量子輸運，特別是Landauer-Keldysh-Floquet 法用來了解時間相關的有自旋的傳輸現象。拓樸絕緣體上的spin pumping的特殊行為會是主要研究方向之一‧次微米尺寸時，粒子的擴散性使得Boltzmann 傳輸方程式變成可行，這也是研究地方向之一 。近日的自旋量子Hall效應與拓樸絕緣體的成熟，更使得此一研究有新的意義‧利用量子場論來研究自旋相關傳輸及其相關的自旋-軌道所引發的Yang-Mills 場在二維電子氣中的影響及其相關行為，也是新開始的課題，這部分的研究應該也能對新穎材料有極大幫助。在過去的二十年間，人們已經認識到奇異量子態，如分數量子霍爾態，是超越了傳統的Landau對稱破壞和費米液體的典範所可以描述的。拓撲序的概念被提出來描述這些奇異態。 嶄新的拓樸有序態在凝態系統中出現。我們對這些奇異態，例如具有不同規範對稱性的自旋液體，以及價鍵固體等的了解仍然是非常有限的。本計畫的進行將可協助量子材料的設計與了解。 <br> Abstract: With the advance of both Physics and computer technologies, it is now possible to do the quantum design and then synthesize nanoscale materials with novel properties. In order to understand the physics of the novel materials it is essential to develop new theoretical methods of studying many-body effects in these systems. In this project we focus on several challenging areas of condensed matter theory and their associated materials properties. 1.Multiscale modeling in condensed matter: The fast progress of computation power makes the numerical simulations in complex systems become feasible. Recent ab initio calculations in electronic structure systems have become almost parameter-free. The primary aim of this research direction is the study of nanomaterials by Density Functional Theory and Quantum Monte Carlo methods. However, the multiple spatial and time scales contained within the theory present great challenges. The ultimate goal of this study is to combine the band theory calculation, Green`s function and Boltzmann transport equation to understand the multiscale response in condensed matters systems. We intend to focus our study on clusters, single molecules and two-dimensional electronic gas. 2.Exotic quantum states and quantum transport in novel materials Our research will focus on understanding and controlling the quantum properties of structures in spin-polarized transport system. Non-equilibrium Green`s function method will be applied to study the quantum transport behavior on nanoscale. In particular, the Landauer-Keldysh-Floquet method can be used to study the ac response of spin-polarized transport phenomena. Moreover, in the past two decades, it has been realized that exotic quantum states, such as the fractional quantum Hall states, are beyond the description of conventional Landau symmetry-breaking and Fermi-liquid paradigms. A new kind of order, the topological order, has been proposed to describe these new states. Topologically ordered states emerge in a new class of materials, and prove to be even richer than symmetry breaking states. Our understanding of these exotic states, such as spin liquids with different gauge symmetries is still limited. A new class of material, topological insulator attracts quite a lot interests and we shall also study the spin pumping effect within topological insulator.多尺度模擬奇異量子態拓樸序自旋相關傳輸拓樸絕緣體Multiscale modelingtopological orderexotic quantum statesspin-polarized transporttopological insulator