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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 李定國 | |
| dc.contributor.author | Wei-Lin Tu | en |
| dc.contributor.author | 杜韋霖 | zh_TW |
| dc.date.accessioned | 2021-06-17T03:21:10Z | - |
| dc.date.available | 2019-06-29 | |
| dc.date.copyright | 2018-06-29 | |
| dc.date.issued | 2018 | |
| dc.date.submitted | 2018-06-22 | |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/69615 | - |
| dc.description.abstract | 本篇論文致力於使用強關聯電子模型之t-J漢密頓量來了解物質之微觀行為，關於解釋強關聯之哈伯模型與其之極限對應的t-J模型有一長久以為無法解決的問題為，我們無法用解析解完美詮釋此量子模型；因此，在探討此模型時數值解便變得極為重要，在此篇論文中，我們利用重整化平均場論近似(RMFT)之數值理論來探討t-J模型的可能詮釋，歸功於Gutzwiller的發現，我們將可以把此模型中最困難之部分：電子的強關聯性重整化為係數置於模型前，在得到這些相關係數後，我們將可以利用平均場論的方法來對角化此一模型以便取得其本徵函數，此一方法為此一論文之標準方法。
接下來，我們關心的物理情境分為兩大類，第一類為高溫超導體之研究；在其最初發現於1987年以來已經過了30年，但科學家們仍無法為其定調，但隨著實驗器具的精準度上升，我們越來越能清楚得知其在微觀下的表現，這有助於幫助理論學家針對其建立一完整模型，但同時也增加其困難因為要預想一合理之模型能夠完整解釋所有實驗驗結果並非易事；我們的計算結果取得了許多數據，一一與實驗對比的結果發現兩者之契合度非常之高，這也是我們對此模型抱有高度信心之原因，詳細的比較結果將會在文中一一詳列。 第二類我們感興趣之系統為電子在強磁場作用之下的運動，霍夫斯塔德蝴蝶與哈伯 -霍夫斯塔德模型在自由電子於強磁場下在晶格內之運動給了一完整描述，因此，探討同樣之運動唯電子具有關聯性便成為一有趣課題，而我們的t-J模型在動能項增加一相位後，便成為一個用來探討此物理情境的可靠模型；在此一研究之中，為了能更好得比較計算結果，我們的合作者採用了另一數值方法：完整對角化，我們將會比較這兩種方法所計算出之結果並強調其可驗證性於未來之冷原子實驗中。 | zh_TW |
| dc.description.abstract | This thesis is aiming in utilizing the strongly correlated t-J Hamiltonian for better understanding the microscopic pictures of certain condensed matter scenario. One of the long existing issues in the Hubbard model and its extreme version, t-J model, lies in the fact that there is not an analytical way of solving them. Therefore, when dealing with these models, numerical approaches become very crucial. In this thesis, we will present one of the methods called renormalized mean-field theory(RMFT) and exploit it upon the t-J model. Thanks to the concept proposed by Gutzwiller, all we have to do is to try to include the correlation of electrons, which is mainly the most difficult part, with several renormalization factors. After obtaining the correct form of these factors, we can apply the routine mean-field theory in solving for the Hamiltonian, which is the principle methodology throughout this thesis.
Next, the physical systems that we are interested in consist of two parts. The mystery of High-Tc superconductivity comes first. After 30 years of its discovery, people still cannot settle down a complete microscopic theory in describing this exotic phenomenon. However, with more and more experimental equipment with higher accuracy nowadays, lots of behavior of copper oxide superconductor(also known as cuprate) have been revealed. Those discoveries can definitely help us better understand its microscopic mechanism. Therefore, from the theoretical side, to compare the calculated data with experiments leads us to know whether our theory is on the right track or not. We have produced tons of data and made a decent comparison which will be shown in the main text. The second system we are curious about is the mechanism of electrons under magnetic field. The Hofstadter butterfly along with its Hamiltonian, the Harper-Hofstadter model has achieved great success in describing free electrons’ movement with lattice present. Thus, it will be also interesting to ask the question: what will happen if the electrons are correlated. Our RMFT for t-J Hamiltonian, by adding an additional phase in the hopping term, happens to serve as a great preliminary model for answering this question. We will compare the results of ours with our collaborators, who solved this model by a different approach, the exact diagonalization(ED). Together with our calculations, we proposed several discoveries which might be realized by the cold atom experiments in the future. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-17T03:21:10Z (GMT). No. of bitstreams: 1 ntu-107-F01222026-1.pdf: 10126360 bytes, checksum: 2f2708787db3c082bb7b119f67e4aa0a (MD5) Previous issue date: 2018 | en |
| dc.description.tableofcontents | 口試委員會審定書iii
Acknowledgements v Abstract ix 摘要xi Résumé xiii List of Abbreviations xv 1 Introduction 1 1.1 High-Tc copper oxide superconductivity . . . . . . . . . . . . . . . . . . 1 1.1.1 The density waves . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.2 The pseudo-gap phase . . . . . . . . . . . . . . . . . . . . . . . 7 1.2 Correlated electrons under strong magnetic field . . . . . . . . . . . . . 11 2 Renormalized Mean Field Theory 15 2.1 BdG equation of mean-field Hamiltonian . . . . . . . . . . . . . . . . . 15 2.2 Green’s function and LDOS . . . . . . . . . . . . . . . . . . . . . . . . 20 2.3 Spectra weight and many-body Chern number . . . . . . . . . . . . . . 24 3 Results I – High Tc Cuprate 27 3.1 Real space properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.1.1 Charge-ordered patterns . . . . . . . . . . . . . . . . . . . . . . 27 3.1.2 Continuum LDOS . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.1.3 Bias and doping dependence . . . . . . . . . . . . . . . . . . . . 37 3.1.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.2 Momentum space properties . . . . . . . . . . . . . . . . . . . . . . . . 43 3.2.1 Particle-hole asymmetry . . . . . . . . . . . . . . . . . . . . . . 43 3.2.2 Two-gap in the SC phase . . . . . . . . . . . . . . . . . . . . . 46 3.2.3 Finite temperature IPDW states . . . . . . . . . . . . . . . . . . 47 3.2.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 3.3 Some details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 3.3.1 Method to determine kG . . . . . . . . . . . . . . . . . . . . . . 56 3.3.2 Two-gap plots . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.3.3 Choices of Gamma . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 3.3.4 Fermi arcs and LDOS . . . . . . . . . . . . . . . . . . . . . . . 58 4 Results II – Correlated Electrons Under Magnetic Field 61 4.1 Uniform and modulated singlet flux phase . . . . . . . . . . . . . . . . . 62 4.2 Fully polarized electron systems . . . . . . . . . . . . . . . . . . . . . . 68 4.3 Topological properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5 Conclusions and Outlooks 73 Bibliography 77 A Exact Diagonalization 97 A.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 A.2 Many-body Chern number . . . . . . . . . . . . . . . . . . . . . . . . . 97 A.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 B Induced Topological-Trivial Transition 101 | |
| dc.language.iso | en | |
| dc.subject | t-J 模型 | zh_TW |
| dc.subject | 高溫超導體 | zh_TW |
| dc.subject | 拓譜相 | zh_TW |
| dc.subject | RMFT | zh_TW |
| dc.subject | 強關聯系統 | zh_TW |
| dc.subject | RMFT | en |
| dc.subject | t-J model | en |
| dc.subject | Strongly correlated systems | en |
| dc.subject | Topological phase | en |
| dc.subject | High-Tc superconductivity | en |
| dc.title | 重整化平均場論在新穎量子材料上之應用 | zh_TW |
| dc.title | Utilization of Renormalized Mean-Field Theory upon
Novel Quantum Materials | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 106-2 | |
| dc.description.degree | 博士 | |
| dc.contributor.oralexamcommittee | 牟中瑜,高英哲,仲崇厚,Titus Neupert | |
| dc.subject.keyword | 強關聯系統,t-J 模型,RMFT,高溫超導體,拓譜相, | zh_TW |
| dc.subject.keyword | Strongly correlated systems,t-J model,RMFT,High-Tc superconductivity,Topological phase, | en |
| dc.relation.page | 104 | |
| dc.identifier.doi | 10.6342/NTU201801046 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2018-06-25 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 物理學研究所 | zh_TW |
| 顯示於系所單位： | 物理學系 | |
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