請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/83246完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 高英哲 | zh_TW |
| dc.contributor.advisor | Ying-Jer Kao | en |
| dc.contributor.author | 陳允中 | zh_TW |
| dc.contributor.author | Yun-Chung Chen | en |
| dc.date.accessioned | 2023-02-01T17:03:11Z | - |
| dc.date.available | 2023-11-09 | - |
| dc.date.copyright | 2023-02-01 | - |
| dc.date.issued | 2023 | - |
| dc.date.submitted | 2023-01-13 | - |
| dc.identifier.citation | C. L. Kane and E. J. Mele. Z2 Topological Order and the Quantum Spin Hall Effect. Phys. Rev. Lett., 95:146802, Sep 2005.
M. Z. Hasan and C. L. Kane. Colloquium: Topological insulators. Rev. Mod. Phys., 82:3045–3067, Nov 2010. XiaoLiang Qi, Taylor L. Hughes, and ShouCheng Zhang. Topological field theory of time-reversal invariant insulators. Phys. Rev. B, 78:195424, Nov 2008. Xiao-Liang Qi and Shou-Cheng Zhang. Topological insulators and superconductors. Rev. Mod. Phys., 83:1057–1110, Oct 2011. Cenke Xu and J. E. Moore. Stability of the quantum spin Hall effect: Effects of interactions, disorder, and Z2 topology. Phys. Rev. B, 73:045322, Jan 2006. Liang Fu, C. L. Kane, and E. J. Mele. Topological Insulators in Three Dimensions. Phys. Rev. Lett., 98:106803, Mar 2007. Liang Fu and C. L. Kane. Topological insulators with inversion symmetry. Phys. Rev. B, 76:045302, Jul 2007. Andreas P. Schnyder, Shinsei Ryu, Akira Furusaki, and Andreas W. W. Ludwig. Classification of topological insulators and superconductors in three spatial dimensions. Phys. Rev. B, 78:195125, Nov 2008. Alexei Kitaev. Periodic table for topological insulators and superconductors. AIP Conference Proceedings, 1134(1):22–30, 2009. Shinsei Ryu, Andreas P Schnyder, Akira Furusaki, and Andreas W W Ludwig. Topological insulators and superconductors: tenfold way and dimensional hierarchy. New Journal of Physics, 12(6):065010, Jun 2010. Ching-Kai Chiu, Jeffrey C. Y. Teo, Andreas P. Schnyder, and Shinsei Ryu. Classification of topological quantum matter with symmetries. Rev. Mod. Phys., 88:035005, Aug 2016. F. D. M. Haldane. Model for a quantum hall effect without landau levels: Condensed-matter realization of the “parity anomaly”. Phys. Rev. Lett., 61:2015–2018, Oct 1988. Jeffrey C. Y. Teo, Liang Fu, and C. L. Kane. Surface states and topological invariants in three-dimensional topological insulators: Application to Bi1−xSbx. Phys. Rev. B, 78:045426, Jul 2008. Liang Fu. Topological Crystalline Insulators. Phys. Rev. Lett., 106:106802, Mar 2011. Timothy H. Hsieh, Hsin Lin, Junwei Liu, Wenhui Duan, Arun Bansil, and Liang Fu. Topological crystalline insulators in the SnTe material class. Nature Communications, 3(1):982, Jul 2012. Junwei Liu, Timothy H. Hsieh, Peng Wei, Wenhui Duan, Jagadeesh Moodera, and Liang Fu. Spin-filtered edge states with an electrically tunable gap in a two-dimensional topological crystalline insulator. Nature Materials, 13(2):178–183, Feb 2014. Hoi Chun Po, Ashvin Vishwanath, and Haruki Watanabe. Symmetry-based indicators of band topology in the 230 space groups. Nature Communications, 8(1):50, Jun 2017. Titus Neupert and Frank Schindler. Topological Crystalline Insulators. In Topological Matter, pages 31–61. Springer International Publishing, 2018. Zhida Song, Zhong Fang, and Chen Fang. (d − 2)-Dimensional Edge States of Rotation Symmetry Protected Topological States. Phys. Rev. Lett., 119:246402, Dec 2017. Wladimir A. Benalcazar, B. Andrei Bernevig, and Taylor L. Hughes. Electric multipole moments, topological multipole moment pumping, and chiral hinge states in crystalline insulators. Phys. Rev. B, 96:245115, Dec 2017. Wladimir A. Benalcazar, B. Andrei Bernevig, and Taylor L. Hughes. Quantized electric multipole insulators. Science, 357(6346):61–66, 2017. Josias Langbehn, Yang Peng, Luka Trifunovic, Felix von Oppen, and Piet W. Brouwer. Reflection-Symmetric Second-Order Topological Insulators and Superconductors. Phys. Rev. Lett., 119:246401, Dec 2017. Frank Schindler, Ashley M. Cook, Maia G. Vergniory, Zhijun Wang, Stuart S. P. Parkin, B. Andrei Bernevig, and Titus Neupert. Higher-order topological insulators. Science Advances, 4(6):eaat0346, 2018. Eslam Khalaf. Higher-order topological insulators and superconductors protected by inversion symmetry. Phys. Rev. B, 97:205136, May 2018. Guido van Miert and Carmine Ortix. Higher-order topological insulators protected by inversion and rotoinversion symmetries. Phys. Rev. B, 98:081110, Aug 2018. Max Geier, Luka Trifunovic, Max Hoskam, and Piet W. Brouwer. Second-order topological insulators and superconductors with an order-two crystalline symmetry. Phys. Rev. B, 97:205135, May 2018. Luka Trifunovic and Piet W. Brouwer. Higher-Order Bulk-Boundary Correspondence for Topological Crystalline Phases. Phys. Rev. X, 9:011012, Jan 2019. Luka Trifunovic. Bulk-and-edge to corner correspondence. Phys. Rev. Research, 2:043012, Oct 2020. Motohiko Ezawa. Topological Switch between Second-Order Topological Insulators and Topological Crystalline Insulators. Phys. Rev. Lett., 121:116801, Sep 2018. Yafei Ren, Zhenhua Qiao, and Qian Niu. Engineering Corner States from Two-Dimensional Topological Insulators. Phys. Rev. Lett., 124:166804, Apr 2020. Cong Chen, Zhida Song, Jian-Zhou Zhao, Ziyu Chen, Zhi-Ming Yu, Xian-Lei Sheng, and Shengyuan A. Yang. Universal Approach to Magnetic Second-Order Topological Insulator. Phys. Rev. Lett., 125:056402, Jul 2020. Moon Jip Park, Youngkuk Kim, Gil Young Cho, and SungBin Lee. Higher-Order Topological Insulator in Twisted Bilayer Graphene. Phys. Rev. Lett., 123:216803, Nov 2019. Frank Schindler, Zhijun Wang, Maia G. Vergniory, Ashley M. Cook, Anil Murani, Shamashis Sengupta, Alik Yu. Kasumov, Richard Deblock, Sangjun Jeon, Ilya Drozdov, Hélène Bouchiat, Sophie Guéron, Ali Yazdani, B. Andrei Bernevig, and Titus Neupert. Higher-order topology in bismuth. Nature Physics, 14(9):918–924, Sep 2018. Bi-Ye Xie, Hong-Fei Wang, Hai-Xiao Wang, Xue-Yi Zhu, Jian-Hua Jiang, Ming-Hui Lu, and Yan-Feng Chen. Second-order photonic topological insulator with corner states. Phys. Rev. B, 98:205147, Nov 2018. Xiang Ni, Matthew Weiner, Andrea Alù, and Alexander B. Khanikaev. Observation of higher-order topological acoustic states protected by generalized chiral symmetry. Nature Materials, 18(2):113–120, Feb 2019. Xiao-Dong Chen, Wei-Min Deng, Fu-Long Shi, Fu-Li Zhao, Min Chen, and Jian-Wen Dong. Direct Observation of Corner States in Second-Order Topological Photonic Crystal Slabs. Phys. Rev. Lett., 122:233902, Jun 2019. Wladimir A. Benalcazar, Tianhe Li, and Taylor L. Hughes. Quantization of fractional corner charge in Cn-symmetric higher-order topological crystalline insulators. Phys. Rev. B, 99:245151, Jun 2019. Frank Schindler, Marta Brzezińska, Wladimir A. Benalcazar, Mikel Iraola, Adrien Bouhon, Stepan S. Tsirkin, Maia G. Vergniory, and Titus Neupert. Fractional corner charges in spin-orbit coupled crystals. Phys. Rev. Research, 1:033074, Nov 2019. Haruki Watanabe and Seishiro Ono. Corner charge and bulk multipole moment in periodic systems. Phys. Rev. B, 102:165120, Oct 2020. Katsuaki Naito, Ryo Takahashi, Haruki Watanabe, and Shuichi Murakami. Fractional hinge and corner charges in various crystal shapes with cubic symmetry. Phys. Rev. B, 105:045126, Jan 2022. Ryo Takahashi, Tiantian Zhang, and Shuichi Murakami. General corner charge formula in two-dimensional Cn-symmetric higher-order topological insulators. Phys. Rev. B, 103:205123, May 2021. Haruki Watanabe and Hoi Chun Po. Fractional Corner Charge of Sodium Chloride. Phys. Rev. X, 11:041064, Dec 2021. Yu-Ping Lin. Higher-order topological insulators from 3Q charge bond orders on hexagonal lattices: A hint to kagome metals. arXiv:2106.09717, 2021. Barry Bradlyn, L. Elcoro, Jennifer Cano, M. G. Vergniory, Zhijun Wang, C. Felser, M. I. Aroyo, and B. Andrei Bernevig. Topological quantum chemistry. Nature, 547(7663):298–305, Jul 2017. Jennifer Cano, Barry Bradlyn, Zhijun Wang, L. Elcoro, M. G. Vergniory, C. Felser, M. I. Aroyo, and B. Andrei Bernevig. Building blocks of topological quantum chemistry: Elementary band representations. Phys. Rev. B, 97:035139, Jan 2018. Jennifer Cano, Barry Bradlyn, Zhijun Wang, L. Elcoro, M. G. Vergniory, C. Felser, M. I. Aroyo, and B. Andrei Bernevig. Topology of Disconnected Elementary Band Representations. Phys. Rev. Lett., 120:266401, Jun 2018. Hoi Chun Po. Symmetry indicators of band topology. Journal of Physics: Condensed Matter, 32(26):263001, Apr 2020. Eslam Khalaf, Hoi Chun Po, Ashvin Vishwanath, and Haruki Watanabe. Symmetry Indicators and Anomalous Surface States of Topological Crystalline Insulators. Phys. Rev. X, 8:031070, Sep 2018. W. P. Su, J. R. Schrieffer, and A. J. Heeger. Soliton excitations in polyacetylene. Phys. Rev. B, 22:2099–2111, Aug 1980. Hoi Chun Po, Haruki Watanabe, and Ashvin Vishwanath. Fragile Topology and Wannier Obstructions. Phys. Rev. Lett., 121:126402, Sep 2018. Barry Bradlyn, Zhijun Wang, Jennifer Cano, and B. Andrei Bernevig. Disconnected elementary band representations, fragile topology, and Wilson loops as topological indices: An example on the triangular lattice. Phys. Rev. B, 99:045140, Jan 2019. Zhi-Da Song, Luis Elcoro, and B. Andrei Bernevig. Twisted bulk-boundary correspondence of fragile topology. Science, 367(6479):794–797, 2020. Shang Liu, Ashvin Vishwanath, and Eslam Khalaf. Shift Insulators: Rotation-Protected Two-Dimensional Topological Crystalline Insulators. Phys. Rev. X, 9:031003, Jul 2019. Adrien Bouhon, Annica M. Black-Schaffer, and Robert-Jan Slager. Wilson loop approach to fragile topology of split elementary band representations and topological crystalline insulators with time-reversal symmetry. Phys. Rev. B, 100:195135, Nov 2019. Yoonseok Hwang, Junyeong Ahn, and Bohm-Jung Yang. Fragile topology protected by inversion symmetry: Diagnosis, bulk-boundary correspondence, and Wilson loop. Phys. Rev. B, 100:205126, Nov 2019. Hoi Chun Po, Liujun Zou, T. Senthil, and Ashvin Vishwanath. Faithful tight-binding models and fragile topology of magic-angle bilayer graphene. Phys. Rev. B, 99:195455, May 2019. Zhida Song, Zhijun Wang, Wujun Shi, Gang Li, Chen Fang, and B. Andrei Bernevig. All Magic Angles in Twisted Bilayer Graphene are Topological. Phys. Rev. Lett., 123:036401, Jul 2019. Zhijun Wang, Benjamin J. Wieder, Jian Li, Binghai Yan, and B. Andrei Bernevig. Higher-Order Topology, Monopole Nodal Lines, and the Origin of Large Fermi Arcs in Transition Metal Dichalcogenides XTe2 (X = Mo, W). Phys. Rev. Lett., 123:186401, Oct 2019. Shingo Kobayashi and Akira Furusaki. Fragile topological insulators protected by rotation symmetry without spin-orbit coupling. Phys. Rev. B, 104:195114, Nov 2021. Sander H. Kooi, Guido van Miert, and Carmine Ortix. Classification of crystalline insulators without symmetry indicators: Atomic and fragile topological phases in twofold rotation symmetric systems. Phys. Rev. B, 100:115160, Sep 2019. Benjamin J. Wieder and B. Andrei Bernevig. The Axion Insulator as a Pump of Fragile Topology. arXiv:1810.02373, 2018. A. Alexandradinata, J. Höller, Chong Wang, Hengbin Cheng, and Ling Lu. Crystallographic splitting theorem for band representations and fragile topological photonic crystals. Phys. Rev. B, 102:115117, Sep 2020. Zhi-Da Song, Luis Elcoro, Yuan-Feng Xu, Nicolas Regnault, and B. Andrei Bernevig. Fragile Phases as Affine Monoids: Classification and Material Examples. Phys. Rev. X, 10:031001, Jul 2020. A. Alexandradinata, Chen Fang, Matthew J. Gilbert, and B. Andrei Bernevig. Spin-Orbit-Free Topological Insulators without Time-Reversal Symmetry. Phys. Rev. Lett., 113:116403, Sep 2014. A. Alexandradinata and B. Andrei Bernevig. Berry-phase description of topological crystalline insulators. Phys. Rev. B, 93:205104, May 2016. Lukasz Fidkowski, T. S. Jackson, and Israel Klich. Model Characterization of Gapless Edge Modes of Topological Insulators Using Intermediate Brillouin-Zone Functions. Phys. Rev. Lett., 107:036601, Jul 2011. Maryam Taherinejad, Kevin F. Garrity, and David Vanderbilt. Wannier center sheets in topological insulators. Phys. Rev. B, 89:115102, Mar 2014. Maryam Taherinejad and David Vanderbilt. Adiabatic Pumping of Chern-Simons Axion Coupling. Phys. Rev. Lett., 114:096401, Mar 2015. Nicodemos Varnava, Ivo Souza, and David Vanderbilt. Axion coupling in the hybrid Wannier representation. Phys. Rev. B, 101:155130, Apr 2020. Chao-Xing Liu, Rui-Xing Zhang, and Brian K. VanLeeuwen. Topological nonsymmorphic crystalline insulators. Phys. Rev. B, 90:085304, Aug 2014. A. Alexandradinata, Zhijun Wang, and B. Andrei Bernevig. Topological Insulators from Group Cohomology. Phys. Rev. X, 6:021008, Apr 2016. Thomas Olsen, Tomá š Rauch, David Vanderbilt, and Ivo Souza. Gapless hinge states from adiabatic pumping of axion coupling. Phys. Rev. B, 102:035166, Jul 2020. Aleksandra Nelson, Titus Neupert, Tomáš Bzdušek, and A. Alexandradinata. Multicellularity of Delicate Topological Insulators. Phys. Rev. Lett., 126:216404, May 2021. Aleksandra Nelson, Titus Neupert, A. Alexandradinata, and Tomáš Bzdušek. Delicate topology protected by rotation symmetry: Crystalline Hopf insulators and beyond. Phys. Rev. B, 106:075124, Aug 2022. Frank Schindler and B. Andrei Bernevig. Noncompact atomic insulators. Phys. Rev. B, 104:L201114, Nov 2021. Python tight binding open-source package. Ken Shiozaki and Masatoshi Sato. Topology of crystalline insulators and superconductors. Phys. Rev. B, 90:165114, Oct 2014. Hui Li and F. D. M. Haldane. Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States. Phys. Rev. Lett., 101:010504, Jul 2008. Ari M. Turner, Yi Zhang, and Ashvin Vishwanath. Entanglement and inversion symmetry in topological insulators. Phys. Rev. B, 82:241102, Dec 2010. Lukasz Fidkowski. Entanglement Spectrum of Topological Insulators and Superconductors. Phys. Rev. Lett., 104:130502, Apr 2010. Taylor L. Hughes, Emil Prodan, and B. Andrei Bernevig. Inversion-symmetric topological insulators. Phys. Rev. B, 83:245132, Jun 2011. Chen Fang, Matthew J. Gilbert, and B. Andrei Bernevig. Entanglement spectrum classification of Cn-invariant noninteracting topological insulators in two dimensions. Phys. Rev. B, 87:035119, Jan 2013. A. Alexandradinata, Xi Dai, and B. Andrei Bernevig. Wilson-loop characterization of inversion-symmetric topological insulators. Phys. Rev. B, 89:155114, Apr 2014. Rui Yu, Xiao Liang Qi, Andrei Bernevig, Zhong Fang, and Xi Dai. Equivalent expression of Z2 topological invariant for band insulators using the non-Abelian Berry connection. Phys. Rev. B, 84:075119, Aug 2011. Tomáš Rauch, Thomas Olsen, David Vanderbilt, and Ivo Souza. Mirror Chern numbers in the hybrid Wannier representation. Phys. Rev. B, 103:195103, May 2021. Yuanfeng Xu, Luis Elcoro, Zhi-Da Song, Benjamin J. Wieder, M. G. Vergniory, Nicolas Regnault, Yulin Chen, Claudia Felser, and B. Andrei Bernevig. High-throughput calculations of magnetic topological materials. Nature, 586(7831):702–707, Oct 2020. Luis Elcoro, Benjamin J. Wieder, Zhida Song, Yuanfeng Xu, Barry Bradlyn, and B. Andrei Bernevig. Magnetic topological quantum chemistry. Nature Communications, 12(1):5965, Oct 2021. Ingo Peschel. Calculation of reduced density matrices from correlation functions. Journal of Physics A: Mathematical and General, 36(14):L205–L208, Mar 2003. Ching Hua Lee and Peng Ye. Free-fermion entanglement spectrum through Wannier interpolation. Phys. Rev. B, 91:085119, Feb 2015. Penghao Zhu, Kieran Loehr, and Taylor L. Hughes. Identifying Cn-symmetric higher-order topology and fractional corner charge using entanglement spectra. Phys. Rev. B, 101:115140, Mar 2020. Po-Yao Chang, Christopher Mudry, and Shinsei Ryu. Symmetry-protected entangling boundary zero modes in crystalline topological insulators. Journal of Statistical Mechanics: Theory and Experiment, 2014(9):P09014, Sep 2014. Kenneth G. Wilson. Confinement of quarks. Phys. Rev. D, 10:2445–2459, Oct 1974. Mahito Kohmoto. Topological invariant and the quantization of the Hall conductance. Annals of Physics, 160(2):343–354, 1985. Qian Niu, D. J. Thouless, and Yong-Shi Wu. Quantized Hall conductance as a topological invariant. Phys. Rev. B, 31:3372–3377, Mar 1985. Nicola Marzari and David Vanderbilt. Maximally localized generalized Wannier functions for composite energy bands. Phys. Rev. B, 56:12847–12865, Nov 1997. Nicola Marzari, Arash A. Mostofi, Jonathan R. Yates, Ivo Souza, and David Vanderbilt. Maximally localized Wannier functions: Theory and applications. Rev. Mod. Phys., 84:1419–1475, Oct 2012. Lixin He and David Vanderbilt. Exponential Decay Properties of Wannier Functions and Related Quantities. Phys. Rev. Lett., 86:5341–5344, Jun 2001. Christian Brouder, Gianluca Panati, Matteo Calandra, Christophe Mourougane, and Nicola Marzari. Exponential Localization of Wannier Functions in Insulators. Phys. Rev. Lett., 98:046402, Jan 2007. Alexey A. Soluyanov and David Vanderbilt. Wannier representation of Z2 topological insulators. Phys. Rev. B, 83:035108, Jan 2011. Chen Fang, Matthew J. Gilbert, and B. Andrei Bernevig. Bulk topological invariants in noninteracting point group symmetric insulators. Phys. Rev. B, 86:115112, Sep 2012. Zhida Song, Tiantian Zhang, and Chen Fang. Diagnosis for Nonmagnetic Topological Semimetals in the Absence of Spin-Orbital Coupling. Phys. Rev. X, 8:031069, Sep 2018. Zhida Song, Tiantian Zhang, Zhong Fang, and Chen Fang. Quantitative mappings between symmetry and topology in solids. Nature Communications, 9(1):3530, Aug 2018. B. Andrei Bernevig, Taylor L. Hughes, and Shou-Cheng Zhang. Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells. Science, 314(5806):1757–1761, 2006. Bilbao Crystallogr. Server, Bandrep: Band representations of the double space groups. Congjun Wu, B. Andrei Bernevig, and Shou-Cheng Zhang. Helical Liquid and the Edge of Quantum Spin Hall Systems. Phys. Rev. Lett., 96:106401, Mar 2006. Chang-Tse Hsieh, Takahiro Morimoto, and Shinsei Ryu. CPT theorem and classification of topological insulators and superconductors. Phys. Rev. B, 90:245111, Dec 2014. | - |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/83246 | - |
| dc.description.abstract | 拓樸絕緣體是一種具有整體性拓樸或邊界性異常的一系列材料。其中，整體-邊界對應關係是拓樸絕緣體中很重要的特徵，包括陳絕緣體和Z2拓樸絕緣體。這些拓樸絕緣體具有威爾森迴圈光譜環繞的特性，並且無法被構造出對稱局域萬尼爾函數。然而，最近的研究指出這些整體性拓樸特徵並不一定能反映出邊界的保護無隙態。本論文第一個提出穩定保護邊界態也可以在沒有前述整體性拓樸的情況下出現。我們發現這些「無義拓樸絕緣體」具有穩定的多胞性拓樸。特別地是，本論文模型中的穩定保護無隙態並不是被晶體對稱性保護而是被鏡像反對稱給保護。另外，我們也給出了拓樸不變量以及確認了糾纏光譜中的環繞。本論文因此得到了即使原子絕緣體也可以有穩定無隙邊界態的結論。 | zh_TW |
| dc.description.abstract | Topological insulator is a class of materials that exhibits nontrivial bulk topology or boundary anomalies. The associated bulk-boundary correspondence serves as an important feature of topological insulators, including Chern insulators and Z2 topological insulators. These topological insulators have spectral flow in the Wilson-loop spectrum and encounter Wannier obstruction. However, recent studies show that the bulk topological features may not imply the existence of protected gapless boundary states. In this thesis, we first provide an example where the stably protected gapless edge states arise without the aforementioned bulk topological features. We show that this "trivialized topological insulator" belongs to the first example of systems with stable multicellularity and non-delta like Wannier functions. The gapless edge states in the model are not protected by the crystalline symmetry but the mirror antisymmetry. In addition, we identify the associated topological invariant and the spectral flow in the entanglement spectrum. This thesis thus clarifies that even the atomic insulators can host stably protected gapless edge states. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2023-02-01T17:03:11Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2023-02-01T17:03:11Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | 口試委員審定書 i
致謝 iii 摘要 v Abstract vii Contents ix Chapter 1 Introduction 1 1.1 Background and Motivation 1 1.2 Outline of the Thesis 2 Chapter 2 Characterization of Topological Insulators 5 2.1 K theory 6 2.2 Entanglement Spectrum 10 2.3 Wilson-loop Spectrum 12 2.3.1 Theory 12 2.3.2 Interpolation Theorem 15 2.4 Wannier Function 16 2.4.1 Basic Properties 17 2.4.2 Wannier Obstruction 19 Chapter 3 Trivialized Topological Insulator 25 3.1 Model 25 3.2 Mirror Antisymmetry 27 3.3 Wannier Function 29 3.3.1 Pairing Condition 30 3.3.2 Exponentially Localized Wannier Function 31 3.3.3 Multicellularity 34 3.4 Entanglement Spectrum 35 Chapter 4 Summary and Outlook 37 References 39 | - |
| dc.language.iso | en | - |
| dc.subject | 萬尼爾函數 | zh_TW |
| dc.subject | 鏡像反對稱 | zh_TW |
| dc.subject | 保護無隙邊緣態 | zh_TW |
| dc.subject | 拓樸絕緣體 | zh_TW |
| dc.subject | 威爾森迴圈 | zh_TW |
| dc.subject | 多胞性 | zh_TW |
| dc.subject | 纏結光譜 | zh_TW |
| dc.subject | multicellularity | en |
| dc.subject | topological insulator | en |
| dc.subject | protected gapless edge states | en |
| dc.subject | mirror antisymmetry | en |
| dc.subject | Wannier function | en |
| dc.subject | entanglement spectrum | en |
| dc.subject | Wilson loop | en |
| dc.title | 無義拓樸中之穩定保護無隙邊緣態 | zh_TW |
| dc.title | Stably Protected Gapless Edge States in Trivial Topology | en |
| dc.title.alternative | Stably Protected Gapless Edge States in Trivial Topology | - |
| dc.type | Thesis | - |
| dc.date.schoolyear | 111-1 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 張博堯;謝長澤 | zh_TW |
| dc.contributor.oralexamcommittee | Po-Yao Chang;Chang-Tse Hsieh | en |
| dc.subject.keyword | 拓樸絕緣體,保護無隙邊緣態,鏡像反對稱,萬尼爾函數,纏結光譜,威爾森迴圈,多胞性, | zh_TW |
| dc.subject.keyword | topological insulator,protected gapless edge states,mirror antisymmetry,Wannier function,entanglement spectrum,Wilson loop,multicellularity, | en |
| dc.relation.page | 49 | - |
| dc.identifier.doi | 10.6342/NTU202300012 | - |
| dc.rights.note | 同意授權(全球公開) | - |
| dc.date.accepted | 2023-01-14 | - |
| dc.contributor.author-college | 理學院 | - |
| dc.contributor.author-dept | 物理學系 | - |
| 顯示於系所單位： | 物理學系 | |
文件中的檔案：
| 檔案 | 大小 | 格式 | |
|---|---|---|---|
| U0001-0338230103172002.pdf | 1.15 MB | Adobe PDF | 檢視/開啟 |
系統中的文件，除了特別指名其著作權條款之外，均受到著作權保護，並且保留所有的權利。