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Quantum Geometry and Localization in Crystalline and Disordered Solids
Quantum Geometry and Localization in Crystalline and Disordered Solids
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260202105156
- ISBN
- 9798293883851
- DDC
- 530
- 서명/저자
- Quantum Geometry and Localization in Crystalline and Disordered Solids
- 발행사항
- [Sl] : Columbia University, 2025
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2025
- 형태사항
- 205 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 87-03, Section: B.
- 주기사항
- Advisor: Queiroz, Raquel.
- 학위논문주기
- Thesis (Ph.D.)--Columbia University, 2025.
- 초록/해제
- 요약We study the localization properties of electrons in solid-state systems, both with and without disorder. A key focus is to describe how the real-space extent of electronic eigenstates influences measurable physical quantities, such as the AC conductivity and dielectric properties. An essential link in this analysis, which connects microscopic localization and macroscopic responses, is the quantum metric - a geometric measure that quantifies the strength of dipole fluctuations in the many-electron ground state.In the first part of this thesis (Chapters 2 and 3), we study the quantum metric and the electric susceptibility (or capacitance), both analytically and numerically, across a diverse range of material systems, ranging from the microscale two-dimensional electron gases (2DEG) in magnetic fields to moire systems, and down to nanoscale conventional and topological insulators and semiconductors. This analysis reveals that the dielectric properties of matter can serve as diagnostics for certain correlated states (e.g., fractional quantum Hall phases) and exotic localization phenomena, such as the zero flux localization occurring in twisted bilayer graphene at the magic angle. Moreover, we propose that the relationship between the quantum metric and the dielectric constant can be instrumental in determining the dominant bonding character of the valence electrons (covalent vs. ionic) and even in detecting the non-trivial wavefunction topology.In the second part of the study (Chapters 4 and 5), we focus on Anderson insulators - materials where electrons are localized due to the destructive wavefunction self-interference induced by the presence of impurities. In these materials, hybridized pairs of localized eigenstates, known as Mott resonances, play a crucial role in the transport phenomena. We focus on investigating this mechanism in chiral disordered topological insulators, where we show that the hybridizing pairs of topological zero modes give rise to remarkable transport properties. In particular, in the chains with bond disorder, we identify the existence of an unusual "Anderson metal" phase, in which the electronic eigenstates appear localized yet exhibit finite DC conductivity. We also predict a novel phase, the superdielectric matter, characterized by a finite quantum metric (vanishing DC conductivity) and a divergent dielectric constant.Our work establishes the quantum metric and the hybridization analysis of disorder-localized eigenstates as crucial and unifying frameworks for understanding how the features of microscopic localization influence macroscopic observables, providing insight into how the transport properties of correlated, disordered, and topological systems can be efficiently studied.
- 일반주제명
- Physics
- 일반주제명
- Applied physics
- 일반주제명
- Quantum physics
- 키워드
- Quantum geometry
- 기타저자
- Columbia University Physics
- 기본자료저록
- Dissertations Abstracts International. 87-03B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■00520260202105156
■006m o d
■007cr#unu||||||||
■020 ▼a9798293883851
■035 ▼a(MiAaPQ)AAI32243219
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a530
■1001 ▼aKomissarov, Ilia.
■24510▼aQuantum Geometry and Localization in Crystalline and Disordered Solids
■260 ▼a[Sl]▼bColumbia University▼c2025
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2025
■300 ▼a205 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 87-03, Section: B.
■500 ▼aAdvisor: Queiroz, Raquel.
■5021 ▼aThesis (Ph.D.)--Columbia University, 2025.
■520 ▼aWe study the localization properties of electrons in solid-state systems, both with and without disorder. A key focus is to describe how the real-space extent of electronic eigenstates influences measurable physical quantities, such as the AC conductivity and dielectric properties. An essential link in this analysis, which connects microscopic localization and macroscopic responses, is the quantum metric - a geometric measure that quantifies the strength of dipole fluctuations in the many-electron ground state.In the first part of this thesis (Chapters 2 and 3), we study the quantum metric and the electric susceptibility (or capacitance), both analytically and numerically, across a diverse range of material systems, ranging from the microscale two-dimensional electron gases (2DEG) in magnetic fields to moire systems, and down to nanoscale conventional and topological insulators and semiconductors. This analysis reveals that the dielectric properties of matter can serve as diagnostics for certain correlated states (e.g., fractional quantum Hall phases) and exotic localization phenomena, such as the zero flux localization occurring in twisted bilayer graphene at the magic angle. Moreover, we propose that the relationship between the quantum metric and the dielectric constant can be instrumental in determining the dominant bonding character of the valence electrons (covalent vs. ionic) and even in detecting the non-trivial wavefunction topology.In the second part of the study (Chapters 4 and 5), we focus on Anderson insulators - materials where electrons are localized due to the destructive wavefunction self-interference induced by the presence of impurities. In these materials, hybridized pairs of localized eigenstates, known as Mott resonances, play a crucial role in the transport phenomena. We focus on investigating this mechanism in chiral disordered topological insulators, where we show that the hybridizing pairs of topological zero modes give rise to remarkable transport properties. In particular, in the chains with bond disorder, we identify the existence of an unusual "Anderson metal" phase, in which the electronic eigenstates appear localized yet exhibit finite DC conductivity. We also predict a novel phase, the superdielectric matter, characterized by a finite quantum metric (vanishing DC conductivity) and a divergent dielectric constant.Our work establishes the quantum metric and the hybridization analysis of disorder-localized eigenstates as crucial and unifying frameworks for understanding how the features of microscopic localization influence macroscopic observables, providing insight into how the transport properties of correlated, disordered, and topological systems can be efficiently studied.
■590 ▼aSchool code: 0054.
■650 4▼aPhysics
■650 4▼aApplied physics
■650 4▼aQuantum physics
■653 ▼aDisordered systems
■653 ▼aHopping conductivity
■653 ▼aQuantum geometry
■653 ▼aQuantum phase transitions
■653 ▼aTopological materials
■690 ▼a0605
■690 ▼a0599
■690 ▼a0215
■71020▼aColumbia University▼bPhysics.
■7730 ▼tDissertations Abstracts International▼g87-03B.
■790 ▼a0054
■791 ▼aPh.D.
■792 ▼a2025
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17359672▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
