Magneto-optical Properties in SrAs3 and Van Hove Singularity-associated Ordered States in CeRh2As2 = SrAs3에서의 자기 광학 성질 및 CeRh2As2의 반 호프 특이점과 연관된 질서 상태 연구

국문 초록 (Abstract)

응집 물질의 거시적 물성은 근본적으로 물질의 전자 구조에 의해 결
정된다. 본 학위논문에서는 이러한 전자 구조가 외부 자극에 대해 어떠한
선형 응답을 보이는지, 그리고 전자 간 상호작용을 통해 어떠한 독특한
양자 현상을 형성하는지를 중점적으로 탐구하였다.
첫째,선형응답이론을기반으로노달링준금속(nodal ring semimetal)
인 SrAs3의 전자 구조를 자기 광학적으로 분석하였다. 특히 자기 반사율
실험 결과를 이론적 계산과 정밀하게 비교 분석함으로써, 밴드 구조의 세
밀한 특징을 규명하였다. 연구 결과, 노달 링 내부에는 고전적(classical),
디락(Dirac), 그리고 준-디락(semi-Dirac) 페르미온이 공존함을 확인하였
으며, 이들은 자기장의 방향에 따라 선택적으로 관측할 수 있음을 보였다.
또한, 광학 전이 에너지 분석을 통해 일반적인 분산 관계와 구별되는 준-
디락 페르미온만의 고유한 특징인 ε ∼ B^2/3 스케일링을 보고하였다.
둘째, 이중층 Rashba-Hubbard 모델을 도입하여 재규격화된 상호작
용에의해발현되는자기적성질을연구하였다.무작위위상근사(RPA)를
이용하여, 반 호프 특이점(Van Hove singularities, vHs) 근처에서 전자 상
관관계가 자성 형성의 경향성을 어떻게 변화시키는지 기술하였다. 분석
결과, vHs 인근의 강한 상호작용이 시스템을 특정 자기 상태로 유도함을
밝혔으며, 특히 층 내 강자성 및 층 간 반강자성 결합을 특징으로 하는
A-타입 반강자성 질서와 비정합 자성(incommensurate magnetism)이 두
드러지게 나타남을 확인하였다. 이는 CeRh2As2와 같이 국소 반전 대칭이
깨진 초전도체의 복잡한 상평형도를 이해하는 데 중요한 이론적 단서를
제공한다.
마지막으로, 다중 페르미온(multifold fermion) 시스템에서 특정 상
호작용 채널이 위상 초전도성(topological superconductivity)을 유도할 가
능성을 간략히 논의하였다. 종합적으로 본 학위논문은 반응 함수를 통한
분광학적 해석부터 상관관계에 기인한 독특한 양자 현상의 이해에 이르
기까지, 전자 구조와 그 물성을 총체적으로 탐구하는 이론적 기틀을 마련
하였다.

다국어 초록 (Multilingual Abstract)

The macroscopic physical properties of condensed matter systems are
fundamentally governed by two key mechanisms: the linear response to
external perturbations and the formation of emergent quantum phenomena
driven by renormalized electronic interactions. This thesis investigates these
two aspects to elucidate the interplay between electronic excitations and
correlation effects.
First, we analyze the magneto-optical response of the topological nodal
ring semimetal SrAs3 within the framework of linear response theory. Specifically,
we interpret the magneto-reflectivity measurements through a rigorous
analysis based on theoretical calculations, thereby elucidating the underlying
electronic structure. We identify the coexistence of three distinct types of
fermions within the nodal ring: classical, Dirac, and semi-Dirac fermions.
These carriers can be selectively distinguished by varying the magnetic field
direction. Notably, we report a unique ε ∼ B^2/3 scaling behavior in the optical
transition energies, a signature of the semi-Dirac fermions that contrasts
with conventional dispersion relations.
Second, we investigate the emergence of exotic magnetic phases stabilized
by renormalized interactions in a bilayer Rashba-Hubbard model. By
employing the Random Phase Approximation (RPA), we determine how the
magnetic ordering tendencies are modified by the electronic correlations near
Van Hove singularities (vHs). Our analysis reveals that these fluctuations
drive the system toward specific magnetic instabilities, notably the A-type
antiferromagnetic order, characterized by ferromagnetic layers coupled antiferromagnetically,
and incommensurate magnetic order near vHs. These
results provide theoretical insights into the complex phase diagram of locally
non-centrosymmetric systems, such as the heavy fermion superconductor
CeRh2As2.
Finally, we briefly discuss the potential for topological superconductivity
in multifold fermion systems, proposing a mechanism where internode
pairing is induced by specific interaction channels. Collectively, this thesis
establishes a comprehensive framework for investigating the electronic structure,
encompassing both its spectroscopic signatures observed in response
functions and the emergent quantum phenomena driven by its inherent correlations.

목차 (Table of Contents)

• Abstract i
• List of Contents vi
• List of Figures xxi
• List of Tables xxii
• List of Publications xxiii
• Chapter 1 Introduction 1
• Chapter 2 Theoretical Background 4
• 2.1 Generalized susceptibility 4
• 2.2 Linear response theory 7
• 2.2.1 Basics of linear response 8
• 2.2.2 Optical conductivity and reflectivity 10
• 2.3 Random Phase Approximation (RPA) 12
• 2.3.1 Renormalization of susceptibility 12
• 2.3.2 Emergent quantum phases 14
• Chapter 3 Magneto-Optical Properties of the Nodal Ring Semimetal SrAs3 16
• 3.1 Introduction 16
• 3.2 Simplified nodal ring model 18
• 3.2.1 Model 18
• 3.2.2 Landau levels 20
• 3.2.3 Magneto-optical transitions 23
• 3.3 SrAs3 model 27
• 3.3.1 Model 27
• 3.3.2 Landau levels 28
• 3.3.3 Magneto-optical transitions 33
• 3.4 Comparison with experimental and theoretical results 44
• 3.4.1 Theoretical calculations: Magneto-optical conductivity 44
• 3.4.2 Magneto-optical spectroscopy measurements 45
• 3.4.3 Experimental result: magneto-optical spectroscopy 46
• 3.4.4 Extracted Landau levels and their scaling behavior 47
• 3.4.5 Effect of broadening on peak merging 49
• 3.5 Conclusion 50
• Chapter 4 The Effect of Van Hove Singularity on the Magnetism in Bilayer Rashba-Hubbard Model 53
• 4.1 Introduction 53
• 4.2 Bilayer Rashba-Hubbard model 57
• 4.3 Bare susceptibilities for particle-hole instabilities 61
• 4.3.1 Bare susceptibilities and the magnetic order 61
• 4.3.2 Classification of magnetic orders and susceptibility signatures 66
• 4.3.3 Analytical investigation of the susceptibility at high-symmetry points 68
• 4.4 RPA phase diagram with various Hamiltonian parameters 71
• 4.4.1 Changing the Rashba SOC α 71
• 4.4.2 Changing the interlayer hopping t⊥ 75
• 4.5 Conclusion 80
• Chapter 5 Topological Multiband s-wave Superconductivity in Coupled Multifold Fermions 82
• 5.1 Introduction 82
• 5.2 The low energy effective model of RhSi 84
• 5.3 Topological superconductivity from s+ ⊕ s− pairings 87
• 5.4 Phase diagram in various interactions 93
• 5.5 Conclusion 95
• Chapter 6 Conclusion 97
• 6.1 Summary 97
• 6.2 Future works 98
• Appendix A Magneto-optical properties of the nodal ring semimetal SrAs3 101
• A.1 Experimental details 101
• A.2 The effective model of SrAs3 105
• A.3 Analysis of the Landau levels 108
• A.4 Details of the numerical calculations 111
• A.5 Magneto-optical properties for ˆE ∥ ˆkx mode 112
• A.6 Comparison with previous magneto-optical experiments on topological semimetals 115
• Appendix B The Effect of Van Hove Singularity on the Magnetism in CeRh2As2 116
• B.1 Lifshitz Transitions and Fermi Surface Topology 116
• B.2 Dependence on the Next-Nearest-Neighbor Hopping Parameter 118
• B.2.1 Changing the Rashba SOC α 118
• B.2.2 Changing the interlayer hopping t⊥ 120
• Appendix C Topological Multiband s-wave Superconductivity in Coupled Multifold Fermions 124
• C.1 Lattice and Continuum Models for RhSi 124
• C.1.1 Tight-binding model 124
• C.1.2 Continuum model near the Γ point 126
• C.1.3 Continuum model near the R point 129
• C.2 Gap functions 132
• C.2.1 Expansion of Mi,k near the Γ point 134
• C.2.2 Expansion of Mi,k near the R point 135
• C.3 Generic DIII Topological Superconducting phases with the s+ ⊕ s− gap functions 136
• C.4 Nodal rings around R and their stability 137
• C.5 Linearized gap equation 141
• C.5.1 Calculation of the linearized gap equation 141
• C.5.2 Δ±, I6(4) and other superconducting gap functions 144
• C.5.3 Ambiguity of SOC parameters and their effect on the superconducting gap functions 146
• Bibliography 148
• Abstract in Korean 159