Linear and Nonlinear Optical Responses of Chiral Multifold Semimetals. Doctoral Thesis accepted by Université Grenoble Alpes, Grenoble, France

Since the initial predictions for the existence of Weyl fermions in condensed matter, many different experimental techniques have confirmed the existence of Weyl semimetals. Among these techniques, optical responses have shown a variety of effects associated with the existence of Weyl fermions. In chiral crystals, we find a new type of fermions protected by crystal symmetries — the chiral multifold fermions — that can be understood as a higher-spin generalization of Weyl fermions. This work provides a complete description of all chiral multifold fermions, studying their topological properties and the k·p models describing them. We compute the optical conductivity of all chiral multifold fermions and establish their optical selection rules. We find that the activation frequencies are different for each type of multifold fermion, thus constituting an experimental fingerprint for each type of multifold fermion. Building on the theoretical results obtained in the first part of our analysis, we study two chiral multifold semimetals: RhSi and CoSi. We analyze the experimental results with k·p and tight-binding models based on the crystal symmetries of the material. We trace back the features observed in the experimental optical conductivity to the existence of multifold fermions near the Fermi level and estimate the chemical potential and the scattering lifetime in both materials. Finally, we provide an overview of second-order optical responses and study the second-harmonic generation of RhSi. We find a sizeable second-harmonic response in the low-energy regime associated with optical transitions between topological bands. However, this regime is extremely challenging to access with the current experimental techniques. We conclude by providing an overview of the main results, highlighting potential avenues to further research on chiral multifold semimetals and the future of optical responses as experimental probes to characterize topological phases. Supervisor’s Foreword Abstract Acknowledgments Contents Abbreviations 1 Introduction 1.1 Experimental Signatures of Topological Metals 1.1.1 ARPES and the Discovery of Weyl Semimetals 1.1.2 The Chiral Anomaly and Negative Magnetoresistance of Weyl Semimetals 1.1.3 Optical Responses as Probes for Topological Phases 1.2 Beyond Weyl Crossings: Multifold Fermions 1.3 Structure of the Thesis References 2 Chiral Multifold Fermions 2.1 Weyl Fermions 2.2 The Classification of Chiral Multifold Fermions 2.2.1 Double-Weyl Fermion 2.2.2 Threefold Fermion 2.2.3 Sixfold Fermion 2.2.4 Fourfold Fermion 2.3 Material-Oriented Tight-Binding Models of Chiral Multifold Fermions 2.3.1 Space Group 199 2.3.2 Space Group 198 and Candidate Materials 2.4 Conclusions References 3 Linear Optical Conductivity of Chiral Multifold Fermions: kcdotp and Tight-Binding Models 3.1 Linear Optical Response in the Length Gauge 3.2 Optical Fingerprints in the Multifold kcdotp Models 3.2.1 Optical Conductivity of Fully Rotationally Symmetric Models 3.2.2 Optical Conductivity of Non-symmetric Low-Energy Models 3.3 Imaginary Part of the Optical Conductivity and Sum Rules 3.4 Optical Conductivity of Realistic Tight-Binding Models 3.4.1 Space Group 199 3.4.2 Space Group 198: RhSi 3.5 Conclusions References 4 Linear Optical Conductivity of CoSi and RhSi: Experimental Fingerprints of Chiral Multifold Fermions in Real Materials 4.1 Introduction 4.2 CoSi 4.2.1 Experimental Features of the Optical Conductivity 4.2.2 Low-Energy Regime: kcdotp and Tight-Binding Models 4.2.3 The Role of Spin-Orbit Coupling and the Spin-3/2 Multifold Fermion 4.2.4 Summary 4.3 RhSi 4.3.1 Experimental Features of the Optical Conductivity 4.3.2 Low-Energy Regime: kcdotp and Tight-Binding Models 4.3.3 Summary 4.4 Conclusions References 5 Nonlinear Optical Responses: Second-Harmonic Generation in RhSi 5.1 The Zoo of Nonlinear Responses 5.2 The Circular Photogalvanic Effect in RhSi 5.2.1 Experimental Features of the Circular Photogalvanic Effect 5.2.2 DFT Calculation of Circular Photogalvanic Effect in RhSi 5.2.3 Circular Photogalvanic Effect Calculation with a Tight-Binding Model for RhSi 5.3 Second-Harmonic Generation in RhSi 5.3.1 Second-Harmonic Generation in the Length Gauge 5.3.2 Second-Harmonic Generation of the Threefold Fermion at Γ: Low-Energy kcdotp Model 5.3.3 Experimental Features of the Second-Harmonic Generation in RhSi: Characterization with DFT Calculations 5.4 Comparing Low-Energy Second-Harmonic Generation Using First-Principles and kcdotp Calculations 5.5 Conclusions References 6 Conclusions References Appendix A Optical Conductivity of a Tetrahedral Fourfold Fermion Appendix B Temperature and Broadening of the Step Function Appendix C Imaginary Part of the Optical Conductivity from the Kramers-Kronig Relations Appendix D Sum Rules Appendix E Parallelized Code for Computing Second-Harmonic Generation Appendix F Accounting for Many-Body Effects in the Second-Harmonic Generation of RhSi: Scissors Potential in DFT Calculations Appendix Curriculum Vitae Appendix Scientific Production Appendix References