On the Nature of Charge Density Waves, Superconductivity and Their Interplay in 1T-TiSe2

This thesis presents analytical theoretical studies on the interplay between charge density waves (CDW) and superconductivity (SC) in the actively studied transition-metal dichalcogenide 1T-TiSe2. It begins by reapproaching a years-long debate over the nature of the phase transition to the commensurate CDW (CCDW) state and the role played by the intrinsic tendency towards excitonic condensation in this system. A Ginzburg-Landau phenomenological theory was subsequently developed to understand the experimentally observed transition from commensurate to incommensurate CDW (ICDW) order with doping or pressure, and the emergence of a superconducting dome that coexists with ICDW. Finally, to characterize microscopically the effects of the interplay between CDW and SC, the spectrum of CDW fluctuations beyond mean-field was studied in detail. In the aggregate, the work reported here provides an encompassing understanding of what are possibly key microscopic underpinnings of the CDW and SC physics in TiSe2. Supervisor’s Foreword 6 Abstract 8 Publications Related To This ThesisChuan Chen, Bahadur Singh, Hsin Lin, and Vitor M. Pereira. “Reproduction of the charge density wave phase diagram in 1T-TiSe2 exposes its excitonic character.” Phys. Rev. Lett. 121, 226602 (2018)Chuan Chen, Lei Su, A. H. Castro Neto, and Vitor M. Pereira. “Discommensuration-enhanced superconductivity in the charge density wave phases of transition-metal dichalcogenides.” Phys. Rev. B 99, 121108 (R) (2019)Linjun Li, Chuan Chen, Kenji Watanabe, Takashi Taniguchi, Yi Zheng, Zhuan Xu, Vitor M. Pereira, Kian Ping Loh, and A. H. Castro Neto. “Anomalous quantum metal in a 2D crystalline superconductor with intrinsic electronic non-uniformity.” Nano Lett. 19, 4126 (2019)Chuan Chen, A. H. Castro Neto, and Vitor M. Pereira.“Pairing induced by fluctuations of an excitonic insulator: the case of superconductivity in TiSe2.” (manuscript submitted). 10 Acknowledgement 11 Contents 13 Acronyms 15 1 Introduction 17 1.1 Brief Introduction to Charge Density Waves 17 1.2 Overview of the Properties of 1T-TiSe2 19 1.2.1 Structural Properties 19 1.2.2 CDW in TiSe2 19 1.2.3 Superconductivity in TiSe2 21 1.3 Brief History of the Theoretical Understanding of the CDW Transition in TiSe2 23 1.3.1 Electronic Structure 23 1.3.2 Electron-Phonon Coupling and Electron-Electron Correlation in TiSe2 23 1.3.3 Signatures of Exitonic Condensation 25 1.4 Recent Experimental Developments on Two-Dimensional TiSe2 26 1.5 Organization of the Thesis 27 References 28 2 Excitonic Character of CDW in TiSe2 31 2.1 Excitonic Instability (EI) of TiSe2 31 2.1.1 The EI Hamiltonian 31 2.1.2 Mean Field Approach to the EI 32 2.1.3 Phase Diagram 34 2.2 DFT Study of the Lattice Instability 37 2.2.1 Isolating the Effect of Cu Doping 37 2.2.2 Phonon Softening with Cu Doping 41 2.3 Discussion 43 References 44 3 Phenomenological Model of Coexisting CDW and Superconductivity in TiSe2 46 3.1 The CDW Is Not Alone 46 3.2 Phenomenological Ginzburg–Landau Theory 48 3.3 Harmonic Expansion 50 3.4 CDW Phase Diagram 53 3.5 Coupling Between a Charge Density Wave and Superconductivity 56 3.6 More on Superconductivity 58 3.7 Summary 61 References 62 4 Excitonic CDW Fluctuations and Superconductivity 65 4.1 An Inspiration From the Spin-Bag Mechanism 65 4.2 Simplified Parameterization of the Excitonic Hamiltonian 66 4.3 Charge Density and Auxiliary Field 68 4.4 The Mean Field CDW Solution 69 4.5 Effective Action of CDW Fluctuations 71 4.6 Fluctuation-Induced Pairing Between Quasiparticles 72 4.7 Exploration of the Joint CDW-Superconductivity Phase Diagram 77 4.8 Summary 80 References 81 5 Anomalous Quantum Metal Phase in TiSe2 82 5.1 A Brief Introduction to the Anomalous Quantum Metal Phase 82 5.2 Summary of the Experiments 85 5.3 Theoretical Interpretation and Background 87 5.3.1 Thermally Activated Flux Flow 87 5.3.2 Bose Metal and Vortex Quantum Creeping 88 5.3.3 Importance of the CDW Background 90 5.4 Summary 92 References 93 6 Conclusions 95 References 97 Appendix A Mean Field Treatment of CDW with Both Excitons and Phonons1 98 Appendix B The Lattice Instability Ab initio2 101 B.1 Renormalized Band Structure: Mexican Hat Features 101 B.2 Phonon Hardening with Cu Doping 101 B.3 Robustness of the PLD and CDW Transition with Smearing Function 103 Appendix C Effective Action of CDW Fluctuations 106 C.1 Expansion for the Mass Term 106 C.2 Expansion for the Spatial Derivative (Momentum) Term 109 C.3 Expansion for the Stiffness Term 112 C.4 Effective Action for CDW Amplitude and Phase Modes 114 Front Matter ....Pages i-xvi Introduction (Chuan Chen)....Pages 1-14 Excitonic Character of CDW in TiSe2 (Chuan Chen)....Pages 15-29 Phenomenological Model of Coexisting CDW and Superconductivity in TiSe2 (Chuan Chen)....Pages 31-49 Excitonic CDW Fluctuations and Superconductivity (Chuan Chen)....Pages 51-67 Anomalous Quantum Metal Phase in TiSe2 (Chuan Chen)....Pages 69-81 Conclusions (Chuan Chen)....Pages 83-85 Back Matter ....Pages 87-105