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First-Principles Study of Charge Density Waves, Electron-Phonon Coupling, and Superconductivity in Transition-Metal Dichalcogenides

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First-Principles Study of Charge Density Waves, Electron-Phonon Coupling, and Superconductivity in Transition-Metal Dichalcogenides First-principles study of charge density waves, electron-phonon coupling, and superconductivity in transition-metal dichalcogenides A Dissertation submitted to the Faculty of the Graduate School of Arts and Sciences of Georgetown University in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics By Yizhi Ge, B.S. Washington, DC July 22, 2013 Copyright c 2013 by Yizhi Ge All Rights Reserved ii First-principles study of charge density waves, electron-phonon coupling, and superconductivity in transition-metal dichalcogenides Yizhi Ge, B.S. Dissertation Advisor: Amy Y. Liu, Ph.D. Abstract In this thesis we investigate the electronic and vibrational properties of sev- eral transition-metal dichalcogenide materials through first-principles calculations. First, the charge-density-wave (CDW) instability in 1T-TaSe2 is studied as a func- tion of pressure. Density-functional calculations accurately capture the instability at ambient pressures and predict the suppression of the CDW distortion under pressure. The instability is shown to be driven by softening of selected phonon modes due to enhanced electron-phonon matrix elements, rather than by nesting of the Fermi sur- face or other electronic mechanisms. We also discuss the possibility of electron-phonon superconductivity in compressed 1T-TaSe2. Another polymorph of TaSe2 is then investigated. We focus on the origin of the CDW instability in bulk and single-layer 2H-TaSe2. The role of interlayer interactions and the effect of spin-orbit coupling are examined. The results show that the CDW instability has weak dependence on interlayer interactions and spin-orbit coupling, which is in contrast to the closely related 2H-NbSe2 material, where the CDW ordering vector is predicted to depend on dimensionality. The electron-phonon interaction in electron-doped single-layer MoS2 is also studied. The calculation predicts a weak coupling at low doping levels. It then grows rapidly to a maximum of λ 1.7, after which it begins to decrease with additional ≈ iii doping. The superconducting transition temperature is expected to follow the same trends. This behaviour is explained by the appearance, disappearance, growth, and shrinkage of Fermi sheets with different orbital character. These results, which are similar to the experimentally observed superconducting dome in gate-tuned thin flakes of MoS2, reveal the importance of having the right mix of states at the Fermi level to enhance the electron-phonon interaction in this material. Finally, we present a new implementation of an iterative algorithm for the cal- culation of lattice thermal conductivity. By applying it to a simple two-dimensional system with interatomic interactions described by pair potentials, we show that the algorithm works, but further work is needed to improve the computational efficiency of the method. Index words: density functional theory, charge density wave, superconductivity, transition metal dichalcogenides, TaSe2, MoS2 iv ACKNOWLEDGEMENTS First of all, I would like to thank my thesis advisor, Dr. Amy Liu, for her patience and encouragement during the past years. Amy is a great advisor. She has been involved in every aspect of my research experience, gave me lessons from the fun- damental physics to conducting research work of complex topics. Since I joined her group, the way she does research has shaped my attitude towards it. And the impact would be far reaching into the future. It has been an unforgettable experience to work with Dr. Liu. I would like thank Prof. Freericks, Prof. Barbara, and Prof. Kertesz for their guidance and support in my research work and in final defense. One of the rewarding aspects of my graduate life has been working with a strong group. I would like to thank Wen Shen and Jesus Cruz for helpful discussions in the- oretical physics and computational techniques whenever I faced a problem. Working together with them has been constructive and fun. Finally, I would like to thank my wife, my parents, and the whole family for their never ending support and love. v Table of Contents Chapter 1 Introduction................................. 1 1.1 Transition-Metal Dichalcogenide Materials . ... 1 1.1.1 Bonding and Electronic Structure . 2 1.1.2 Charge Density Waves in TMDs . 5 1.1.3 Superconductivity in TMDs . 8 1.1.4 Interlayer Interactions and Dimensionality . 9 1.2 Electronic Structure Calculations . 10 1.3 OutlineofThesis .......................... 13 Bibliography................................ 15 2 TheoreticalBackground .......................... 19 2.1 Density Functional Theory . 19 2.1.1 Thomas-Fermi Theory . 21 2.1.2 Hohenberg-Kohn Theorems . 21 2.1.3 The Kohn-Sham Ansatz . 23 2.1.4 LDA and GGA approximations . 24 2.1.5 Solving the KS equations . 26 2.1.6 Plane Waves and Pseudopotentials . 26 2.2 Density Functional Perturbation Theory . 27 2.2.1 LatticeDynamics. 28 2.2.2 Electron-Phonon Coupling . 31 2.3 WannierFunction.......................... 32 Bibliography................................ 34 3 First-principles investigation of the charge-density-wave instability in 1T-TaSe2 .................................. 36 3.1 Introduction............................. 36 3.2 ComputationalMethod. 38 3.3 DescriptionofStructures . 39 3.4 ResultsandDiscussion . 40 3.4.1 Structural Instability . 40 3.4.2 ElectronicStructure . 43 3.4.3 Origin of the instability . 48 3.4.4 Superconductivity under pressure . 52 vi 3.5 Conclusions ............................. 54 Bibliography................................ 55 4 Effect of dimensionality and spin-orbit coupling on charge-density-wave transition in 2H-TaSe2 ........................... 57 4.1 Introduction............................. 57 4.2 ComputationalMethod. 60 4.3 DescriptionofStructures . 60 4.4 ResultsandDiscussion . 62 4.4.1 Structural instability . 62 4.4.2 Electronicstructure. 65 4.4.3 Origin of the instability and effect of interlayer interactions 69 4.5 Conclusions ............................. 75 Bibliography................................ 78 5 Phonon-mediated superconductivity in electron-doped single-layer MoS2: Afirst-principlesprediction . 81 5.1 Introduction............................. 81 5.2 Method ............................... 83 5.3 ResultsandDiscussion . 84 Bibliography................................ 93 Appendix A LatticeThermalConductivity . 96 A.1 Introduction............................. 96 A.2 Method ............................... 97 A.2.1 LatticeDynamics . 97 A.2.2 Boltzmann Transport Equation . 99 A.2.3 Iterative Approach to Solve Linearized BTE . 102 A.3 Algorithm and Implementation . 102 A.4 Test Case: Two-Dimensional Argon Solid . 105 Bibliography................................ 108 B PublicationListofYizhiGe . 109 vii List of Figures 1.1 Schematics of the two common structural polytypes. (a) Hexagonal(H) symmetry with trigonal prismatic coordination around metal sites. (b) Trigonal(T) symmetry with approximately octahedral coordina- tion around metal sites. Yellow dots represents chalcogens; blue dots representmetalatoms. .......................... 3 1.2 Schematic illustration showing that the electronic structure of TMDs depends on the number of valence electrons and the coordination envi- ronment. (a) corresponds to a group 5 metallic TMD with octahedral coordination, such as 1T-TaSe2. The lower d subband is partially filled, making it a metal. (b) corresponds to a group 6 TMD with trigonal prismatic coordination, such as 2H-MoS2. The lowest d band is filled, making it a semiconductor. The dashed line represents the Fermi level of a TMD with group 5 metal atom, such as 2H-TaSe2. In this case, the lowest dz2 band is half filled, making it a metal. 4 1.3 (a) √13 √13 CDW super lattice of 1T-TaSe2. The Ta sites form a 13- atom cluster× in a Star-of-David shape. (b)3 3 supercell of the CDW × phase in 2H-TaSe2. Different colors distinguish symmetry-inequivalent metalsitesinthesupercell. 6 1.4 The Peierls picture of charge-density-wave instability in a 1D lattice. Black dots represent lattice sites and the red line represents electron charge density. A gap is opened at the new zone boundary when the periodicity of the lattice is doubled. Credit: Ref. [27] . ..... 7 1.5 (a) Temperature-pressure phase diagram of the CDW and supercon- ducting transitions in 2H-NbSe2. Inset shows the dependence of super- conducting Tc on pressure. Credit: Ref. [34, 35] (b) Schematic plot of the temperature-pressure phase diagram of 1T-TaS2. NCCDW denotes the nearly commensurate CDW phase. The low temperature commen- surate CDW (CCDW) phase is also a Mott state. Pressure suppresses the CDW and superconductivity develops within the NCCDW state. Credit:Ref.[9]. .............................. 9 viii 3.1 1T-TaSe2 crystal structure and qz = 0 plane of the Brillouin zone. The large spheres (gray) represent Ta atoms and the small spheres (yellow) represent Se atoms. The in-plane components of the ordering vectors for the ICDW and CCDW phases are shown. In both cases, the structure is characterized by a triplet of ordering wave vectors. Since the structure has trigonal symmetry, the M and M′ points are labeled separately. ................................ 40 3.2 (a) Phonon spectrum of 1T-TaSe2 plotted along high-symmetry direc- tions in the Brillouin zone. Results are shown for pressures of P = 0 and 45 GPa. (b) Dependence of P = 0 unstable acoustic modes on qz. Results are plotted for wave vectors with in-plane projections of q = b1/2, corresponding to the arrow in (a). In both (a) and (b), imaginary frequencies are plotted as negative.
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