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Mott Transition in Strongly Correlated Materials: Many-Body Methods and Realistic Materials Simulations Tsung-Han Lee

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Mott Transition in Strongly Correlated Materials: Many-Body Methods and Realistic Materials Simulations Tsung-Han Lee Florida State University Libraries Electronic Theses, Treatises and Dissertations The Graduate School 2017 Mott Transition in Strongly Correlated Materials: Many-Body Methods and Realistic Materials Simulations Tsung-Han Lee Follow this and additional works at the DigiNole: FSU's Digital Repository. For more information, please contact [email protected] FLORIDA STATE UNIVERSITY COLLEGE OF ARTS AND SCIENCES MOTT TRANSITION IN STRONGLY CORRELATED MATERIALS: MANY-BODY METHODS AND REALISTIC MATERIALS SIMULATIONS By TSUNG-HAN LEE A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy 2017 Copyright c 2017 Tsung-Han Lee. All Rights Reserved. Tsung-Han Lee defended this dissertation on July 12, 2017. The members of the supervisory committee were: Vladimir Dobrosavljevic Professor Directing Dissertation Naresh S. Dalal University Representative Efstratios Manousakis Committee Member Luis Balicas Committee Member Jorge Piekarewicz Committee Member The Graduate School has verified and approved the above-named committee members, and certifies that the dissertation has been approved in accordance with university requirements. ii To my beloved family. iii ACKNOWLEDGMENTS The time at Florida State University was certainly one of the best time in my life. I owe so much gratitude to the people who helped me and supported me during this period. I would like to express my appreciation to all of them. First of all, I would like to thank my advisor, Vladimir Dobrosavljevic, for all his support and encouragement. His deep knowledge and perspective in condensed matter physics always stimulated me to contemplate critically on the subjects that I have learned, and his bright ideas always inspired me the direction to tackle the problems. From him, I learned the attitude of being a rigorous scientist and a critical thinker. It was my pleasure to learn and work with him during my Ph.D. degree. I am also very grateful that he always supported me to study the problems that I am interested in, encouraged me to attend important summer schools and conferences, and helped me whenever I had any difficulties. During this process, I explored many interesting fields in condensed matter physics and broadened my horizon in material science. Besides my advisor, I would also like to thank my collaborators, Serge Florens, Nicola Lanata, Yongxin Yao, Jaksa Vucicevic, Darko Tanaskovic, Eduardo Miranda, and Vladan Stevanovic. From them, I learned so much invaluable knowledge and powerful techniques that will help me to proceed in my future career. I am especially thankful to Serge, Nicola, Yongxin, and Jaksa, who always gave me prompt responses regarding my technical and theoretical questions during our research. I would also like to express my gratitude to my committee members, Efstratios Manousakis, Luis Balicas, Jorge Piekarewicz, Simon Capstick, and Naresh S. Dalal, for spending their time to participate in my Ph.D. evaluation, and all their precious suggestions on my dissertation. My life as a Ph.D. student would not have been complete without colleagues and friends. I would like to thank my colleagues, Shao Tang, Hossein Javan Mard, and Samiyeh Mahmoudian. I enjoyed many interesting and inspiring discussions in our cubicle, which made our working en- vironment very pleasant. I would also like to thank my friends, Shiuan-Fan Liou, Daniel Zuech, Mohammad Pouranvari, Wangwei Lan, and Niraj Aryal, for all the insightful discussions in our condensed matter study group. I am also happy to thank Yu-Che Chiu, Andrew Gallagher, Qiong Zhou, You Lai, Hiram Santiago, Nabin Rijal, Anish Bhardwaj, and Adewale Akinfaderin, for their iv friendship. Furthermore, I would like to thank all my firends, whose names are too many to list, for accompanying me during this journey. Last but not least, I would like to thank my parents, Bong-Che Lee and Sau-Chin Ting, my wife, Ya-Huei Huang, and my brother, Hsien-Han Lee, for always being there to support me pursuing my dreams. I would like to dedicate this dissertation to them. v TABLE OF CONTENTS List of Tables .............................................viii List of Figures ............................................ ix List of Symbols ............................................xiii Abstract ................................................xiv 1 Introduction 1 2 Models and Methods 3 2.1 Introduction ......................................... 3 2.2 First principle approach: Density functional theory ................... 4 2.3 Multiorbital Hubbard Model ............................... 5 2.4 Dynamical mean field theory ............................... 7 2.4.1 Mapping to Anderson impurity model ...................... 8 2.4.2 Iterative Perturbation Theory (IPT) ....................... 10 2.4.3 Slave-Rotor Non-crossing Approximation (NCA) . 11 2.4.4 Continuous Time Quantum Monte Carlo Method (CTQMC) . 13 2.5 Rotationally invariant slave-boson method (RISB) ................... 14 2.5.1 Rotationally invariant slave boson mapping ................... 15 2.5.2 Rotationally invariant slave boson Mean field theory . 16 2.6 The combination of first principle methods and many-body methods . 18 2.6.1 Correlated basis set ................................ 19 2.6.2 LDA+RISB functional ............................... 20 3 Unstable Domain Wall Solution in the Metal-Mott Insulator Coexistence Regime 22 3.1 Introduction ......................................... 22 3.2 Method ........................................... 24 3.2.1 Free energy and unstable solution ........................ 24 3.2.2 Resistivity calculation and Sommerfeld approximation . 25 3.3 Result ............................................ 27 3.3.1 Along the first order transition line ........................ 27 3.3.2 Along the constant U trajectory ......................... 29 3.4 Conclusion ......................................... 30 4 The Fate of Spinons at the Mott Point 33 4.1 Introduction ......................................... 33 4.2 Method ........................................... 35 4.3 Results ............................................ 37 4.3.1 Density of state and specific heat ......................... 37 4.3.2 Phase diagram ................................... 39 vi 4.3.3 Spinon orthogonality catastrophe ......................... 41 4.4 Conclusion ......................................... 42 5 Emergent Bloch Excitations in Mott Matter 44 5.1 Introduction ......................................... 44 5.2 Ghost GA theory ...................................... 45 5.3 Results ............................................ 48 5.3.1 Benchmark: Energy, double occupancy, and quasiparticle weight . 48 5.3.2 Benchmark: Single-particle Green’s function ................... 50 5.4 Conclusion ......................................... 52 6 Structural Predictions and Polymorphism in Transition Metal Compounds 54 6.1 Introduction ......................................... 54 6.2 Method ........................................... 57 6.3 Results ............................................ 57 6.3.1 Predicted structures and unit cell volumes .................... 57 6.3.2 LDA ......................................... 58 6.3.3 LDA+RISB ..................................... 59 6.3.4 LDA+U ....................................... 61 6.3.5 Comparison: LDA+RISB and LDA+U ..................... 63 6.4 Conclusion ......................................... 65 7 Nature of Am-O Bonding in Americian Chromate CsAm(CrO4)2 68 7.1 Introduction ......................................... 68 7.2 Method ........................................... 70 7.3 Electronic structure study ................................. 71 7.3.1 LDA ......................................... 71 7.3.2 LDA+RISB ..................................... 72 7.4 Conclusion ......................................... 74 8 Conclusion and Outlook 75 Appendices A Parametrization of the Multiorbital Coulomb Interaction 78 B Analytical Continuation 80 B.1 Pade Approximation .................................... 80 B.2 Maximum Entropy Method (MEM) ............................ 81 C Total Energy and Specific Heat Calculation for Hubbard Heisenberg Model 83 References ............................................... 85 Biographical Sketch ......................................... 98 vii LIST OF TABLES 6.1 The smallest LDA+RISB quasiparticle weight, Z, among all the orbitals for all the materials at U = 13 eV and J = 0.9 eV at the experimental equilibrium volumes. Z = 0 corresponds to the Mott-insulating phase in Brinkman-Rice picture, and finite Z corresponds to the correlated metallic phase. ...................... 61 6.2 The electronic phases predicted by LDA+U for all the materials and structures around the experimental equilibrium volumes. Here we set U = 13 eV and J = 0.9 eV. 63 6.3 Stable structures, electronic phases, and equilibrium volumes (in unit A˚3/f.u. ) pre- dicted by LDA, LDA+U at U = 13 eV and J = 0.9 eV, and LDA+SB at U = 13 eV and J = 0.9 eV. ....................................... 67 7.1 Parameters of the Am-5f reduced density matrix computed by LDA+RISB assuming U=6 and J=0.7, see Eq. 7.1: Probability weights wi, corresponding quantum labels Ni (number of electrons) and Ji (total angular momentum). 74 viii LIST OF FIGURES 2.1 Schematic representation for the DMFT mapping: Mapping a lattice problem to an impurity coupled to a cavity field, ∆(ω). .......................... 9 2.2 Schematic representation for the LDA+RISB algorithm. 21 3.1 (a) Schematic representation for the near-field
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