Electronic and Transport Properties of Weyl Semimetals
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Electronic and Transport Properties of Weyl Semimetals Dissertation Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Timothy M. McCormick, B.S. Graduate Program in Physics The Ohio State University 2018 Dissertation Committee: Professor Nandini Trivedi, Advisor Professor Yuri Kovchegov Professor Mohit Randeria Professor Rolando Valdes Aguilar c Copyright by Timothy M. McCormick 2018 Abstract Topological Weyl semimetals have attracted substantial recent interest in con- densed matter physics. In this thesis, we theoretically explore electronic and transport properties of these novel materials. We also present results of experimental collabora- tions that support our theoretical calculations. Topological Weyl semimetals (TWS) can be classified as type-I TWS, in which the density of states vanishes at the Weyl nodes, and type-II TWS, in which an electron pocket and a hole pocket meet at a singular point of momentum space, allowing for distinct topological properties. We consider various minimal lattice models for type-II TWS. We present the discovery of a type II topological Weyl semimetal (TWS) state in pure MoTe2, where two sets of WPs (W2±, W3±) exist at the touching points of electron and hole pockets and are located at different binding energies above EF . Using ARPES, modeling, DFT and calculations of Berry curvature, we identify the Weyl points and demonstrate that they are connected by different sets of Fermi arcs for each of the two surface terminations. Weyl semimetals possess low energy excitations which act as monopoles of Berry curvature in momentum space. These emergent monopoles are at the heart of the extensive novel transport properties that Weyl semimetals exhibit. We show how the Nernst effect, combining entropy with charge transport, gives a unique signature for the presence of Dirac bands. The Nernst thermopower of NbP (maximum of 800 ii µV·K−1 at 9 T, 109 K) exceeds its conventional thermopower by a hundredfold and is significantly larger than the thermopower of traditional thermoelectric materials. The Nernst effect has a pronounced maximum near TM = 90±20K = µ0=kB (µ0 is chemical potential at T = 0 K). A self-consistent theory without adjustable parameters shows that this results from electrochemical potential pinning to the Weyl point energy at T ≥ TM , driven by charge neutrality and Dirac band symmetry. We propose that Fermi arcs in Weyl semimetals lead to an anisotropic magne- tothermal conductivity, strongly dependent on externally applied magnetic field and resulting from entropy transport driven by circulating electronic currents. The circu- lating currents result in no net charge transport, but they do result in a net entropy transport. This translates into a magnetothermal conductivity that should be a unique experimental signature for the existence of the arcs. We analytically calculate the Fermi arc-mediated magnetothermal conductivity in the low-field semiclassical limit as well as in the high-field ultra-quantum limit, where only the chiral Landau levels are involved. By numerically including the effects of higher Landau levels, we show how the two limits are linked at intermediate magnetic fields. This work pro- vides the first proposed signature of Fermi arc-mediated thermal transport and sets the stage for utilizing and manipulating the topological Fermi arcs in experimental thermal applications. iii To my parents, who inspired my love of science. iv Acknowledgments There are many people who have been indispensible during my time in graduate school. First and foremost, I extend my deepest thanks to my advisor, Professor Nandini Trivedi. Her guidance and support were invaluable during my time here and she was a superb role model for how one should attack an unstructured problem. I can only hope that I picked up some of her physical insight during my time here. I am particularly indebted to her for the many opportunities that I had to collaborate with excellent experimentalists and theorists, as well as to attend several truly amazing conferences in the US and abroad. My time here would have been much less productive had it not been for the won- derful collaborations that I have been apart of. I thank Professor Adam Kaminski for the opportunity to collaborate on the ARPES discovery of type-II Weyl semimetal MoTe2. I am deeply grateful to Professor Jos Heremans and his student Sarah Watz- man for our many collaborations on transport phenomena in Weyl semimetals. From them I learned how truly messy yet rewarding studying transport can be. Much of this thesis was inspired by their excellent experiments. I am thankful to Professor Mohit Randeria, whose precise questions always got to the heart of a matter and were the source of many illuminating discussions on anomalous transport in Skyrmions. I also had the pleasure of collaborating with a very hard-working undergraduate student, Robert McKay, who was as ideal a mentee as I could ask for. v The Trivedi and Randeria groups were close to a second family to me during my time here. I follow in the footsteps of Will Cole, Mason Swanson, Eric Duchon, Onur Erten, and Nganba Meetei, who all helped to shape my physical intuition. I am particularly thankful for their infinite patience in answering the many questions of a new member of the group. I thank Hasan Khan, James Rowland, Tamaghna Hazra, Po-Kuan Wu, Wenjuan Zhang, Tim Gao, Kyungmin Lee, Kyusung Hwang, David Nozadze, Mehdi Kargarian, and Sumilan Banerjee for their discussions and companionship. I was also fortunate to have the best office-mates that I could ask for in Blythe Moreland and Jiaxin Wu. The condensed matter theory group is particularly lively at Ohio State. My time here was greatly enriched by the many interactions with other students, postdocs, and professors. I extend my thanks to Professor Ilya Gruzberg, Professor Jason Ho, and Professor Yuan-Ming Lu for teaching several excellent classes. I always found their doors open for questions and discussion. My friends and family provided a backbone of support while I completed my dissertation. I thank Jon Zizka, Andrew Hausman, Jake Kerrigan, Drew Gallagher, Chris Wolfe, Marci Howdyshell, Adam Ahmed, Simran Singh, Jyoti Katoch, Igor Pinchuk, Chris Ehemann, Dennis Bazow, and Dante O'Hara for always always being there for me. I thank my wife, Beth McCormick, for her love and support. I also thank my parents for their constant love and encouragement. Last but certainly not least, I would like to thank the NSF and the Center for Emergent Materials for funding the majority of my research. I also acknowledge the OSU presidential fellowship for funding my final year. vi Vita January 24, 1990 . Born - Wilmington, DE, USA 2012 . .B.S. Physics Publications Research Publications Timothy M. McCormick, Sarah J. Watzman, Joseph P. Heremans, Nandini Trivedi, \Fermi arc mediated entropy transport in topological semimetals" Phys. Rev. B 97, 195152 (2018). Sarah J. Watzman, Timothy M. McCormick, Chandra Shekhar, Shu-Chun Wu, Yan Sun, Arati Prakash, Claudia Felser, Nandini Trivedi, Joseph P. Heremans, \Dirac dispersion generates unusually large Nernst effect in Weyl semimetals" Phys. Rev. B 97, 161404 (2018). Timothy M. McCormick, Robert C. McKay, Nandini Trivedi, \Semiclassical the- ory of anomalous transport in type-II topological Weyl semimetals" Phys. Rev. B 96, 235116 (2017) Joseph R. Smith, Amber Byrum, Timothy M. McCormick, Nathan Young, Christo- pher Orban, and Christopher D. Porter, \A controlled study of stereoscopic virtual re- ality in freshman electrostatics" Physics Education Research Conference Series 2017, 363 (2017). Timothy M. McCormick, Itamar Kimchi, Nandini Trivedi, \Minimal models for topological Weyl semimetals" Phys. Rev. B 95, 075133 (2017). Lunan Huang, Timothy M. McCormick, Masayuki Ochi, Zhiying Zhao, Michi-to Suzuki, Ryotaro Arita, Yun Wu, Daixiang Mou, Huibo Cao, Jiaqiang Yan, Nandini vii Trivedi, Adam Kaminski, \Spectroscopic evidence for type II Weyl semimetal state in MoTe2" Nature Materials 15, 1155-1160 (2016). Timothy M. McCormick, Nandini Trivedi, \Tuning the Chern number and Berry curvature with spin-orbit coupling and magnetic textures" Phys. Rev. A 91, 063609 (2015). Fields of Study Major Field: Physics viii Table of Contents Page Abstract . ii Dedication . iv Acknowledgments . .v Vita......................................... vii List of Tables . xii List of Figures . xiii 1. Introduction . .1 2. Topology in Solid State Systems . .5 2.1 Berry Phase . .6 2.1.1 Berry Curvature . .8 2.1.2 Chern Number . 10 2.2 Chern Insulators . 11 2.2.1 Berry Curvature of a 2-Band Hamiltonian . 12 2.2.2 Chern Insulator on the Square Lattice . 13 2.2.3 Chiral Edge Modes . 15 3. Introduction to Weyl Semimetals . 18 3.1 Weyl Fermions . 19 3.1.1 Weyl Fermions in Quantum Materials . 21 3.2 Lattice Models for Weyl Semimetals . 26 3.3 Type II Weyl Semimetals . 30 ix 3.3.1 Time Reversal Breaking Model . 33 3.3.2 Inversion Breaking Model . 42 3.3.3 Surface States: Topological and Track . 46 3.3.4 Comparison with Experiments . 53 3.3.5 Conclusions . 55 3.4 Experimental Discovery of Weyl Semimetal MoTe2 ......... 56 3.4.1 ARPES Results . 59 3.4.2 DFT and Topological Analysis . 65 4. Thermoelectric Transport in Weyl Semimetals . 67 4.1 Boltzmann Transport Theory . 68 4.1.1 Definition of Transport Coefficients . 68 4.1.2 Boltzmann formalism . 71 4.2 Nernst Effect of Isotropic Weyl Nodes . 75 4.2.1 Numerical Results . 80 4.2.2 Analytic Results . 81 4.2.3 Nernst Thermopower in Weyl Semimetal NbP . 83 4.3 Anomalous Transport in Type-II Weyl Semimetals . 86 4.3.1 Model . 88 4.3.2 Anomalous Transport . 94 4.3.3 Relation to Measurable Quantities . 102 4.3.4 Discussion and Conclusion . 103 5. Fermi Arc-Mediated Entropy Transport in Weyl Semimetals . 106 5.1 Fermi arc-mediated magnetothermal transport .