Dirac Fermions in Graphene and Graphite — a view from angle-resolved photoemission spectroscopy by Shuyun Zhou M.A. (UC Berkeley) 2005 B.S. (Tsinghua University) 2002 A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Physics in the GRADUATE DIVISION of the UNIVERSITY OF CALIFORNIA, BERKELEY Committee in charge: Professor Alessandra Lanzara, Chair Professor Dung-Hai Lee Professor Oscar Dubon Fall 2007 The dissertation of Shuyun Zhou is approved. Chair Date Date Date University of California, Berkeley Fall 2007 Dirac Fermions in Graphene and Graphite — a view from angle-resolved photoemission spectroscopy Copyright c 2007 by Shuyun Zhou Abstract Dirac Fermions in Graphene and Graphite — a view from angle-resolved photoemission spectroscopy by Shuyun Zhou Doctor of Philosophy in Physics University of California, Berkeley Professor Alessandra Lanzara, Chair The research in graphene has exploded in the past few years, due to its intriguing physics as an emerging paradigm for relativistic condensed matter physics as well as its great promise for application in next gen- eration electronics. Understanding the low energy electronic structure of graphene is fundamental as most of the intriguing properties of graphene arise from its peculiar electronic dispersion, which resembles that of relativistic Dirac Fermions. This thesis presents a detailed study of the low energy electronic structure of graphene and its related three dimensional material - graphite - by using angle-resolved photoemission spectroscopy (ARPES), a direct probe of the electronic structure. In particular, the evolution of the Dirac Fermions in graphene and graphite as well as the effect of impurities is the focus of this thesis. This thesis is organized as follows. The first chapter is an introduction of the electronic structure of graphene and graphite, and the specialty of Dirac fermions compared to quasiparticles in conventional condensed matter systems. Chapter 2 is an introduction of the techniques used throughout this thesis - angle resolved photoemission spectroscopy (ARPES), X-ray photoemission spectroscopy (XPS) and low energy electron microscopy (LEEM). Chapter 3 discusses the growth and characterization of epitaxial graphene on SiC wafers. Chapters 4 and 5 present the ARPES results on epitaxial graphene, the evolution of the low energy electronic dynamics as a function of sample thickness and how to make graphene a finite band gap semi- conductor. More specifically, chapter 4 discusses how a gap is induced between the valence and conduction bands by graphene-substrate interaction and chapter 5 shows how a reversible metal-insulator transition can be possibly induced in epitaxial graphene by hole doping. Chapter 6 and 7 show the ARPES results on three dimensional graphite samples. Chapters 6 shows the coexistence of Dirac fermions with massive quasiparticles in different momentum space of single crys- talline graphite and the effect of impurity. Chapter 7 shows the surprising results of obtaining the band dispersions even in a partially polycrystalline graphite sample, the comparison with those obtained in sin- gle crystalline graphite, as well as the implication for ARPES study of partially polycrystalline samples in general. Professor Alessandra Lanzara Dissertation Committee Chair 1 Contents Abstract 1 Contents i Acknowledgements iii vitae vi 1 Introduction 1 1.1 Graphene - an emerging paradigm for relativistic condensed matter physics . 1 1.2 Electronic structure of graphene in the tight binding model . 3 1.3 Massless Dirac fermions and massive quasiparticles . 7 1.4 Electronic structure of infinite layer graphite . 8 2 Experimental techniques 10 2.1 Angle resolved photoemission spectroscopy (ARPES) . 10 2.1.1 ARPES and the photoelectric effect . 10 2.1.2 Three step model and sudden approximation . 13 2.1.3 Single particle spectral function description of ARPES . 15 2.1.4 Energy distribution curves (EDCs) and momentum distribution curves (MDCs) . 16 2.1.5 Electron mean free path and the probing depth of ARPES . 18 2.1.6 State of the art ARPES . 19 2.2 X-ray photoelectron spectroscopy (XPS) . 20 2.3 Low energy electron microscopy (LEEM) . 22 3 Growth and characterization of epitaxial graphene 24 3.1 Growth of epitaxial graphene . 24 3.2 Characterization of epitaxial graphene . 26 3.2.1 Scanning electron microscopy (SEM) . 26 3.2.2 X-ray photoemission spectroscopy (XPS) . 27 i 3.2.3 Angle-resolved photoemission spectroscopy - ARPES . 29 3.2.4 Low energy electron microscopy (LEEM) . 30 4 Gap opening in epitaxial graphene 33 4.1 Dirac fermions in epitaxial graphene . 34 4.2 Departure from conical dispersion in single layer epitaxial graphene . 35 4.3 Gap interpretation vs many body interactions . 39 4.4 Thickness dependence of the gap and Dirac point energy . 40 4.5 Possible mechanisms of the gap . 44 4.5.1 Inter-Dirac-point scattering . 44 4.5.2 Quantum confinement . 44 4.5.3 Breaking of the sublattice symmetry due to graphene-substrate interaction . 46 4.6 Conclusions . 49 5 Metal-insulator transition in epitaxial graphene by molecular doping 50 5.1 Motivation . 50 5.2 Valence band of graphene with adsorption of nitrogen dioxide . 51 5.3 Gas adsorption and metal-insulator transition in bilayer graphene . 53 5.4 Metal-insulator transition in single layer graphene . 55 5.5 Conclusions . 57 6 Dirac fermions and effect of impurities in single crystalline graphite 59 6.1 Introduction . 59 6.2 Electronic structure of single crystal graphite . 60 6.2.1 Dispersions at H - massless Dirac fermions . 61 6.2.2 Dispersions at K - massive quasiparticles . 66 6.3 Effect of defect states . 67 6.4 Conclusions . 70 7 ARPES study of partially polycrystalline graphite: HOPG 71 7.1 Electronic structure of polycrystalline materials measured by ARPES . 71 7.2 ARPES study of the electronic structure of polycrystalline graphite . 73 7.3 Explanation of the paradoxical coexistence based on a density of states argument . 75 7.4 Dispersions along the surface normal direction . 77 7.5 Comparison of data taken from HOPG and single crystalline graphite . 79 7.5.1 Interlayer coupling . 79 7.5.2 Low energy dispersions and Dirac fermions . 80 7.5.3 Defect states . 81 ii 7.6 Conclusions and implication of this study . 86 Bibliography 87 List of Figures 96 iii Acknowledgements I am very lucky to work with a group of talented and kind people in my Ph.D., from whom I have benefited greatly. All the work presented here would not have been possible without them. First of all, my deepest thanks go to my advisor, Alessandra Lanzara. I am very lucky to have such an inspiring, creative and considerate advisor, who has made my Ph.D. fruitful and enjoyable. Besides the training, encouragement and support that she gave me in science, I also appreciate her willingness to care about students’ life beyond work. The past few years of working with her has been a fortune for me. Her endless enthusiasm for science, her open-mindedness and her wisdom to balance work and life, have set her as a role model for me. I could not ask for better colleagues than the people in Lanzara group. Dr. Gey-Hong Gweon taught me numerous things in my first three years, ranging from experimental skills to different physics topics. I appreciate his mentoring and the efforts that he has put in to make me a good experimentalist. Dr. Kyle McElroy taught me the importance of understanding the physics problems in different perspectives. Jeff Graf, Chris Jozwiak and I joined the group as the first generation graduate students and we shared the longest memories of our Ph.D. lives. Besides intelligent, they are the best colleagues who are always willing to share their knowledge and skills and provide immediate help whenever needed. Daniel Garcia’s talks are the most wonderful sound of the group and I appreciate his help to improve my speech skills, though I have to admit that I am not a fast learner in this aspect. David Siegel reminded me of the early years of my Ph.D. It is a pleasure to see that he has become very good at communications and experiments. The interaction with visitors Dr. Marco Portalupi and Dr. Andreas Bill, as well as undergrads Elizabeth Rollings, Annie Endozo and Max Watson, has also been very pleasant. The collaboration with many theorists has been quite beneficial and pleasant. Dung-Hai Lee is the longest theoretical collaborator. His deep physics insights and his enthusiasm for finding the most beautiful solutions are very inspiring. The collaboration with A.N. Castro Neto, F. Guinea S.G. Louie and C.D. Spataru has been a great pleasure. Alexei Fedorov has collaborated in most of the research work presented here. His assistance in the experiments and his support for trying new experiments is highly appreciated. I am grateful to Andreas Schmid and Farid El Gably for providing extensive help with the LEEM measurements at the most critical time. John Pepper is very talented in machining and I thank him for making modifications to accommodate the needs of some challenging experiments. I thank Prof. P. N. First and Prof. W. A. de Heer for providing the graphene samples at the beginning of this project. I thank Prof. Oscar Dubon and Prof. Michael F. Crommie for serving as my committee members for the qualifying exam. J. T. Robinson and J. W. Beeman have been very nice to help me with substrate treatment. I thank the friendly and helpful people on the ALS floor: X. J. Zhou, W. L. Yang, N. Manella, K. Tanaka, S.-K. Mo, Y.-D. Chuang, J. H. Guo, B. K. Freelon, B. S. Mun. The LBL security people have been very kind to escort me to work and to home in many late nights. My personal interaction with other physicists also helps me greatly.