Dirac Fermions in Graphene and Graphiteâa view from angle ...

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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 generation 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 semiconductor. 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 crystalline 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 single 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 Acknowledgements vitae i iii 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
Page 1 and 2: Dirac Fermions in Graphene and Grap
Page 3: Dirac Fermions in Graphene and Grap
Page 7 and 8: 7.6 Conclusions and implication of
Page 9 and 10: Curriculum Vitæ Shuyun Zhou Educat
Page 11 and 12: • Selected as Science Highlight f
Page 13 and 14: The unit cell of graphene contains
Page 15 and 16: Projecting this equation into φ(r
Page 17 and 18: Figure 1.5. Schematic drawing of th
Page 19 and 20: Chapter 2 Experimental techniques 2
Page 21 and 22: dispersion E(k z ). Thus k z values
Page 23 and 24: where ɛ is infinitely small. Accor
Page 25 and 26: Langmuirs (1L=10 −6 torr·s) to c
Page 27 and 28: mean free path, E kin is the kineti
Page 29 and 30: a b c d e f graphite SiC f graphite
Page 31 and 32: Figure 3.3. XPS results showing dat
Page 33 and 34: Figure 3.5. Intensity map at -1 eV
Page 35 and 36: Chapter 4 Gap opening in epitaxial
Page 37 and 38: Figure 4.2. Observation of the gap
Page 39 and 40: the EDCs as well as the region of e
Page 41 and 42: Figure 4.7. Dispersions measured in
Page 43 and 44: Figure 4.9. (a-c) LEEM images taken
Page 45 and 46: Figure 4.10. Proposed mechanism for
Page 47 and 48: Chapter 5 Metal-insulator transitio
Page 49 and 50: Figure 5.2. (a) Dispersions through
Page 51 and 52: Figure 5.3. (a-f) Data taken throug
Page 53 and 54: Chapter 6 Dirac fermions and effect
Page 55 and 56:
Figure 6.2. Linear Λ-shaped disper
Page 57 and 58:
Figure 6.4. Detailed low energy dis
Page 59 and 60:
Figure 6.6. Detailed dispersion nea
Page 61 and 62:
Chapter 7 ARPES study of partially
Page 63 and 64:
Figure 7.2. (a) Fermi energy intens
Page 65 and 66:
direction, i.e. perpendicular to gr
Page 67 and 68:
Figure 7.5. ARPES intensity map mea
Page 69 and 70:
Figure 7.7. (a) ARPES intensity map
Page 71 and 72:
Figure 7.9. (a) ARPES intensity map
Page 73 and 74:
19. Hüfner, S. Photoelectron Spect
Page 75 and 76:
59. Jiang, Y. J., Yao, D.-Y., Carls
Page 77 and 78:
99. Luk’yanchuk, I. A. & Kopelevi
Page 79 and 80:
List of Figures 1.1 (a) Sp 2 bondin
Page 81 and 82:
4.8 Thickness dependence of E D and
Page 83 and 84:
7.2 (a) Fermi energy intensity map.
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