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

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Figure 7.1. BZ and measured dispersions on LaSe, from Nakayama et al 122 . with random azimuthal orientations while along the c-axis direction the sample is highly oriented. There on the order of mm scale, HOPG appears as a polycrystalline sample . However, HOPG is widely used since large sample size can be obtained and it is commercially available. In fact, HOPG has been the most common host material for graphite intercalation compounds (GICs). Our ARPES study on HOPG shows that band dispersions can be indeed obtained even from azimuthally disordered samples. 7.2 ARPES study of the electronic structure of polycrystalline graphite ARPES data were collected at beam line 10.0.1 of the Advanced Light Source (ALS) at the Lawrence Berkeley National Laboratory, using an SES-R4000 analyzer. The wide angular mode with acceptance angle of 30 ◦ and angular resolution of 0.9 ◦ was utilized for most scans, while high resolution angular mode with acceptance angle of 14 ◦ and angular resolution of 0.1 ◦ was utilized for one scan. The total instrumental energy resolution was 15 meV at 25 eV photon energy and 25 meV for other photon energies used (40, 55, 60 eV). The sample used was a grade ZYA highly oriented pyrolytic graphite (HOPG), obtained commercially from Structure Probe Inc. The sample was cleaved in situ in an ultra high vacuum better than 1.0×10 −10 Torr and measured at temperature 50 K. Fig. 7.2(a) shows an ARPES intensity map measured at the Fermi energy taken at 40 eV photon energy. Here we use a color scale such that black represents high intensity in the raw data and blue represents low intensity. According to band structure calculation, a constant k z cross section of graphite Fermi surface can be a small hole pocket, a small electron pocket, or a point located at the six corners of the hexagonal Brillouin zone (dashed line in Fig. 7.2(a)), depending on the value of k z 123,9 . Experimentally, the predicted small electron or hole pockets are difficult to be resolved, and measurements on single crystalline samples have shown only small dots of high intensity at these corners 124 , schematically drawn as shaded circles in Fig. 7.2(a). For the graphite sample under study, the Fermi energy intensity map, symmetrized by three fold rotations to fill the entire Brillouin zone, shows a perfectly circular pattern 1 , in contrast to what is expected for single crystalline graphite. This is attributed to the angular spread of the dots to a circle due to the azimuthal disorder of the sample 124 . 1 The intensity variation along the circle is attributed to photoemission matrix element and is not a major concern here. 51
Figure 7.2. (a) Fermi energy intensity map. The hexagonal Brillouin zone (dashed lines) and Fermi surface (shaded circles) expected for single crystalline graphite are drawn schematically. (b) Intensity map versus binding energy and in-plane momentum along the solid line in (a) taken at 60 eV photon energy. Arrow marks the Fermi energy crossing point (k F ). The inset shows EDC at k F taken at 25 eV photon energy in the high angular resolution (0.1 ◦ ) mode. (c) Second derivative of raw data in (b) with respect to energy. LDA dispersions along both Γ-K-M’ direction (solid lines) and Γ-M-Γ’ direction (dashed lines) are plotted for comparison. The Brillouin zones are labeled on top of this panel for the two high symmetry directions. Fig. 7.2(b) shows an ARPES intensity map as a function of binding energy and in-plane momentum k ‖ , corresponding to the momentum cut shown as a solid line in Fig. 7.2(a). Despite the strong azimuthal disorder giving a circular Fermi energy intensity map in Fig. 7.2(a), we observe, surprisingly, very clear dispersions over the entire energy range. Furthermore, at the Fermi energy crossing point k F , a sharp coherent quasi-particle peak is observed. This is shown in the inset, where an energy distribution curve (EDC), energy cut at a constant momentum, is plotted. Here the half width of the EDC peak is 20 meV (50 meV FWHM due to the asymmetry of the line shape), the sharpest peak observed in HOPG so far 104 . In Fig. 7.2(c) we report the second derivative of the raw data of Fig. 7.2(b) with respect to energy. The second derivative method has been used in the literature to enhance the direct view of the ARPES dispersion. Local density approximation (LDA) band dispersions along two high symmetry directions Γ-K- M ′ (solid lines) and Γ-M-Γ ′ (dashed lines) are plotted in the same figure for a direct comparison. Despite a polycrystalline sample implied by the Fermi energy intensity map, an excellent agreement is observed between the experiment and the theory. We can identify the dispersions between 4 eV and 23 eV as originating from the sp 2 orbitals with strong intra-layer σ bonding (black lines), and the dispersions between Fermi energy and 11 eV as originating from the p z orbitals with weaker π bonding (white lines). We note that the calculated dispersions were stretched by 20% in energy throughout this paper, as suggested in the literature 125,104,11 . The stretching of the LDA band dispersions is attributed to missing self-energy corrections in LDA, since ab initio quasiparticle calculations based on the GW method show that for graphite the quasiparticle band dispersion near the Fermi level is 15% larger 11 . The direct comparison between Fig. 7.2(a) and Fig. 7.2(b,c) shows an apparent paradox in our data, namely, the coexistence of azimuthal disorder feature (Fig. 7.2(a)) with single crystalline features (Fig. 7.2(b,c)). This can be readily understood if we consider an angular average of the calculated dispersions. Such an angular average would be necessary if the sample consisted of many small single crystallites with strong azimuthal disorder. 52
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Dirac Fermions in Graphene and Grap
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Dirac Fermions in Graphene and Grap
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Contents Abstract 1 Contents Acknow
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: Chapter 7 ARPES study of partially
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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