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

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3.3 XPS results showing data (connected symbols) and their fits (solid lines) for samples A, B, and C. Individual Voigt functions and Shirley background are shown as lines as well. In the C 1s spectra, peaks G and S are identified with the graphite overlayer and SiC bulk. In each row, the two panels are plotted using a common intensity scale. . . . . . . . . . . . . . . . . . 28 3.4 (a-c) Dispersions of the π bands from single layer, bilayer graphene to trilayer graphene. (d-f) Dispersions near the K point from single layer graphene to trilayer graphene. From Partoens et al 13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3.5 Intensity map at -1 eV as a function of k ‖ and k z . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.6 Measured dispersions from single layer graphene to four layer graphene, from Ohta et al 48 . . 31 3.7 LEEM images taken at an electron energy of 4.2 eV before and after annealing the SiC substrate under Si flux with a field of view of 5µm. . . . . . . . . . . . . . . . . . . . . . . . . 32 3.8 LEEM images taken at an electron energy of 6.6 eV with a 3µm field of view and the energy scans for the buffer layer, 1ML and 2ML graphene. . . . . . . . . . . . . . . . . . . . . . . . 32 4.1 (a-c) ARPES intensity maps taken at E F , -0.4 eV and -1.2 eV respectively on single layer graphene. The dotted line shows the Brillouin zone of graphene. (d) schematic drawing of the dispersion in single layer graphene and the relative energies for data shown in panels a-c. (e) Dispersion of single layer graphene measured along a high symmetric direction through the K point (see black line in the inset). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 4.2 Observation of the gap opening in single layer graphene at the K point. (a) Structure of graphene in the real and momentum space. (b) ARPES intensity map taken along the black line in the inset of panel (a). The dispersions (black lines) are extracted from the EDC peak positions shown in panel (c). (c) EDCs taken near the K point from k 0 to k 12 as indicated at the bottom of panel (b). (d) MDCs from E F to -0.8 eV. The blue lines are inside the gap region, where the peaks are non-dispersive. (e) Angle integrated intensity, which shows a suppression of intensity near E D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4.3 (a,b) Dispersions taken along a symmetric direction for cuts away and through the K point. (c,d) MDCs in the energies as labeled in panels a,b. (e) Angle integrated intensity as a function of energy for data in panel a (black curve) and panel b (gray curve). . . . . . . . . . . . . . . 38 4.4 (a) Schematic drawing for the cuts shown in (b) and (c) in the BZ of graphene and the conical dispersion (not drawn to scale). (b,c) Dispersions measured through and off the K point. The dotted white and dark gray lines are dispersions extracted from the MDCs. (d, e) Extracted dispersions and MDC width as a function of energy for data shown in panels b and c. . . . . 38 4.5 (a,b) Simulation of the conical dispersions with a gap of 150 and 400 meV. (c) Extracted MDC width as a function of energy for data shown in panels a and b. . . . . . . . . . . . . . 40 4.6 Decrease of the gap size as the sample becomes thicker. (a-d) ARPES intensity maps taken on single layer graphene on 6H-SiC, bilayer graphene on 4H-SiC, trilayer graphene on 6H-SiC and graphite respectively. Data were taken along the black line in the inset of Fig. 4.2(a) except panel (c), which was measured along ΓK direction and symmetrized with respect to the K point to remove the strong intensity asymmetry induced by dipole matrix element 65 . (e, f) EDCs taken from the raw data (without symmetrization) for momentum regions labeled by the arrows at the bottom of panels (b) and (c). . . . . . . . . . . . . . . . . . . . . . . . . 41 4.7 Dispersions measured in bilayer graphene on 6H-SiC (panel a) and more insulating 4H-SiC (panel b) substrates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 69
4.8 Thickness dependence of E D and ∆. (a,b) E D and ∆ as a function of sample thickness, for epitaxial graphene on 6H-SiC (black) and on 4H-SiC (blue). The error bar for the sample thickness was taken from the XPS measurements 62 . For graphite, E D is extrapolated from the dispersions at k z ≈π/c 64 , and the gap is estimated from band structure calculation 9,74 . (c, d) Two possible mechanisms to open up a gap at the Dirac point. (e) Schematic drawing to show the inequivalent potentials on the A (blue) and B (red) sublattices induced by the interface. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.9 (a-c) LEEM images taken at electron energy of 6.6 eV to show the surface topology of single layer graphene (gray area) and corresponding ARPES data (d-f) taken through the K point (see vertical line in the inset of Fig.1(d)) for three single layer graphene samples prepared under different growth conditions. The white, gray and black colors in panels (a-c) represent the regions of buffer layer, single layer and bilayer graphene respectively. The red lines in panels (d-f) are dispersions extracted by fitting the EDCs. (g) Plot of the extracted gap size from ARPES as a function of the representative terrace size (red segments in panels a-c) of the single layer graphene. The dotted line is the gap size in graphene nanoribbons due to quantum confinement taken from Han et al 82 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.10 Proposed mechanism for the gap opening and the structure of epitaxial graphene on SiC. . . 47 4.11 Breaking of the six fold symmetry in the intensity map near E D . (a-d) ARPES intensity maps taken on single layer graphene at E F , E D , -0.8 eV and -1.0 eV respectively. Near E D (panel b), the intensity of the six replicas near K shows breaking of six fold symmetry. Note that to enhance the additional feature around E D , the color scale is saturated for the dominant features near K and the replicas. (e) ARPES intensity map of the calculated spectral function at E D in the presence of symmetry breaking on the two carbon sublattices. . . . . . . . . . . 48 5.1 Dispersions through the K point taken from the as-grown single layer graphene (a) and from the sample with the highest doping of NO 2 (c). Panels (b) and (d) show the angle integrated spectra for (a) and (c) respectively. In panels (c) and (d) note the appearance of the NO 2 states at ≈ 5 and 11 eV below E F . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 5.2 (a) Dispersions through the K point taken in as-grown bilayer graphene. Data were taken along the red line through the K point shown in the inset. (b) Dispersions taken after 0.6 L (1 Langmuir=10 6 torr · s) NO 2 adsorption. (c) data taken 6 minutes after panel b. (d) EDCs taken at k 1 , k 2 , k 3 and k 4 as labeled on the top of panels a and b. The black and red arrows point to the midpoint of the leading edge, which is shifted to higher binding energy after NO 2 doping. (e) Zoom in of data shown in panel b. The white dotted line is a guide for the eye for the dispersions. (f) Momentum distribution curve (MDC) at the energy labeled by the dotted black line in panel d. The dots are the raw data and the solid line is the fit using three Lorentzian peaks simulating the cross-section of the hat-like dispersion in panel e. . . . . . . 54 5.3 (a-f) Data taken through the K point for the as-grown (a) and various dopings with NO 2 adsorption (b-f) in single layer graphene. The white lines are dispersions extracted from the MDC peaks when they can be clearly resolved. The dotted lines in panels c and d are linear extrapolation of the dispersion. (g) EDCs taken at the momentum regions (indicated by a small tick mark on top of each panel) where the bands are closest to E F . . . . . . . . . . . . . 56 5.4 (a, b) Plot of the shift in E D and Fermi velocity as a function of the carrier concentration for data shown in Fig. 5.3 In panel b, the data are extracted by fitting the dispersion between E F and -0.3 eV (circles) and between E F and -0.1 eV (diamonds). The open symbols are extracted from the dispersions on the left and the filled symbols from the dispersions on the right. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 70
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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
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7.6 Conclusions and implication of
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Curriculum Vitæ Shuyun Zhou Educat
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• Selected as Science Highlight f
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The unit cell of graphene contains
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Projecting this equation into φ(r
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Figure 1.5. Schematic drawing of th
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Chapter 2 Experimental techniques 2
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dispersion E(k z ). Thus k z values
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where ɛ is infinitely small. Accor
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Langmuirs (1L=10 −6 torr·s) to c
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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: List of Figures 1.1 (a) Sp 2 bondin
Page 83 and 84: 7.2 (a) Fermi energy intensity map.
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