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

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Figure 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. Figure 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). 29
Figure 4.7. Dispersions measured in bilayer graphene on 6H-SiC (panel a) and more insulating 4H-SiC (panel b) substrates. consistent check for the sample thickness determined by other methods 37,62 . Panel (d) shows the ARPES data taken along a line through the H point in graphite, where the dispersion resembles that of graphene through K 64 . Data shown in panels (a-d) allow us to determine how the electronic structure near K point varies as the sample thickness increases. First of all, as the sample thickness increases, E D shifts toward E F . From single layer to trilayer graphene, E D (marked by arrows in panels (a-c)) shifts from -0.4 eV to -0.29 eV then to -0.2 eV. For graphite, E D has been estimated to be at ≈0.05 eV above E F 64 . More importantly, as the sample becomes thicker, the gap (labeled by light blue shaded area in panels (a-c)) decreases rapidly. From single layer to trilayer graphene, the gap decreases from 0.26 eV to 0.14 eV then to 0.066 eV. For graphite, since the Dirac point energy is above E F 64 , whether there is a gap or not cannot be directly addressed by ARPES. However, from band structure calculation, it is expected that the gap at the H point is ≈ 0.008 eV 9,74 , which is almost negligible. Fig. 4.7 shows comparison of data taken on one bilayer graphene sample on a more insulating 4H-SiC substrate with resistivity of 10 5 Ω/cm (panel b) compared to another graphene sample on a 6H-SiC with resistivity of 0.2 Ω/cm (panel a). In both cases, the Dirac point energy appears to be shifted by a similar amount below E F , suggesting that the doping is most likely associated with the surface charges at the interface, rather than the carrier concentration of the substrate. Fig. 4.8 summarizes the evolution of the Dirac point energy E D and the gap ∆ for various sample thickness. The layer dependence of both quantities suggests that, beyond 5 layers, epitaxial graphene behaves as bulk graphite 64 . The amount of doping should decrease as the sample becomes thicker, because the surface layer probed by ARPES is farther away from the interface as the thickness increases. Also, the strong dependence of E D on sample thickness is a direct manifestation of the short interlayer screening length (≈ 5 layers 75 ) of graphene. This result shows that the sample thickness is an effective way of controlling doping in epitaxial graphene. Panel(b) shows the dependence of the gap on the sample thickness. A gap in bilayer graphene has been reported and attributed to the different potentials in the two graphene layers induced by doping or electric field 76,77,78 . While this could contribute to the gap in bilayer and even trilayer graphene, it certainly is not the reason for the gap in the single layer graphene. 30
Page 1 and 2: Dirac Fermions in Graphene and Grap
Page 3 and 4: Dirac Fermions in Graphene and Grap
Page 5 and 6: 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: the EDCs as well as the region of e
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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