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

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Figure 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. 4.5 Possible mechanisms of the gap In the following, we discuss possible scenarios and we propose that the gap is most likely induced by symmetry breaking due to the graphene-substrate interaction. 4.5.1 Inter-Dirac-point scattering One possible scenario that can open up a gap is the scattering between the K and K ′ points, the inter- Dirac-point scattering. This requires translation symmetry breaking. The two known reconstructions on epitaxial graphene 79 , 6×6 and (6 √ 3 × 6 √ 3)R30 ◦ are obvious candidates for the source of this symmetry breaking. However, in order to mix K and K ′ , a large scattering wave vector is required. This is much longer than the reciprocal lattice vectors of both reconstructions mentioned above. High ordering process involving consecutive small scattering wave vectors will be weak in general. Another source of inter-Diracpoint scattering is impurity scattering, which, as recently shown, can mix the wave functions at the two K points 80,81 . This however would give rise to a gap that strongly depends on the impurity concentration, in contrast to our finding. The gap is in fact the same in all the samples that we have studied, prepared under different conditions (with and without hydrogen etching of the SiC substrate) and on differently doped substrates, insulating vs slightly electron doped substrate. 4.5.2 Quantum confinement It has been predicted that a gap can be opened in nanometer size graphene ribbons as a result of quantum confinement 83,69,82 . This section investigates whether the gap observed in the epitaxial graphene here can be interpreted as a result of quantum confinement or not. To study the role of electron confinement for the gap opening in epitaxial graphene, in Fig. 4.9 we study the dependence of the gap on the graphene terrace or domain size and compare it with the results reported for nanoribbons 82 . The terrace size of single layer 31
Figure 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 . 32
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 and 40: the EDCs as well as the region of e
Page 41: Figure 4.7. Dispersions measured in
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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