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

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Figure 7.4. (a) Angle-integrated intensity curves taken near normal emission measured at different photon energies from 40 to 140 eV. Filled circles mark the peak positions of the π bands. (b) Extracted peak positions from the angle-integrated intensity curves as a function of k z . The dotted line is the guide to the periodicity of the dispersion. From the symmetry of the final states detected, the inner potential is determined. (c) LDA band structure of the π bands at k z =0 and k z =0.5 c ∗ . The energies are stretched by 20%. variation in the bonding and antibonding bands is attributed to the photoemission dipole matrix element 65 . The splitting of the π bands can be confirmed in the (MDCs) shown in panels d and h, where two peaks each from the bonding and antibonding π bands are clearly observed. From the MDC dispersions shown and the peak positions in the energy distribution curve (EDC) at the K point (not shown), this splitting is estimated to be ≈ 0.7 eV. The splitting of π bands near the K point but not near the H point is in agreement with band structure calculation, which confirms the validity of extracting the k z values. This is the first clear demonstration of the splitting of the π bands near E F , while we note that some data in the literature 100,127,104 may now be seen as suggestive of this splitting, as discussed above. Furthermore, the linear Λ-shaped dispersions shown in panels a and c, strongly resemble those of Dirac quasiparticles, are signatures of Dirac quasiparticles. 7.5.2 Low energy dispersions and Dirac fermions To gain more information on the low energy excitations, in Fig. 7.6 we show high resolution ARPES data measured along AHL ′ direction for HOPG (panels a-b) and single crystal graphite (panels c-d). By following the maximum intensity in both panels (a, c), it is clear that the dispersion shows a linear behavior. In panels b and d we show the raw MDCs at different binding energies. In all the MDCs, one can clearly distinguish a main peak and a weaker one. The extracted dispersion extracted from MDC (open circles in 55
Figure 7.5. ARPES intensity map measured on HOPG near the BZ corners at photon energies of 43 (k z ≈ 0.35 c ∗ ) and 55 eV (k z ≈ 0.10 c ∗ ) respectively. AB and BB label the antibonding and bonding π bands. (c-d) MDCs at -1.2 eV for data shown in panels a and b respectively. (e-f) ARPES intensity map measured on single crystal graphite near the zone corner at photon energies of 140 eV (k z ≈ 0.50 c ∗ ) and 80 eV (k z ≈ 0.07 c ∗ ) respectively. (g-h) MDCs at -1.2 eV for data shown in panels e and f. panels a,c) shows a linear behavior, strongly resembling the behavior of Dirac quasiparticles. The Fermi velocity, or the effective speed of light, is determined to be 0.8±0.2×10 −6 m·s −1 . By extrapolating the dispersion, the crossing point of these two linear bands (known as the Dirac point) lies 50±20 meV above E F , suggesting that the low energy excitations near H point are holes. Finally, by measuring the volume of the hole pocket 3 , we estimate a total hole concentration 64 of 3.1±1.3×10 18 cm −3 , in agreement with transport measurements 112,111 . 7.5.3 Defect states Within each plane of graphene or stack of plane in graphite a varying number of imperfections can be found such as vacancies, when lattice sites are unfilled indicating a missing atom within a basal plane; stacking faults when the ABAB sequence of the layers planes is no longer maintained; and zigzag edge occurring near unfilled lattice sites 116,128 . Because of the unique electronic structure of Dirac quasiparticles and the negligible density of states near the Fermi energy, graphite is extremely sensitive to topological defects which can strongly modify the electronic structure and the scattering process of quasiparticles, thus resulting in important changes in transport properties. For example, it has been predicted 116 that extended defects as lattice dislocation can lead to self doping effects and presence of localized states at the Fermi energy. Self doping effect results in electron or hole pocket at E F rather than a single point, as predicted for an ideal graphene system. Zigzag edge on the other hand induces localized states near the Fermi energy resulting in a peak in the local density of states near the Fermi energy 83,115 . Finally the presence of vacancies strongly modifies the scattering process resulting in a minimum of the scattering rate at finite energy 116 instead of E F as what is expected for Fermi liquid. In Fig. 7.7, we introduce disorder/inhomogeneity features that are pronounced only in the case of HOPG samples. This figure shows the first derivative in energy of an ARPES map, from E F to -11 eV. The first derivative is a method which allows to enhance the dispersive features as well as rising or falling edges in the data, and thus is particularly useful for detecting nondispersive peaks and edges. In panel a we can 3 We assume that the hole pocket is an ellipsoid that occupies half of the BZ along k z direction, and the cross section in the k x-k y plane plane has a diameter of 0.02 Å −1 (measured from the separation of the peaks at E F ). 56
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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
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Curriculum Vitæ Shuyun Zhou Educat
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• 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: direction, i.e. perpendicular to gr
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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