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

More documents

Recommendations

Info

Figure 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. Figure 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. Since the white regions are observed at lower temperature before the single layer graphene (gray region) is formed, these are attributed to the buffer layer. 23
Chapter 4 Gap opening in epitaxial graphene Graphene is considered one of the most exciting materials in solid-state physics. Since its discovery in 2004 a variety of novel phenomena have been discovered and predicted, from an anomalous quantum Hall effect 51,52,53 , ballistic transport 5 , easy control of charge carriers by externally applying voltage 5 , half metallicity 54 , Kondo physics 55,56,57 , superconductivity 58,59,60 etc. The secret to all of these fascinating phenomena lies in the unique nature of the electronic properties of graphene, where the low energy excitations resemble massless Dirac fermions. Although several experiments have shown results in agreement with the existence of Dirac fermions, so far direct experimental evidence has been limited. Here we present a detailed study of the electronic structure of graphene by using ARPES. How this evolves from single layer graphene to infinite layers graphite is also discussed. In general graphene can be obtained by rubbing a piece of graphite on a SiO 2 surface 5,61 . This method however gives rise to very small samples of the order of few microns, which are difficult to investigate with ARPES, where the average beam size is of the order of 100 micron. The graphene samples we have investigated are epitaxial graphene grown by thermal decomposition of a SiC single crystal 62 . As we will discuss below, the resulting graphene layer is tightly bounded with the substrate. The graphene-substrate interaction will modify the Dirac cone by inducing a gap between the conduction band and the valence band, making it an ideal candidate for next generation electronic devices. 4.1 Dirac fermions in epitaxial graphene Figs. 4.1(a-c) show ARPES intensity maps at constant energies of E F , -0.4 eV and -1.2 eV. At E F (panel a), the intensity map shows a finite and almost circular contour centered around the K point. As the binding energy increases, the contour first decreases in size and becomes a point at -0.4 eV (panel b). Beyond -0.4 eV, the size of the contour expands again. This behavior is consistent with the presence of Dirac fermions, where a conical dispersion centered at the K point is expected. The Dirac point energy is shifted to 0.4 eV below E F , which shows that the as-grown graphene is electron-doped 48,63 . At higher binding energy (panel c) the high intensity region in the intensity map deviates from the circular shape. Similar trigonal distortions have been reported for graphite 64 . Note that the intensity along the circular contour is not isotropic and is strongly suppressed on the left (first BZ) for energy above the Dirac point energy (panel a) and on the right (second BZ) for energy below the Dirac point energy (panel c). This is a well-known effect in graphite and is due to the ARPES dipole matrix element which suppresses or enhances the intensity in different BZs 65 . Fig. 4.1(e) shows the overall dispersion of the π bands measured for a symmetric cut through the K point. Following the maximum in the intensity plot, two cones dispersing in opposite directions (one upward and another downward) can be clearly distinguished, in overall agreement with the presence of Dirac fermions. 24
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: Figure 3.5. Intensity map at -1 eV
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 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.

Dirac Fermions in Graphene and Graphiteâa view from angle ...

Create successful ePaper yourself

Delete template?

Save as template?

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