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

More documents

Recommendations

Info

Figure 6.3. Constant energy maps taken near the H point, showing that the electronic structure is isotropic in the k x -k y plane from E F to -0.6 eV. (a-e) ARPES intensity maps near H (hν=140 eV, k z ≈ 0.50 c ∗ ) taken at energies from E F to -1.2 eV. The circles are guides for the circular intensity pattern near the H point. Arrows in panels d and e point to deviation from the circle. (f) Schematic diagram of the dispersion for graphene near six BZ corners in the three dimensional E-k x -k y space. thus the electronic structure is isotropic near H. As the energy changes to -0.9 eV, the constant energy map slightly deviates from the circular shape (see arrow in panel d). This deviation increases with binding energy and a trigonal distortion is clearly observed at -1.2 eV (panel e). This trigonal distortion is determined by the relevant tight binding parameters for graphite and further studies to analyze this trigonal distortion are in progress. Overall, Fig. 6.3 shows that from E F to -0.6 eV, the electronic structure is isotropic in the k x -k y plane. Similarly, the Fermi velocity measured within the first BZ is 1.0×10 6 m · s −1 with a ≤ 10% variation along different directions, consistent with the circular constant energy maps shown here. Combining the results of Figs. 6.2 and 6.3, we conclude that from E F to -0.6 eV, the dispersion shows a cone-like behavior near each BZ corner H, similar to what is expected for graphene (panel f). To resolve the details of the low energy dispersion and the small object at E F (Fig.6.2(a)), we show in Fig. 6.4 an intensity map measured near H with lower photon energy to give better energy and momentum resolution. In the intensity map, one can distinguish two bands dispersing linearly toward E F , as also clear in the MDCs (panel b) where two peaks can be observed for all binding energies. The extracted dispersion (open circles in panel a) from MDCs (panel b) shows two bands dispersing linearly toward E F , with a minimum separation of 0.020±0.004 Å −1 at E F . This linear dispersion near the H point, as well as the isotropic electronic structure shown in Fig. 6.4 from E F to -0.6 eV, is a basic characteristic of Dirac quasiparticles, which points to the presence of Dirac quasiparticles in the low energy excitations near the H point in graphite. Furthermore, from the extracted dispersions, the Dirac point is extrapolated to be 50±20 meV above E F , and thus the small object observed at E F is a hole pocket, in agreement with previous studies of the three dimensional band structure of graphite 74,99 . Assuming an ellipsoidal shape for the hole pocket 110 , the hole concentration is estimated to be 3.1±1.3×10 18 cm −3 , from the 0.020 Å −1 separation of the peaks at E F . This hole concentration is in agreement with reported values 111,112,110 . We note that, given the current resolution of ARPES technique, we are not able to resolve the two hole pockets at the H point reported by the other experimental probe 113 . In fact, the difference in energy between these two hole pockets at the H point is ≤ 1 meV 113 , which is beyond the current resolution of the ARPES technique. The presence of holes with Dirac fermion dispersion is further supported by the angle integrated intensity 45
Figure 6.4. Detailed low energy dispersion near the H point shows that low energy excitations are Dirac fermions with the Dirac point slightly above E F . (a) ARPES intensity map near the H point (hν=65 eV, k z ≈ 0.45 c ∗ ) along AHL ′ direction (green line in the BZ shown in Fig. 6.2(c)). The open blue circles in panel a show the MDC dispersion. The dotted straight lines are guides for the linear dispersion. (b) MDCs at energies from E F to -0.2 eV for data shown in panel a. Note that, similar to Fig. 6.3, the intensity of the π band is strongly enhanced in the first BZ (H→A direction), due to the dipole matrix element 65 . (c) Intensity obtained by integrating over both k x and k y for data taken near H (hν=140 eV, k z ≈ 0.50 c ∗ ). The intensity has been symmetrized with respect to the Dirac point energy (E D ≈ 50 meV) to compare directly with the expected intensity for Dirac fermions (inset). An overall linear behavior is observed with some weak additional intensity around 100 meV from the Dirac point energy. The origin of this additional weak intensity is unclear and needs further investigation. 46
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 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: Figure 6.2. Linear Λ-shaped disper
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.
show all

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 ...