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

More documents

Recommendations

Info

Figure 4.3. (a,b) Dispersions taken along a symmetric direction for cuts away and through the K point. (c,d) MDCs in the energies as labeled in panels a,b. (e) Angle integrated intensity as a function of energy for data in panel a (black curve) and panel b (gray curve). Figure 4.4. (a) Schematic drawing for the cuts shown in (b) and (c) in the BZ of graphene and the conical dispersion (not drawn to scale). (b,c) Dispersions measured through and off the K point. The dotted white and dark gray lines are dispersions extracted from the MDCs. (d, e) Extracted dispersions and MDC width as a function of energy for data shown in panels b and c. 27
the EDCs as well as the region of energy where the MDC peaks are non-dispersive (Fig. 4.3(c-d)), which coincides with the regions of vertical intensity in the upper panels. 4.3 Gap interpretation vs many body interactions An alternative picture to the gap scenario has been reported by A. Bostwick et al. 71 , where data similar to Fig. 4.2 have been discussed in terms of electron-plasmon interaction 71 . This interpretation is based on the departure of the dispersion from the anticipated behavior near E D , which we attribute to a gap, and the observation of an anomalous upturn of the MDC width near E D . However, these are not unique features of the K point and they occur every time a gap is present in the spectra. In Fig. 4.4, we present data taken along two lines (panel a): one through the K point (panel b), and another one parallel to it but far from the K point (panel c). These particular cuts are convenient because the intensity is strongly suppressed on one side of the K point, thus allowing the MDC to be fitted with single peaks. This allows for a more reliable fit of the data. The cut far away from the K point is considered because it definitely has a gap, due to the conical nature of the dispersion. Performing an MDC analysis first on the cut through the K point, the anomalous region of Fig. 4.2 is manifested through a kink in the dispersion and a sudden increase of the scattering rate (pointed to by arrows in panels d and e). Such anomalies might be considered to be due to self-energy effects. An appealing explanation is that a decay through plasmon emission is responsible for the deviation from the conical dispersion, as recently proposed 71,72,73 . However, performing a similar analysis on the cut far away from the K point reveals similar features. In both cases, we can identify a region between the conduction and valence bands where the intensity decreases (see horizontal arrows), the dispersion deviates from the linear behavior (see dashed line in panel b-c), and the scattering rate shows a sudden increase (see panel d). These striking similarities cast doubt on the validity of the many-body interaction scenario 71 , as this should be able to account for very similar features far away from the K point where a gap is certainly present and is the natural explanation of the data. We therefore propose that these similarities are simply a manifestation of a gap opening at the Dirac point. It is therefore misleading to discuss the dispersion and scattering rate in the gap region and in general to perform an MDC fit near the bottom or top of a band, despite the possibility that MDC peaks might be present inside the gap region (panel c). Such peaks exist in our data due to the finite width of the EDCs at the bottom of the conduction band and the top of the valence band. This can be better illustrated in the simulated data shown in Fig. 4.5. Dirac-like dispersions with finite band gaps of 150 meV (Fig. 4.5(a)) and 400 meV (Fig. 4.5(b)) and hence finite effective masses are used. The MDC width is modeled to scale linearly with energy with finite constant broadening to account for the finite MDC width at E F . Matrix elements are included to suppress one side of the dispersion by multiplying the results by a step function with a finite width. Ignoring the fact that there is a gap between the valence and conduction bands and performing an MDC analysis in this region, the fit shows a kink in the dispersion (Fig. 4.5(a, b)) and an increase in MDC width (Fig. 4.5(c)). The anomalous region where the MDC width increases scales with the gap region. This simulation shows that disregarding the absence of electronic states and simply fitting MDCs can sometimes produce misleading results. 4.4 Thickness dependence of the gap and Dirac point energy Fig. 4.6 shows how the gap and the distance between E D and E F change as the graphene sample thickness varies. Panels (b) and (c) show the ARPES data for bilayer and trilayer graphene samples. Again the dispersions extracted from the EDCs (panels (e) and (f)) are plotted. In these two panels, two distinct cones can be identified for E
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: Figure 4.2. Observation of the gap
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 ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?

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