Graphene sublattice symmetry and isospin determined by circular dichroism in angle-resolved photoemission spectroscopy — Supporting Information Isabella Gierz,1, ∗ Matti Lindroos,2 Hartmut H¨ochst,3 Christian R. Ast,1 and Klaus Kern1, 4 1
Max-Planck-Institut f¨ ur Festk¨ orperforschung, D-70569 Stuttgart, Germany Tampere University of Technology, Deptartment of Physics, 33101 Tampere, Finland 3 Synchrotron Radiation Center, University of Wisconsin-Madison, Stoughton, WI 53589, USA 4 Institut de Physique de la Mati`ere Condens´ee, Ecole Polytechnique F´ed´erale de Lausanne, CH-1015 Lausanne, Switzerland (Dated: July 9, 2012) 2
EXPERIMENTAL RESULTS FOR PHOTON ENERGIES NOT SHOWN IN THE MAIN PAPER
In Fig. 1 we plot the measured normalized CDADnorm signal for hν = 35, 45 and 75 eV that is not shown in the main paper. The line profiles plotted in the lower right panel represent the normalized CDADnorm signal on a circle of radius 0.06 ˚ A−1 around the K-point as indicated by black lines in the other panels. For all photon energies shown in Fig. 1 the variation of CDADnorm with φ clearly deviates from the shape predicted by equation (3) of the manuscript. Furthermore, the amplitude of CDADnorm is always signifcantly smaller than one. In conclusion, the data displayed in Fig. 1 cannot be described by equation (3), most likely because |hΨf |H|pz i|2 = constant is not fulfilled at these photon energies. This is the reason why the data fitting in the manuscript needs to be restricted to hν = 52 eV. Concerning the determination of the sublattice symmetry parameter A we want to point out that it is sufficient to find a single photon energy where the amplitude of CDADnorm equals one to proof that the sublattice symmtetry in graphene is preserved and thus A = 1. From equation (3) it is easy to deduce that the amplitude of CDADnorm is always smaller or equal to one depending on the value of A. If CDADnorm = 1 this necessarily implies that A = 1. As A is a property of the initial state it is independent of photon energy. Therefore, any variation of CDADnorm with photon energy has to be attributed to some sort of final state effect. Following this line of thought we conclude that if we find that CDADnorm = 1 for one particular photon energy (hν = 52 eV) this necessarily means that A = 1. In Fig. 2 we plot the difference of the band structure measured with RCP and LCP light, respectively, for different
FIG. 1: Measured normalized CDADnorm signal for hν = 35, 45 and 75 eV together with line profiles extracted along the black circles. Note that the upper left region of the 35 eV data cannot be trusted because band structure was not well centered on the detector.
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FIG. 2: Sketch of the Brillouin zone: the red line indicates the direction in momentum space along which the measurements have been performed. The other panels display the difference in photocurrent between RCP and LCP light for hν = 35, 45, 52, 65, and 75 eV.
photon energies. The measurements were done along the red line in the left panel of Fig. 2. The CDAD signals for hν = 35, 45, and 52 eV are similar with one band appearing in blue and the other band appearing in red. For higher photon energies, the CDAD signal changes sign within one band. For hν = 65 eV this sign change occurs around E = −1.5 eV, while for hν = 75 eV the sign changes at the Dirac point. Note that, at hν = 75 eV, the sign of the CDAD signal at the Fermi level is opposite compared to the other photon energies.
COMPARISON WITH REF. [2]
Equation (4) of Ref. [2] states that I = I0 [1 ± cos(θ + 2χ)], where the + (−) sign corresponds to the conduction (valence) band and θ corresponds to φ in the present work. χ = arctan(Ay /Ax ) is related to the position of the dark corridor φ0 via φ0 = −2χ. Ax and Ay describe the projection of the incident light field onto the sample surface. According to this purely geometrical effect, the rotation of the dark corridor is expected to decrease monotonously from 2χ = 88◦ at hν = 35 eV to 2χ = 83◦ at hν = 75 eV, which is clearly in contrast to our experimental and theoretical results presented in Figs. 1 and 2 of the manuscript. However, in the supplementary information of Ref. [2] the authors show that the photoemission cross section for the Ay component of the incident light decreases rapidly with photon energy and becomes negligible for hν > 50 eV. When we include the effect of the photon energy dependence of the Ay cross section both CDADnorm and 2χ are equal to zero for hν > 50 eV in contrast to our experimental findings.
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Electronic address:
[email protected]; present address: Max-Planck Research Group for Structural Dynamics, University of Hamburg, Center for Free Electron Laser Science, 22607 Hamburg, Germany [1] Jung, W. S.; Leem, C. S.; Kim, C.; Park, S. R.; Park, S. Y.; Kim, B. J.; Rotenberg, E.; Kim, C. Phys. Rev. B 2010 82, 235105 [2] Liu, Y.; Bian, G.; Miller, T.; Chiang, T.-C. Phys. Rev. Lett. 2011 107, 166803
