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64 Bibliography [75] Hari C. Manoharan. Topological insulators: A romance with many dimensions. Nature Nanotechnology, 5:477–479, 2010. doi:10.1038/nnano.2010.138. [76] Liang Fu and C. L. Kane. Topological insulators with inversion symmetry. Physical Review B, 76:045302, 2007. doi:10.1103/PhysRevB.76.045302. [77] Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan. Observation of a large-gap topological-insulator class with a single Dirac cone on the surface. Nature Physics, 06:398–402, 2009. doi:10.1038/nphys1274. [78] A. Grüneis, C Attaccalite, A. Rubio, D. V. Vyalikh, S. L. Molodtsov, J. Fink, R. Follath, W. Eberhardt, B. Büchner, and T. Pichler. Angle-resolved photoemission study of graphite interlaction compound KC 8 : A key to graphene. Phys. Rev. B, 80:075431, 2009. doi: 10.1103/PhysRevB.80.075431. [79] M. Z. Hasan and C. L. Kane. Colloquium: Topological insulators. Rev. Mod. Phys., 82:3045–3067, 2010. doi:10.1103/RevModPhys.82.3045. [80] Khuong K. Huynh, Yoichi Tanabe, and Katsumi Tanigaki. Both Electron and Hole Dirac Cone States in Ba(FeAs) 2 Confirmed by Magnetoresistance. Phys. Rev. Lett., 106:217004, May 2011. doi:10.1103/PhysRevLett.106.217004. [81] Takao Morinari, Eiji Kaneshita, and Takami Tohyama. Topological and Transport Properties of Dirac Fermions in an Antiferromagnetic Metallic Phase of Iron-Based Superconductors. Phys. Rev. Lett., 105(3):037203, Jul 2010. doi:10.1103/PhysRevLett.105.037203. [82] N. Harrison and S. E. Sebastian. Dirac nodal pockets in the antiferromagnetic parent phase of FeAs superconductors. Phys. Rev. B, 80:224512, 2009. doi:10.1103/PhysRevB. 80.224512. [83] A. Varykhalov, J. Sánchez-Barriga, A. M. Shikin, C. Biswas, E. Vescovo, A. Rybkin, D. Marchenko, and O. Rader. Electronic and Magnetic Properties of Quasifreestanding Graphene on Ni. Phys. Rev. Lett., 101:157601, Oct 2008. doi:10.1103/PhysRevLett. 101.157601. [84] Di Xiao, Ming-Che Chang, and Qian Niu. Berry phase effects on electronic properties. Rev. Mod. Phys., 82:1959–2007, Jul 2010. doi:10.1103/RevModPhys.82.1959. [85] Yugui Yao, Leonard Kleinman, A. H. MacDonald, Jairo Sinova, T. Jungwirth, Dingsheng Wang, Enge Wang, and Qian Niu. First Principles Calculation of Anomalous Hall Conductivity in Ferromagnetic bcc Fe. Phys. Rev. Lett., 92:037204, Jan 2004. doi:10.1103/PhysRevLett.92.037204.
List of Figures 65 List of Figures 2.1 DFT self-consistency scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 muffin tin with pastries: the construction of the potential in LMTO . . . . . . . 10 2.3 mean free inelastic scattering path of electrons . . . . . . . . . . . . . . . . . . . 11 2.4 photoemission: one- and three-step model . . . . . . . . . . . . . . . . . . . . . . 12 2.5 the three step model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.6 initial and final states in photoemission . . . . . . . . . . . . . . . . . . . . . . . 14 3.1 manipulator including sample holder inside the preparation chamber: left: raw sample with lever stick; right: cleaved sample . . . . . . . . . . . . . . . . . . . . 17 3.2 characteristics of the dipole radiation of a charged particle [35, p. 25] . . . . . . . 19 3.3 (a) general setup of a photoemission endstation at synchrotron facilities, (b) on the left-hand side: the 1 3 ARPES, (c) on the right-hand side: the SIS ARPES endstation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.1 overview: real space symmetry and slab configurations . . . . . . . . . . . . . . . 24 4.2 overview of the BZ structure: differences between space group 123 – 139 and their projections onto the surface BZ . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.3 band structure folding: comparison between SPG 123 and SPG 139 . . . . . . . . 26 4.4 comparison: L(S)DA+U vs. open core approximation . . . . . . . . . . . . . . . 28 4.5 charge isosurfaces and lattice configuration of EuRh 2 Si 2 illustrating the charge transfer inside the unit cell as well as stronger and weaker bonds . . . . . . . . . 30 4.6 calculated cleavage behaviour: interlayer distances and slab representatives . . . 31 4.7 atomic cross section for photoemission and an overview spectrum . . . . . . . . . 33 4.8 spectral overview for different surface termination measured at hν = 120 eV . . . 34 4.9 characterisation of the 4f final state multiplet – comparison between atomic calculation and different surface terminations . . . . . . . . . . . . . . . . . . . . . . 35 4.10 projected Fermi surface: experiment and theory . . . . . . . . . . . . . . . . . . . 37 4.11 band structure of EuRh 2 Si 2 along Γ − X − M − Γ with characterization of bulk and surface originated states (calculation) . . . . . . . . . . . . . . . . . . . . . . 38 4.12 theoretical bulk Fermi surfaces (4f open core) . . . . . . . . . . . . . . . . . . . . 39 4.13 band structure of SrRh 2 Si 2 along Γ − X − M − Γ with characterization of bulk and surface originated states (calculation) . . . . . . . . . . . . . . . . . . . . . . 40 4.14 symmetry and dispersion of the FPLO 4f basis set (LDA+U) demonstrated in a particular direction in the BZ for EuRh 2 Si 2 . . . . . . . . . . . . . . . . . . . . . 41 4.15 Wannier representation based on Eu 4f orbitals . . . . . . . . . . . . . . . . . . . 44 4.16 hybridization strength: distribution of the 5f weight in LMTO for both terminations and associated states from FPLO calculations . . . . . . . . . . . . . . . . . 46 4.17 analytically-modelled coupling strength for both terminations . . . . . . . . . . . 47 4.18 comparison of two different hybridization models: superposition of localized levels and coupled localized levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.19 evolution of the PE spectrum for Si termination taking into account different contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.20 simulated spectra based on the distribution of V ij (k) in comparison to the experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.21 linear dispersion in the vicinity of the Γ-point for Si / Eu termination . . . . . . 53 4.22 k z dispersion of EuRh 2 Si 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 5.1 polarization dependent PE spectra of EuRh 2 Si 2 . . . . . . . . . . . . . . . . . . . 57
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- Photoemission on EuRh 2 Si 2 - di
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Abstract A thorough knowledge of co
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vii Nomenclature AF APW ARPES BO BZ
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2 1 Introduction conflicting limits
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4 2 Theoretical foundation fore the
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6 2 Theoretical foundation system a
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8 2 Theoretical foundation such a s
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10 2 Theoretical foundation Figure
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12 2 Theoretical foundation Figure
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Page 25 and 26: 17 3 Experimental foundations 3.1 P
Page 27 and 28: 3.2 General setup 19 Figure 3.2: ch
Page 29 and 30: 3.4 SLS: SIS-HRPES 21 1 3 ARPES the
Page 31 and 32: 23 4 EuRh 2 Si 2 - semi-localized e
Page 33 and 34: 4.1 Overview - properties and class
Page 49 and 50: 4.2 Hybridization: localized versus
Page 61 and 62: 4.3 Perspective: quasi-linear dispe
Page 63: 4.3 Perspective: quasi-linear dispe
Page 66 and 67: 58 5 Summary to the f-d interaction
Page 68 and 69: 60 Bibliography [13] B. Kramer. A P
Page 70 and 71: 62 Bibliography [44] T. M. Rice and
Page 75: List of Tables 67 List of Tables 2.
Page 79: Erklärung Hiermit versichere ich,
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