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50 4 EuRh 2 Si 2 – semi-localized electrons Figure 4.18: comparison of different hybridization models: on the left-hand side the input is displayed followed by the eigenvalue redistribution, and the photoemission spectrum on the right-hand side (left: f emission, right: VB emission). As initial point, two localized levels (ef = [−0.15, −1.15] eV) and a parabolic ) hole- (−10 ∗ k ‖ 2 + 0.2 like band (ɛ(k) = eV) are used. Since atomic PE emission can have different transition probabilities, the spectral weight of the localized levels was chosen as 1 : 2 to demonstrate this influence and a broadening proportional to σ(ɛ) = 100/15 · (ɛ/5 + 1) eV was applied (ɛ in units of binding energy). (a) superposition of localized levels: the hybridization model has been solved two times, for each localized level once, the eigenvalue distributions of which are shown next to the initial configuration. The superposition of both represents the final eigenvalue dispersion. The hybridization parameter has been chosen constant as Vij = 0.15 eV. (b) coupled localized levels: in difference to the former model, hybridization gaps evolve for both levels and due to the coupling between both also their absolute distance gets larger for regions where the hybridization with the VB can be neglected. Vij is the same as in (a) with Cij = 0.2 eV
4.2 Hybridization: localized versus itinerant states 51 the VB yields a more appropriate model [67] (denoted by model 2 “superposition of localized levels”). To illustrate this distinction, both models are presented in fig. 4.18. Exemplarily, two localized levels differing by a factor of two in spectral intensity and a hole-like parabolic VB with its apex located 0.2 eV above the Fermi level are taken. On the left-hand side in (a) as well as in (b) the initial configuration is depicted followed by the rearranged eigenenergy distribution. A sketch of both components in model 2 the sum of which represents the spectrum, clarifies the degeneracy of the spectral eigenvalues in regions of the VB separated from the localized levels. The main disparity between both is the occurance of a band gap in the case of coupled localized levels, which is not present in case of superposition. Furthermore, due to the constant symmetry parameter C ij also the localized states in model 1 will be pushed apart if no valence band approaches. A feasible correction would be to make it proportional to the distance between the valence band and the second localized level or solving the model self-consistently re-adjusting the input parameters of the localized levels so the solution fits in the limit of ɛ i → ∞ to the original PE spectrum. In the following part, the motivated model 2 for europium (hence C ij (k) = 0 and N f = 1) will be evaluated for Si and Eu terminated surfaces. As input for the subsurface PE levels the spectrum calculated by Gerken et. al shifted by 0.15 eV is used. In the case of a Eu terminated surface, the surface 4f emission is chosen proportional to the subsurface emission adopted in intensity (6x) and energy position (shifted by 1 eV to higher binding energies) to the experiment. The distribution of V ij (k), the evolution of which already has been sketched, is given in fig. 4.17. To verify the coupling to the projected band structure for the Si terminated surface, different numbers of bands have been taken to simulate the transition from a single band to a continuously-projected band structure. On the one hand, this effect displaces spectral weight to the edges of the region where the VB is located and on the other hand distributes the residual weight in the coupled area yielding an almost homogeneous intensity distribution. In fig. 4.19, this process is indicated for the triangularly shaped area A1 next to the linear dispersive state at Γ. The final spectra for Si and Eu terminated surfaces in Γ−X direction are depicted in fig. 4.20. The main spectral features are well-reproduced for both terminations. Besides, the measured spectrum for Si termination evidences additional interaction with the projected band structure especially in the region marked by 2. Furthermore, there has to be a some part of the band structure which causes the accumulation of spectral weight at the tip of the state S1 (1) not evidenced in the calculated spectrum. Because only f emission is taken into account in the simulation, the weak VB like contribution (3) is missing. For the Eu terminated surface, the shift of surface 4f emission with respect to the subsurface emission has been estimated imprecisely, as well as its width. The latter is probably related to a different multiplet structure, because the potential is no longer rotationally symmetric as it can be regarded in bulk as a first approximation.
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- Photoemission on EuRh 2 Si 2 - di
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Abstract A thorough knowledge of co
Page 7: vii Nomenclature AF APW ARPES BO BZ
Page 10 and 11: 2 1 Introduction conflicting limits
Page 12 and 13: 4 2 Theoretical foundation fore the
Page 14 and 15: 6 2 Theoretical foundation system a
Page 16 and 17: 8 2 Theoretical foundation such a s
Page 18 and 19: 10 2 Theoretical foundation Figure
Page 20 and 21: 12 2 Theoretical foundation Figure
Page 22 and 23: 14 2 Theoretical foundation Fi
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 57: 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 72 and 73: 64 Bibliography [75] Hari C. Manoha
Page 75: List of Tables 67 List of Tables 2.
Page 79: Erklärung Hiermit versichere ich,
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Diploma - Max Planck Institute for Solid State Research

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