Thesis High-Resolution Photoemission Study of Kondo Insulators ...

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54 Chapter 4. Evolution of Electronic States in the Kondo Alloy ... Figure 4.8: Schematic illustration of the basis states. For Yb compounds, solid circles represent holes and open circles show electrons. The shaded parts indicate the unoccupied conduction band and the horizontal lines indicate the f level [4.22]. in the middle [4.24]. We have included lowest order f 14 , f 13 , and f 12 states and second order f 14 state (state (0), (a), (b), and (c) in Fig. 4.8) for the calculation of the initial state [4.23] and lowest order f 13 , f 12 , and f 11 states and second order f 14 and f 13 states for the photoemission final states. Here, the lowest order f 14−n state stands for the state with n holes in the f level and n (n − 1) electrons in the conduction band for the initial (final) state. An electron-hole pair is added in the second order states. Using this model, we have reproduced both the intensity ratio I(4f 13 → 4f 12 )/I(4f 14 → 4f 13 ), corrected for the difference in Nf (= 8 and 14), and the Kondo peak position in the YbB12 spectrum with ∆ = 0.21 eV, ε0 f = 0.7 eV, and Uff =7eV2 . The AIM calculations have thus given an asymmetric Kondo peak as shown in the lower panel of Fig. 4.6 although they cannot fully reproduce the experimentally observed asymmetry [4.25] 3 . 2 13 12 14 13 In our calculation, the equation I(4f → 4f )/I(4f → 4f )=[(Nf−1)¯nf]/[Nf (1 − ¯nf )] underestimates ¯nf by 5% owing to the Yb 4f-B sp hybridization. The same discrepancy has been discussed in Ref. [4.7] in the case of Ce compounds. 3 We calculated the spectra by changing the conduction-band width from 0.3 eV to 3 eV, and found that the calculated Kondo peak was most asymmetric for 0.3 eV although the total B sp band width is as large as several eV. The effectively narrow band width would be a consequence of the renormalization of those effects which do not enter the AIM explicitly. Within a single impurity model, O. Gunnarsson and K. Schönhammer [Phys. Rev. B 40, 4160 (1989)] have reported that for low-energy excitations of order kBT , Coulomb interaction between the 4f and conduction electrons renormalizes the hopping
4.3. Results and Discussion 55 Intensity (arb. units) ∆ = 0.29 eV 0.27 eV 0.25 eV 0.23 eV 0.21 eV 0 εf = 0.50 eV 0.55 eV 0.60 eV 0.65 eV 0.70 eV x = 0 meV 10 meV 30 meV (a) (b) (c) 6.8 6.6 6.4 6.2 Binding Energy (eV) (A) (B) ∆ = 0.29 eV 0.27 eV 0.25 eV 0.23 eV 0.21 eV 0 εf = 0.50 eV 0.55 eV 0.60 eV 0.65 eV 0.70 eV x = 0 meV 10 meV 30 meV (a) (b) (c) 0.20 0.15 0.10 0.05 0.00 -0.05 Binding Energy (eV) Figure 4.9: Calculated photoemission spectra which correspond to the 4f 13 → 4f 12 transition (A) and the 4f 14 → 4f 13 transition (B) with Uff = 7.0 eV. We have varied ∆ in (a), ε0 f in (b), and the gap width x in the conduction band in (c) with other parameters fixed. All the spectra are convoluted with 40 meV Gaussian. As already clear in Eq.(4.1), both decreasing ∆ and increasing ε0 f causes qualitatively similar changes in the Kondo peak: The weight of the Kondo peak becomes smaller with its position approaching EF and the weight of the 4f 13 → 4f 12 transition increases; the f-hole occupancy ¯nf approaches unity. As ε0 f changes, the position of the 4f 13 → 4f 12 structure at the binding energy of about −ε0 f + Uff should be shifted by the same amount as shown in Fig. 4.9 (b). Since the shift of the 4f 13 → 4f 12 signal is much less than 0.1 eV (Fig. 4.4), we conclude that the change of ∆ rather than that of ε0 f dominates the spectral change caused by the Lu-substitution. In order to reproduce the changes in both the intensity ratio I(4f 13 → 4f 12 )/I(4f 14 → 4f 13 ) and the Kondo integral so that it has a maximum at EF . Interaction between different Yb sites mediated by the Yb 4f-B sp hybridization might be another cause of the renormalization.
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Thesis High-Resolution Photoemissio
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ii CONTENTS 5.2 Experimental . . .
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2 Chapter 1. Introduction Figure 1.
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Page 14 and 15: 10 Chapter 1. Introduction directio
Page 16 and 17: 12 Chapter 1. Introduction activati
Page 18 and 19: 14 References [1.14] F. Iga, M. Kas
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Page 23 and 24: 2.1. General Principles 19 Photoele
Page 25 and 26: 2.1. General Principles 21 where R(
Page 27 and 28: 2.2. Experimental 23 DOS Intensity
Page 29 and 30: 2.2. Experimental 25 Figure 2.5: Il
Page 31 and 32: 2.2. Experimental 27 baking out the
Page 33: References [2.1] O. Gunnarsson and
Page 36 and 37: 32 Chapter 3. Photoemission Study o
Page 48 and 49: 44 References the Kondo peak positi
Page 50 and 51: 46 Chapter 4. Evolution of Electron
Page 63 and 64: References [4.1] G. Aeppli and Z. F
Page 65: References 61 [4.25] P. Weibel,M. G
Page 68 and 69: 64 Chapter 5. Temperature Dependenc
Page 78 and 79: 74 References [5.10] N. Shimizu, F.
Page 81 and 82: Chapter 6 Substitution and Temperat
Page 83 and 84: 6.1. Introduction 79 Figure 6.2: Ma
Page 85 and 86: 6.3. Results and Discussion 81 6.3
Page 87 and 88: 6.3. Results and Discussion 83 DOS
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Page 97: 6.4. Summary 93 and consistent anal
Page 100 and 101: 96 References [6.11] M. J. Rozenber
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104 Chapter 7. Temperature and Co-S
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106 Chapter 7. Temperature and Co-S
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References [7.1] G. Aeppli and Z. F
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Chapter 8 Temperature and Al-Substi
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8.2. Experimental 113 and Fisk [8.2
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8.3. Results and Discussion 115 8.3
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8.3. Results and Discussion 117 Int
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8.3. Results and Discussion 119 dep
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8.3. Results and Discussion 121 σ
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8.4. Summary 123 temperature magnet
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126 References [8.14] T. Tonogai, A
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128 Chapter 9. Conclusion has shown
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130 Chapter 9. Conclusion (a) FeSi
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132 Chapter 9. Conclusion developed
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