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

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22 Chapter 2. Photoemission Spectroscopy shows the B p band DOS, both the original one and that convoluted with the Gaussian of 7 meV, which corresponds to the instrumental resolution (Chap. 5), and the middle panel shows calculated photoemission spectra, which have been obtained from the band DOS by multiplying it with FD function of each temperature and then convoluting them with the 7 meV Gaussian. We have divided these spectra by FD function of each temperature convoluted with the 7 meV Gaussian to obtain the spectral DOS as shown in the bottom panel. The obtained spectral DOS are identical below − 5 meV; the 75 K and 305 K DOS perfectly reproduce the original DOS within the resolution of 7 meV. The reproducibility is not perfect for the 6 K spectrum at and above EF . In the following Chapters we show such spectral DOS up to ∼ 2kBT above EF , where the FD function falls off to ∼ 0.1. In the case for Fig. 2.2, the discrepancy between the deduced spectral DOS and the simply broadened DOS at ∼ 2kBT is 6 %, 4 %, and 1 % for 6 K, 75 K, and 305 K, respectively. Since we deal with the narrow-gap semiconductor of YbB12 5 and FeSi, we have tried a similar simulation for a DOS with an extremely sharp structure. We show a model DOS with a square-well-shaped gap of 3 meV at EF in the top panel of Fig. 2.3 with that convoluted with the 7 meV Gaussian. The curves in the bottom panel are the DOS rederived from the calculated photoemission spectra shown in the middle panel. The derived DOS is almost identical to the simply broadened DOS even at 75 K, where the temperature width (kBT ) is comparable to the instrumental resolution. We have again compared the derived DOS and the original DOS and have found that the discrepancy between the deduced DOS and the simply broadened DOS up to ∼ 2kBT above EF is 15 %, 8 %, and 2 % for 6 K, 75 K, and 305 K, respectively. In the case for a spectral DOS symmetric with respect to EF , one can eliminate the effect of FD function by just adding Pobs(−ω) to the original observed spectrum [2.8]: � � Pobs(ω)+Pobs(−ω) ∝ f(ω1)A(ω1)R(ω − ω1)dω1 + f(−ω1)A(−ω1)R(−ω − ω1)dω1 � � = f(ω1)A(ω1)R(ω − ω1)dω1 + (1 − f(ω1))A(ω1)R(ω − ω1)dω1 � = A(ω1)R(ω − ω1)dω1 (2.19) where A(−ω) =A(ω), R(−ω) =R(ω), and f(−ω) =1− f(ω). We have applied the dividing procedure for all the temperature-dependent photoemission spectra in Chaps 5-8. In Chap. 6, the Pobs(ω) +Pobs(−ω) procedure has also 5 The calculated DOS of YbB12 is semimetallic and has a pseudogap with its bottom at 60 meV above EF .
2.2. Experimental 23 DOS Intensity DOS 6 K 75 K 305 K 6 K 75 K 305 K DOS broadened -40 -20 0 20 40 Energy relative to E F (meV) Figure 2.3: Top: Model DOS with a square-well-shaped gap of 3 meV (solid curve) with the same DOS convoluted with a 7 meV Gaussian (dashed curve). Middle: Photoemission spectra for the DOS in the top panel at 6 K, 75 K, and 305 K. Bottom: Spectral DOS deduced from the spectra in the middle panel. been applied. 2.2 Experimental 2.2.1 Photoemission-Spectroscopy Technique Photoemission spectroscopy is performed in an ultrahigh vacuum chamber equipped with an excitation light source and an electron energy analyzer. An x-ray tube with Al and Mg anodes and a He discharge lamp are widely used as the photon source. We have used a VG He lamp, a Gammadata He lamp, and a synchrotron radiation (hν = 125 eV) at beam line BL-3B of the Photon Factory, Institute of Materials Structure Science, High Energy Accelerator Research Organization. For energy analysis, a
Page 1: Thesis High-Resolution Photoemissio
Page 4 and 5: ii CONTENTS 5.2 Experimental . . .
Page 6 and 7: 2 Chapter 1. Introduction Figure 1.
Page 8 and 9: 4 Chapter 1. Introduction Figure 1.
Page 10 and 11: 6 Chapter 1. Introduction peaks, wh
Page 12 and 13: 8 Chapter 1. Introduction only the
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
Page 21 and 22: Chapter 2 Photoemission Spectroscop
Page 23 and 24: 2.1. General Principles 19 Photoele
Page 25: 2.1. General Principles 21 where R(
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
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72 Chapter 5. Temperature Dependenc
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74 References [5.10] N. Shimizu, F.
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Chapter 6 Substitution and Temperat
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6.1. Introduction 79 Figure 6.2: Ma
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6.3. Results and Discussion 81 6.3
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6.3. Results and Discussion 83 DOS
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6.3. Results and Discussion 85 dist
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6.3. Results and Discussion 87 Apar
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6.3. Results and Discussion 89 of E
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6.3. Results and Discussion 91 the
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6.4. Summary 93 and consistent anal
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96 References [6.11] M. J. Rozenber
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98 Chapter 7. Temperature and Co-Su
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100 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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