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

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68 Chapter 5. Temperature Dependence of the High-Resolution Photoemission ... the spectra by the FD distribution function (convoluted with a Gaussian corresponding to the instrumental resolution) [5.16–18] as shown in the lower panel of Fig. 5.4. We present the spectral DOS up to ∼ 2kBT above EF where the FD function falls off to ∼ 0.1. The results show that the DOS with a V-shaped dip varies with temperature in such a wide energy region as ∼ 100 meV around EF . This widely extended dip compared with the activation energy of 6 meV has already been implied in the previous measurements on polycrystalline YbB12 [5.5]. Here, the improved energy resolution has clarified the shape of the dip at low temperatures: The closer to EF one goes, the steeper the slope appears. From the measurements on polycrystals at ∼ 30 K we estimated that the spectral DOS at EF was depressed by ∼ 25% compared with that of LuB12. Here, the depression amounts to more than 40% in going from 305 K to 6 K because of the improved energy resolution and the extended temperature range. The width of the sharp cusp-like depression in the very vicinity of EF , which has not been observed in the previous work, is ∼ 10 meV. This energy scale falls in the same range as the transport gap of 2∆act ∼ 12 meV. The appearance of this sharp depression only at low temperatures (6 to 75 K) is parallel to the temperature dependence of the magnetic susceptibility and the electrical resistivity: Below Tmax ∼ 75 K the magnetic susceptibility decreases due to the missing Pauli paramagnetism. The electrical resistivity follows an activated form only below ∼ 50 K. Above ∼ 100 K it decreases slowly with temperature following − log T , like a metallic Kondo material[5.19]. Except for the residual DOS at EF at low temperatures the spectra imply that a narrow gap is formed at low temperatures while a Fermi edge exists at high temperatures. Here, we note that the bottom of the pseudogap in YbB12 is not located exactly at EF but slightly below EF . This may indicate that the dip feature are caused by hybridization of the conduction-band states with the 4f states since the 4f states are located largely below EF . A recent reflectivity study by Okamura et al.[5.20] has also revealed two energy scales in the spectrum of YbB12 as shown in Fig. 5.3: a gap of ∼ 25 meV (threshold) with a shoulder at ∼ 40 meV develops below 70 K in the optical conductivity (Fig. 5.3 (b)). They are superposed on a broad dip with a shoulder at ∼ 0.25 eV, which is present at all temperatures (Fig. 5.3 (b)). Okamura et al. have attributed the broad structure to a 4f-5d transition, which has no direct relation with the peculiar behavior of the Kondo insulator. That the energy of the optical threshold is larger than the transport gap (2∆act ∼ 12 meV) is characteristic of an indirect gap, implying a formation of a
5.3. Results and Discussion 69 Figure 5.3: (a) Reflectivity (R) and optical conductivity (σ) of YbB12 at 290 K (dotdashed curve), 160 K (dots), 78 K (dashed curve), and 20 K (solid curve). (b) R and σ in lower-energy region at 78, 70, 60, 50, 40, and 20 K from top to bottom. The inset shows the magnetic susceptibility of YbB12 single crystal [5.20]. renormalized hybridization gap1 . This is contrasted with the behavior of FeSi, in which the valence-band edge is located ∼ 35 meV below EF [5.21], nearly half of the optical gap (threshold) of ∼ 60 meV[5.4]. The origin of the residual DOS at EF in FeSi as well as in YbB12 remains unclear at present. This may be due to an extrinsic signal from a possibly metallic surface layer. Also, the residual DOS may have been caused partly by the finite energy resolution. The high-temperature spectra of the conduction band is also worth remarking. The spectral DOS continues to be recovered even above 150 K and the broad V-shaped dip still survives at 305 K. The lower panel of Fig. 5.4 shows that the DOS is not conserved within ∼ 100 meV of EF , indicating spectral weight transfer with temperature over an energy scale larger than ∼ 100 meV. Such a temperature dependence is most likely associated with changes in the 4f electronic states because the presence of the Yb 4f 1 If the narrow 4f band and the broad conduction band are hybridized with each other, then the bottom of the conduction band can be far from the top of the valence band because the magnitude of the dispersion (dE/dk) between the two hybridized bands is quite different.
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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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4 Chapter 1. Introduction Figure 1.
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6 Chapter 1. Introduction peaks, wh
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8 Chapter 1. Introduction only the
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10 Chapter 1. Introduction directio
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12 Chapter 1. Introduction activati
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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 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
Page 89 and 90: 6.3. Results and Discussion 85 dist
Page 91 and 92: 6.3. Results and Discussion 87 Apar
Page 93 and 94: 6.3. Results and Discussion 89 of E
Page 95 and 96: 6.3. Results and Discussion 91 the
Page 97: 6.4. Summary 93 and consistent anal
Page 100 and 101: 96 References [6.11] M. J. Rozenber
Page 102 and 103: 98 Chapter 7. Temperature and Co-Su
Page 104 and 105: 100 Chapter 7. Temperature and Co-S
Page 113 and 114: References [7.1] G. Aeppli and Z. F
Page 115 and 116: Chapter 8 Temperature and Al-Substi
Page 117 and 118: 8.2. Experimental 113 and Fisk [8.2
Page 119 and 120: 8.3. Results and Discussion 115 8.3
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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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