Figure 1.1: Schematic illustrations for (top) ideal lattice structures in various low dimensions: 3D bulk of atoms, 2D sheet of atoms, 1D string of atoms and for (bottom) the corresponding Fermi-surface topologies of free electrons. 25

Figure 1.2: Development of the transistor size in integrated circuits versus time. Soon after the year 2030, the curve will reach the dimensions of a single atom. From Ref. 3 26

Figure 1.3: (a) Simple visualization of strong interactions between electrons in a 1D system. Electrons cannot escape from each other when moving along a line, which leads to the formation of collective excitations and the breakdown of the single electron picture. (b)... 28

Figure 1.4: Overview of CDWs in a 1D atom chain with a half electron fitting. The red balls are the atoms consisting of the 1D chain. The lines above the balls represent charge densities. The bottom part shows the respective band dispersions of 1D free electrons in the... 29

Figure 1.5: Response functions of free-electron gases in one-, two-, and three-dimensions. Taken from Ref. 17. 30

Figure 1.6: Cartoons showing the prototypical examples of low-dimensional materials. (a),(b) anisotropic bulk crystals: (a) Cuprates high-temperature superconductors, stacked 2D layers of the CuO₂ plane and the charge reservoir plane, where the chemical doping takes... 32

Figure 1.7: Schematic illustrations for various surface reconstructions: (a) Dimer-Adatom-Stacking fault (DAS) model for the Si(111)7×7 surface superstructure. (b) Low-dimensional structures of metal adsorbates (red balls) fabricated on the silicon surface (grey balls). 35

Figure 1.8: STM images for various low-dimensional structures realized on Si(111) with metal adsorbates. (center) bare Si(111)7×7. (a) array of Indium nanoclusters (0D), (b) array of Indium nanowires (1D), (c) lead overlayer (2D), (d) lead thin films and (e) lead... 37

Figure 1.9: (a) Microscopic images of a Si(557) surface with a periodicity of 5.73 nm, together with a side view of the unreconstructed unit cell. A single Si(111)7×7 unit is combined with a triple step that can be approximated by a Si(112) facet. The overview... 38

Figure 1.10: (a) Simplified 1D model of a periodic crystal potential terminating at an ideal surface. At the surface the model potential jumps abruptly to the vacuum level (solid line). The dashed line represents a more realistic picture, where the potential reaches the vacuum... 40

Figure 1.11: Fermi surfaces (top) and band dispersions (bottom) of (a) 2D Si(111)√3×√3-Ag at various levels of doping with extra Ag atoms and (b) of Si(553)-Au. In (a), the area of Fermi circles increases with the doping level (value above each panel in electrons/Si unit).... 41

Figure 1.12: Schematic illustrations for a few surface sensitive techniques: (a) STM (b) ARPES (c) surface conductivity measurements. 42

Figure 1.13: (a) Zigzag model for Si(111)4×1-In at RT. (b) Hexagon model for Si(111)8×2-In at low temperature. The dimerization and shear movements during the (4×1 ↔ 8×2 phase transition) are indicated by the arrows. From Ref. 96. STM topographs for Si(111)4×1-In... 44

Figure 1.14: (a) Fermi surface for Si(111)4×1-In at RT (b) underlying band dispersions at RT (above Tc, left) and at 45 K (below Tc, right). Taken from Refs. 62, 93.(이미지참조) 45

Figure 1.15: (a) Structural model for prototypical gold chain structures on stepped Si(111), Si(557)-Au. from Ref. 70. (b) It's STM image with the Au coverage 0.02 ML below optimum: there are a few patches of clean Si(111)7×7 left over forming long strips that are... 46

Figure 1.16: (a) Band dispersions for Si(557)-Au (left) and Si(553)-Au (right) near EF. Both exhibit a doublet of 1/2-filled bands, and Si(553)-Au has all extra fractionally-filled band. (b) Temperature dependence of the conductivity (circle) and resistance (cross) of the...(이미지참조) 47

Figure 1.17: STM topographs of Si(553)-Au at (a) 300 and (b) 45 K for an area of 10×10 nm² at 0.2 and 0.5 V biases (empty states), respectively. Taken from Ref. 68. 48

Figure 1.18: (a)-(c) Structure models for devil's stair case phases. two building block phases of (a) √7×√3 and (c) √3×√3. (b) An example of devil's staircase phases [the (1,1) phase], consisting of one √7×√3 and one √3×√3 unit cells. The phase notation was referred... 50

Figure 1.19: Evolution of the Fermi surface in dense Pb overlayers on Si(111). It has been suggested that the Fermi contours evolves systematically as Pb coverage changes. Taken from Ref. 78 51

Figure 1.20: Phase diagram for the dense Pb overlayers on Si(111). The thick arrows indicate the phases mainly focussed in this thesis varying the temperature (red) and coverage (blue), respectively. Reproduced from Ref. 120. 52

Figure 1.21: STM images of the Pb nanowires at (a) T ＝ 100 K (22×16 nm²) and (b) T ＝ 40 K (37×21 nm², The sample bias and the tunneling current are 0.5 V and 1 nA, respectively. Insets: Relief mode, emphasizing the weak modulation in (b) at 40 K that is absent in (a)... 53

Figure 1.22: (a) High-resolution STM image of the Pb nanowires taken at 78 K. (b) and (c) The structural model for Pb nanowires: (b) Pb monolayers sitting on the uniform step structures like a red carpet dressed on the stairs illustrated in (c). 54

Figure 1.23. (a) Conductance of the Pb nanowires measured as a function of temperature along the step-edge (σ∥, upper panel) aud the perpendicular direction (σ⊥, lower panel) (b) Conductance along the nanowires below Tc of 78 K versus 1/T. (c) Schematic drawing of...(이미지참조) 55

Figure 1.24: Description of two materials systems, the Pb overlayer on flat si(111) and the Pb nanowires on stepped Si(111), studied in this thesis. The red and white balls represent the Pb and Si atoms, respectively. 57

Figure 1.25: Chart to show the flow of issues in this thesis. They are topically divided into two parts on Pb overlayers (Part I.) and Pb nanowires (Part II.) 58

Figure 2.1: Schematic drawing of an early "photoemission" experiment. Light is sent on a film of an alkali metal (Na, K). The energy of the photoemitted electrons is measured by applying a retarding voltage. 61

Figure 2.2: Technological development in PES since the first observation of the Ag(111) surface state in photoemission spectra, showing vast improvements in instrumental resolution. For the data bottom, the peak width is dominated by intrinsic lifetime broadening, and... 63

Figure 2.3. Geometry of an ARPES experiment in which the emission direction of the photoelectron is specified by the polar (φ) and azimuthal (ψ) angles. 65

Figure 2.4: Schematic view of the photoemission process in the single particle picture. The electron energy distribution produced by incoming photons and measured as a function of the kinetic energy Ekin of the photoelectrons (right) is more conveniently expressed in terms...(이미지참조) 67

Figure 2.5: Illustration of the three-step model, with (1) optical excitation of an electron in the bulk, (2) transport of the photoelectron to the surface, and (3) escape of the photoelectron into vacuum free space. Taken from Ref. 80 70

Figure 2.6: Electron mean free path λ, measured for various metals, as a function of the kinetic energy. The solid line indicates the "universal curve" with a minimum of 2.5 Å in the kinetic energy range of 50-100 eV. Despite the universal character of the energy... 71

Figure 2.7: Illustration of the effects of interactions on the single-particle spectral function. On the left is the case of non-interacting electrons where the single-particle excitations are δ-function. On the right is the moderately interacting case where electron-electron interactions... 76

Figure 2.8: Simulation of A(k,ω) using a model self-energy. The solid and dashed lines show A(k,ω), and the coherent quasiparticle peak which was lineary expanded around Ek, respectively. The remaining spectral weight represents the incoherent part of the spectral...(이미지참조) 78

Figure 2.9: 2D spectral plot showing the intensity of photoelectrons as a function of the binding energy and the momentum. A cross section through the intensity at constant energy (ω ＝ 0) as a function of momentum (an MDC), and a cross section through the intensity at... 81

Figure 2.10: Series of EDCs for the surface state of Be(0001) near EF taken at 15 K. The spectral functions calculated for the corresponding emission angles (solid lines) are compared. The dispersion shows an unusual lineshapes because of electron-phonon coupling....(이미지참조) 82

Figure 2.11: An illustration of the effects of electron-phonon coupling. (a) Electron-phonon coupling causes a distortion in the band dispersions near EF and generate the two pole structures. (b) Electron-hole pair excitations across the Fermi surface leading to Kohn... 83

Figure 2.12: Schematic representation of the polarization and photon energy effects in the photoemission process: (a) mirror plane emission, (b) sketch of the optical transition between atomic orbitals with different angular momenta (the wave functions of the harmonic... 85

Figure 2.13: (a) Initial/final state picture of CLPES for free atoms. In the first step, the core electron is removed while leaving the other electrons frozen in their original orbitals. In the second step, the other electrons are allowed to relax. This relaxation contributes... 89

Figure 2.14: Example of Doniach-Sunjic profiles with two different asymmetry parameters. 92

Figure 2.15: Schematic layout of the U7-beamline. U: undulator as a radiation source, J: jaws with copper plates, M1: condensing toroid mirror, S1: entrance slit, M2: plane mirror, G: plane grating, M3: refocusing cylindrical mirror, S2: exit slit, M4 and M5: variable radius... 94

Figure 2.16: Pictures taken for the U7-beamline (top) and the 8A2 endstation for the high-resolution ARPES (bottom). This station is equipped with a Scienta 2002 electron analyzer. 95

Figure 2.17: (a) Schematic drawing of VUV source head (VG-Scienta, Sweden). (b) Graph showing the relative intensities of multiple emissions from the He-discharge lamp (see text). The spectra were measured on the Al photodiode with a bias of -15 V. (c) Picture of VUV... 97

Figure 2.18: Pictures taken for the ARPES stations equipped with the high-performance Scienta electron analyzers and high-flux He-discharge sources: (top) Scienta 100 with an acceptance angle of ±4˚ and (bottom) the latest model of Scienta R4000 with a much wider... 99

Figure 2.19: (a) CAD drawing of SES R4000 electron analyzer (VG-Scienta, Sweden). (b) Schematic drawing of the internal structure of the analyzers. They can be categorized into three parts; the lens, hemispheres, and detector plates. (c) Enlarged image of detector part... 101

Figure 2.20: (a) CAD drawing of the low-temperature manipulator. The sample temperature can be cryogenically cooled down to 28 K. (b) Continuous mapping of the Fermi surfaces of Pb/Si(111) √7×√3 at various temperature, using the manipulator shown in (a), which... 103

Figure 2.21: Schematic illustration of the Knudsen-type cell evaporator (home-made). The head-shield part is not shown here. Taken from Ref. 188. 105

Figure 2.22: (a) LEED apparatus. Electrons thermally emitted from the filament are focussed onto the sample. Elastically scattered electrons are passed by the grids and accelerated onto the fluorescent collector grid. (b) Surface crystal truncation rods intersect the... 106

Figure 3.1: (a) Schematic illustration of the lattice and electronic structures of graphene. Taken from Ref. 190. (b) Cartoons showing the difference of band dispersions near EF between graphene and silicon.(이미지참조) 111

Figure 3.2: Simple calculations of k·p perturbation theory with the Kane model. Band dispersion becomes more linear as Eg → 0.(이미지참조) 112

Figure 3.3: Surface band dispersion of Ag/Si(111)√3×√3. The band dispersion of the Ag 5p surface states gets linear as the energy separation from the hybridized bands of Si 3p and Ag 5s states approaches to zero. Accordingly, the effective mass of the surface band (those... 113

Figure 3.4: Surface crystal structures for the well-established model of the Pb overlayer on Si(111) with a √7×√3 structure; (a) Top view and (b) side view. Pb atoms are densely packed within a single layer upon almost bulk-terminated Si(111) to form the... 114

Figure 3.5: (a) Reciprocal lattice structure of Pb /Si(111) with a √7×√3 structure. Grey and dashed lines represent √7×√3 and 1×1 symmetries, respectively. (b) and (c) ARPES data collected along (b) short and (c) long arrows in (a) (hv ＝ 21.2 eV, T ＝ 95 K), crossing... 115

Figure 3.6: Calculated shape of the band bending in n-type Si substrate (see the Methods section below for the details). Valence band maximum and conduction band minimum are plotted as a function of the distance perpendicular to the surface. 116

Figure 3.7: (a) ARPES intensity map of the R band. Data below the dashed lines are those symmetrized with respect to the Γs point in order to eliminate the strong neighboring feature S2. (b) Spectral peak positions of the R band extracted from MDCs shown in (c)... 118

Figure 3.8: (a) Constant energy contours at EF calculated from DFT based on the single-domain model and (b) after considering the overlap of triply-rotated domains. Contours from each domain [A, B, and C at the bottom of (b)] are indicated by different colors in...(이미지참조) 120

Figure 3.9: DFT bard dispersions along the arrow in Figure 3.8(b) for (a) domain A and (b) domains B and C, which are overlapped together in (c). The contributions from domains B and C are degenerated. The shaded area represents the projected bulk band structure. 121

Figure 3.10: Schematic illustration of the key mechanism for linear dispersion (extremely small-effective-mass value) in the inversion layers of semiconductors. VB (CB) denotes the valence (conduction) band. 123

Figure 3.11: (a)-(c) Schematics or surface state (SS) and LH band dispersions near Γ in Pb (a), Au (b), and Ag (c) overlayers on Si(111) with a common √3×3√ symmetry. (d)-(f) Corresponding ARPES dispersions of LH bands for (d) Pb, (e) Au, and (f) Ag systems taken... 124

Figure 3.12: (a) ARPES band dispersion of Au/Si(111)√3×√3 reported in Ref. 71. We noticed that the linear dispersion of Si-hole bands in ILs (near Γ as indicated by the red arrow) is clearly seen. (c) and (d) First principle calculations for the band dispersions of (c)... 126

Figure 3.13: (a) LEED image for triple domain Pb/Si(111)√7×√3 taken at 90 K with a primary electron energy of 81 eV. (b) Reciprocal lattice structure for the triple-domain Pb/Si(111)√7×√3 phase. The black dots denote the lattice points of Si(111)1×1, while... 129

Figure 3.14: Relationship of the transition temperature versus the lateral size of the domain. One set of data is taken with increasing sample temperature and the other with decreasing sample temperature. Taken from Ref. 124. 130

Figure 3.15: (a)-(c) Band dispersions calculated from DFT along the arrow in Figure 3.8 from domain A (a), from domains B and C (b), and the superimposed one of all triple domains (c). The shaded area represents the projected bulk band structure. All bands are... 132

Figure 4.1: (a) CoSi₂ nanowires is hundreds-nanometer scale. (b) Silicon nanowires self-assembled on the SiO₂/Si substrate in tens-nanometer scale. (c) Yt silicide nanowires self-assembled on Si(001) in sub-nanometer scale. From Refs. 113,222,223. 138

Figure 4.2: LEED patterns for different annealing temperatures after a deposition of 2 ML Pb on Si(557); (a) bare Si(557) before the deposition, (b) as Pb deposited without any annealing, and after an annealing at (c) 640, (d) 660, (e) 700, (f) 720, (g) 750, and (h) 850... 141

Figure 4.3: Detailed intensity profiles [(d), (e), and (f), respectively for (a), (b), and (c)] for the LEED patterns of (a) α×2, which gradually mixes up with [(b) and (c)] √3×10 as the annealing temperature increases. The profile is taken along the horizontal direction as... 143

Figure 4.4: Schematics of the surface morphology at different temperatures (phases) with different step-terrace configurations as deduced from the LEED results. The widths of terraces are given in the unit of the Si(111)1×1 lattice. 144

Figure 4.5: Schematics of structure models for the representative surface phases of Pb/Si(111). (a) The 1×1 phase at 1 ML (Ref. 235), (b) √3×√3 at 1.33 ML (Refs. 119,235), (c) √7×√3 at 1.0 ML (the trimer model, Refs. 124,235), and (d) √3×√3 at 1.2 ML (Refs.... 146

Figure 4.6: Pb 5d photoemission spectra for the series of phases of Si(557)-Pb shown in Figure 4.2. The spectra were taken at 70 K using the photon energy of 140 eV along a grazing emission angle of 60˚. All spectra are normalized by the peak intensity to show... 150

Figure 4.7: Si 2p photoemission spectra for the series of phases of Si(557)-Pb shown in Figure 4.2. The spectra were measured at 70 K using a photon energy of 140 eV along a grazing emission angle of 60˚ for the higher surface sensitivity. 152

Figure 4.8: The Si 2p photoemission spectra of the well-ordered α×2 phase taken at different emission angles with a photon energy of 140 eV. Open circles are the experimental data and the solid lines overlaid are fitting curves. The Lorentzian width of 0.045 eV is optimized,... 154

Figure 4.9: (a) The angle integrated valence-band spectra of Si(557)-Pb measured at 70 K with hv ＝ 140 eV. (b) The spectrum of the α×2 phase (bottom one) near EF is closed up and compared to that of tantalum metal.(이미지참조) 158

Figure 5.1: Illustration of the recipe to fabricate Pb nanowires with an indirect heater. 163

Figure 5.2: LEED patterns of (a) the clean Si(557) surface, Pb-induced (b) streaky α×2, (c) and (d) spotty α × 2, and (e) β×2 phases. The incident electron energy was 80 eV. The unit cells are superimposed on (c)-(e). The phase diagram is summarized in (f). 165

Figure 5.3: Empty-state topographic STM images of the streaky (a) and the spotty (b) α×2 surfaces (70×70 nm²). The images (a) and (b) were taken at 87 and 78 K, respectively, with a sample bias (Vs) of 2.0 V, a tunneling current (It) of 0.30 nA and Vs ＝ 0.5 V, It ＝ 0.05 nA,...(이미지참조) 168

Figure 5.4: (a) The line profile along the "line α" in Figure 5.3(a). The α×2 phase is formed on the Si(223) facet which is cut from the Si(557) as shown in (b). 169

Figure 5.5: (a) STM topograph of the well-ordered Pb nanowires on Si(557) at 78 K with +0.5 V sample bias over an area of 40×22 nm², (b) enlarged image of the area within the dashed box in (a), and (c) height profile along the white line in (a). 170

Figure 5.6: (a) LEED pattern of the Pb nanowire phase at 70 K at 81 eV electron energy. (b) Front and (c) side views of the schematic model of the Pb nanowire structure; the red (blue) balls represent Pb (Si) atoms. The 42/3×2 unit cell is indicated by the white boxes.(이미지참조) 171

Figure 5.7: ARPES data of (a) Fermi surfaces and underlying band dispersions (b), (c) along and (d) perpendicular to the Pb nanowires at 70 K with photon energies of 21.2 eV and 140 eV (darker contrast for higher intensity). The schematics of the Fermi contours within... 172

Figure 5.8: The symmetrized map from the raw Fermi surface data of Figure 5.7(a) showing a wider k-space. The raw data taken over one quadrant (kx, ky) ≥ 0 of the k space are mirror symmetrized across x and y axes with subsequent translational operations. The diamond-...(이미지참조) 174

Figure 5.9: Simple tight-binding model considering only nearest-neighbor hopping and in-plane p orbitals. (a) Possible lattice models of a square and of a hexagon with the lattice constant of Si(111)1×1 (a0). (b) The result of tight-binding calculations with a square...(이미지참조) 176

Figure 5.10: Structure model of Pb nanowires considering the tight-binding analysis of the observed band structure with ARPES, step superstructures found in LEED, and real-space images taken by STM. The present system can be more properly described as Pb nanostripes... 177

Figure 5.11: Depending on the effective step potentials that electrons feel, the electron bands can be either step superlattice states (left) and lateral quantum well states (right). Reproduced from Ref. 248. 178

Figure 5.12: The splitting of large 2D Fermi contours into the multiple quasi-1D and 2D bands as small anti-crossing gaps open at the crossing points. This is the consequence of a unique feature of the present system that the Fermi wavevector of the original 2D bands... 179

Figure 5.13: (a) STM images and (b) LEED patterns above/below the phase transition temperature (Tc) reported previously and also recently. We found no temperature dependence at all both in microscopic and electronic structures. 180

Figure 6.1: Various degrees of freedoms in solids. Interactions between them are responsible for many exotic quantum phenomena such as charge/spin density waves, non-Fermi liquid behaviors, and the superconductivity. Reproduced from Refs. 50,257,258. 184

Figure 6.2: Schematic illustration to explain the kink structure in electron dispersion. The energy scale of the kink is directly relevant to the involved collective excitations, which couple to the electrons. From Ref. 162. 185

Figure 6.3: Giant kinks in electron dispersions reported previously on (a) transition-metal oxides (cuprates) from Ref. 260 and (b) graphene from Ref. 40. 186

Figure 6.4: Various models suggested to explain the giant kinks. (a) Coupling of electrons with collective excitations (here, electron-plasmons interaction), from Ref. 40. (b) Non-Fermi liquid behaviors, from Ref. 260. (c) Interaction between electrons within the Fermi-... 187

Figure 6.5: Illustration of fabrication of the patterned Pb nanowires (or nanoribbons) on the Si(557) substrate. 188

Figure 6.6: (a) STM topograph of the Pb/Si(557) at 78 K with +0.5 V sample bias over an area of 7.4×8.2 nm². The side view of the schematic structure model is at the bottom. The top (bottom) balls represent the Pb (Si) atoms, (b) The schematic Fermi surface reported... 189

Figure 6.7: (a) ARPES intensity map collected along the nanowires at 70 K with a photon energy of 80 eV. The measured k-space cut is indicated by arrows in Figure 6.6(b). Each band is tagged as in Figure 6.6(b). The parabolic lines are the dispersions of m2 and m3... 191

Figure 6.8: (a) Real part of self-energy Re∑(ω) obtained by taking the energy difference between the tight-binding and the measured dispersions. The line is the linear fit of Re∑(ω), whose slope corresponds to the coupling constant (λ). (b) Imaginary part of self-energy... 193

Figure 6.9: Self-energies for the couplings of electrons with collective excitations of (a) phonons and (b) plasmons. From Refs. 259, 280. 195

Figure 6.10: Schematic illustration to explain the electronic kink theory. ZFL denotes a renormalization factor, depending on the strength of electron correlations. The energy of the kink is determined by the point that the electron dispersion returns back to the bare-...(이미지참조) 196

Figure 6.11: Real and imaginary parts of the self-energy predicted in the electronic kink theory. From Ref. 269. 197

Figure 6.12: (a) A series of dispersions of the m4 band along the nanowires for different momentum cuts as shown in (b). Dots represent measured dispersions from MDC's while the lines are those calculated from the tight binding model. (b) Schematics of the Fermi.... 198

Figure 6.13: Schematic illustration for the changes in the electron band dispersions. Only the bands related to the diamond-shaped contour are depicted. The giant kink becomes noticeably enhanced as the measured k-cut approaches the saddle points of large 2D Fermi... 199

Figure 6.14: (a) A series of band dispersions of graphene for different momentum cuts shown in (b). (b) Fermi surface topology of electron-doped graphene showing the relationship between the singular points in the Fermi surface and electron-phonon coupling constants.... 200