Double-sine-Gordon solitons: A model for misfit dislocations on the Au(111) reconstructed surface

El‐Batanouny, M.; Burdick, S.; Martini, K. M.; Stancioff, P.

doi:10.1103/physrevlett.58.2762

Cited by 89 publications

(44 citation statements)

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“…The Au͑111͒ surface has been the subject of much research due to its well-known herringbone reconstruction [7][8][9][10][11][12][13] and the more recent discovery of the spin-orbit splitting of the ⌫ surface state. [14][15][16][17][18] The dispersion of the spinorbit-split surface state can be described as a pair of parabolas offset from each other in momentum.…”

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Electron-phonon mass enhancement parameter of theΓ¯surface state on Au(111) measured by photoemission spectroscopy

2006

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We report the measurement of , the electron-phonon mass enhancement parameter, for the spin-orbit-split ⌫ surface state on Au͑111͒. is determined from the change of the photoemission linewidth as a function of temperature. The difference between the normal emission = 0.34± 0.01 and midband = 0.30± 0.01 is explained as increasing bulk penetration of the surface state as it approaches the Fermi level. DOI: 10.1103/PhysRevB.74.033410 PACS number͑s͒: 73.25.ϩi, 71.70.Gm, 73.20.At, 79.60.Ϫi Low-energy excitations in solids are fundamental to life as we know it. They determine quantities such as conduction and specific heat, which are important properties for things as common as how high the electric bill is. One type of low-energy excitation is the electron-phonon interaction. Understanding the electron-phonon interaction helped unlock the door to the description of traditional superconductivity and may be fundamental to understanding the mechanism of the more technologically exciting high-T c superconductors.As electromechanical miniaturization progresses and the number of surface atoms becomes comparable to the number of bulk atoms for a given sample or device, surface properties are becoming more and more important. The combination of the increasing importance of surface properties and an interest in the electron-phonon interaction has led to a significant increase in research in this area. See the reviews by Plummer et al.1 and Kevan and Rotenberg 2 and references therein.In 1995 McDougall et al. 3 published a seminal paper on the use of photoemission spectroscopy to measure , the electron-phonon mass enhancement parameter. The relevant theory is as follows. The contributions to the hole lifetime and therefore to the total photoemission linewidth, are electron-electron, electron-phonon, and electron-impurity scattering. Electron-impurity scattering is not temperature dependent and the temperature dependence of electronelectron scattering is negligible. For temperatures T with k b T greater than phonon energies the temperature dependence of the photoemission linewidth W should be almost entirely due to the electron-phonon interaction which has the temperature-dependent linewidthThus, can be measured by plotting W vs T and measuring the slope. is formally defined right at the Fermi level ͑E F ͒; 4 therefore, the term is used somewhat loosely here. Nevertheless, for the reasons given above the present data do in fact provide a direct indication of the strength of the electron-phonon interaction near E F . has been measured on the ͑111͒ surfaces of the other noble metals copper 3,5,6 and silver; 6 however, we are not aware of any measurements of on Au͑111͒. We present here data from the ⌫ surface state on Au͑111͒.The Au͑111͒ surface has been the subject of much research due to its well-known herringbone reconstruction 7-13 and the more recent discovery of the spin-orbit splitting of the ⌫ surface state. [14][15][16][17][18] The dispersion of the spinorbit-split surface state can be described as a pair of parabolas...

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Electron-phonon mass enhancement parameter of theΓ¯surface state on Au(111) measured by photoemission spectroscopy

2006

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“…On the Au(100) surface, the gain in elastic strain energy is clearly insufficient to cause the surface to reconstruct. [S0031-9007(97) The reconstruction has been discussed frequently using the Frenkel-Kontorova (FK) model [7][8][9][10]: In the onedimensional (1D) version, a chain of atoms (representing the top layer) linked by springs with nearest-neighbor force constant w 00 and "natural" spacing b is placed in a sinusoidal potential with amplitude W ͞2 representing a rigid substrate with periodicity a. The prime feature of the reconstruction, the soliton domain wall, results from energy minimization.…”

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Stress Relief in Reconstruction

et al. 1997

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We report on the first direct measurement of the change of the surface stress in the reconstruction of the Au(111) and the Au(100) surfaces. For both surfaces the reconstruction relaxes the intrinsic tensile stress, by 22% and 5%, respectively. A discussion of the data on the Au(111) surface in the FrenkelKontorova model shows that the energy gain due to the surface stress is not quite large enough to make the reconstructed phase energetically favored without the formation of the secondary herringbone structure of the solitons. On the Au(100) surface, the gain in elastic strain energy is clearly insufficient to cause the surface to reconstruct. [S0031-9007(97) The reconstruction has been discussed frequently using the Frenkel-Kontorova (FK) model [7][8][9][10]: In the onedimensional (1D) version, a chain of atoms (representing the top layer) linked by springs with nearest-neighbor force constant w 00 and "natural" spacing b is placed in a sinusoidal potential with amplitude W ͞2 representing a rigid substrate with periodicity a. The prime feature of the reconstruction, the soliton domain wall, results from energy minimization. Further minimization of a (very small) strain energy associated with the anisotropy of the stress relief in the soliton reconstruction leads to a secondary ("herringbone") structure of the solitons [11]. Despite the general consensus that the soliton reconstruction is driven by the large tensile stress [12,13] on the Pt(111) [4][5][6]14] and the Au(111) surfaces, there is no direct experimental evidence, e.g., by measurements on the stress relief in the reconstruction.On the reconstructed (100) surfaces of Ir, Pt, and Au, the surface atoms form quasi-hexagonal (hex) commensurate and incommensurate overlayers. The atom density in the surface layer is higher by (20-25)%. From firstprinciples calculations, Fiorentini et al. [15] find the surface stress for the unreconstructed (100) surfaces of Ir, Pt, and Au to be even larger than for the (111) surfaces. Furthermore, the stress on the (100) surfaces of the 5d fcc metals Ir, Pt, and Au is also significantly larger than for the (100) surfaces of the corresponding 4d metals. They [15] identify the tensile stress as driving the reconstruction of the (100) surfaces on the 5d metals. Indirect experimental evidence for stress relief in the reconstruction was obtained for the Ir(100) surface [16]. However, neither theory nor experiment could determine the change in the surface stress quantitatively. Without direct information about the actual amount of stress energy relieved in the reconstruction of the (100) surfaces, this interpretation of the origin of the reconstruction is questionable. We dispute it below.In this Letter we report the first measurements of the change in surface stress which accompanies the reconstruction of both the Au(111) and the Au(100) surfaces. The stress measurements were performed in an electrochemical cell, with the crystals immersed in a 0.1 M HClO 4 solution, using the cantilever bending method [17][18][19]; the bendin...

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“…An early attempt to model charged particles by solitons is due to Born and Infeld [2,3]. Although solitons have very interesting mathematical properties in their own right, various interesting applications have also been found even in one spacial dimension (see [4][5][6][7][8][9][10][11][12][13][14][15][16][17]). It is known that the soliton solutions of some nonlinear systems behave -in many respects-like classical particles [18,19].…”

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confidence: 99%

Wave-Particle Duality in Nonlinear Klein-Gordon Equation

Riazi

2011

Int J Theor Phys

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In this paper, I present a nonlinear potential for the Klein-Gordon equation which leads to localized, non-dispersive wave-packets with remarkable properties. These properties include the deBroglie's wavelength-momentum and the Einstein's energy-momentumrest mass relations and a relativistic total energy which coincides with the mass parameter times the velocity of light squared, also equal to the Planck's constant times the frequency in the rest frame of the wave-packet. Energy and momentum, therefore, can be transported by soliton-like wave-packets with well-defined energy and momentum, without the implementation of the canonical quantum procedure.

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Double-sine-Gordon solitons: A model for misfit dislocations on the Au(111) reconstructed surface

Cited by 89 publications

References 8 publications

Electron-phonon mass enhancement parameter of theΓ¯surface state on Au(111) measured by photoemission spectroscopy

Electron-phonon mass enhancement parameter of theΓ¯surface state on Au(111) measured by photoemission spectroscopy

Stress Relief in Reconstruction

Wave-Particle Duality in Nonlinear Klein-Gordon Equation

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