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Journal ArticleDOI

Surface states in crystals

01 Jul 1957-Annals of Physics (Academic Press)-Vol. 2, Iss: 1, pp 16-27
TL;DR: In this paper, it was shown that if the potential is real and (for convenience) symmetric, then if E is not V everywhere in the unit cell, there are no band crossings, and hence no Shockley levels.
About: This article is published in Annals of Physics.The article was published on 1957-07-01. It has received 37 citations till now. The article focuses on the topics: Surface states.
Citations
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Journal ArticleDOI
TL;DR: In this article, a new method is elaborated for calculating Shockley-type surface states; this method is analogous to a certain modification of the OPW method, using a repulsive potential.

137 citations

Journal ArticleDOI
TL;DR: In this article, a general symmetry criterion is derived for establishing the existence of surface states in solids, which applies to surface states terminating at symmetry planes (or symmetry centers in one dimension).
Abstract: A general symmetry criterion is derived for establishing the existence of surface states in solids. Two kinds of surfaces in solids are distinguished: those coinciding with symmetry planes (or symmetry centers in one dimension) and those in general positions. The symmetry criterion applies to surface states in solids terminating at symmetry planes (or symmetry centers in one dimension). A detailed discussion is given for one-dimensional crystals. The application of the symmetry criterion is demonstrated on the Kronig-Penney, nearly-free-electron, tight-binding, and Mathieu potentials. In particular, it is shown that the Maue and Shockley existence conditions for surface states follow from the general symmetry criterion.

90 citations

Journal ArticleDOI
Pedro Pereyra1
TL;DR: In this article, a simple approach that requires neither the Bloch functions nor the reciprocal lattice is derived for an accurate evaluation of resonant energies, resonant states, energy eigenvalues and eigenfunctions of open and bounded n -cell periodic systems with arbitrary 1D potential shapes, provided the single cell transfer matrix is given.

35 citations

Journal ArticleDOI
Börje Persson1
TL;DR: In this paper, the authors measured the internal bremsstrahlung from the beta decays of P 32, Sr 89, Y 90, Y 90, Y 91 and Bi 210 in a coincidence experiment.

34 citations

References
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Journal ArticleDOI
William Shockley1
TL;DR: In this article, the wave functions and energy levels associated with a finite one-dimensional periodic potential field are investigated and the surface levels appear only at lattice constants so small that the boundary curves for the allowed energy bands have crossed.
Abstract: The wave functions and energy levels associated with a finite one-dimensional periodic potential field are investigated. In a plot of the energy spectrum versus interatomic distance the surface levels appear only at lattice constants so small that the boundary curves for the allowed energy bands have crossed. The levels appear in the "forbidden" region between allowed bands in pairs one coming from each of the adjoining bands. In three dimensions these surface levels give rise to surface bands. The surface bands probably exist and are half-filled for diamond. They exist for all metals and are entirely unoccupied only for the monovalent metals.

930 citations

01 Jun 2011

633 citations

Journal ArticleDOI
TL;DR: In this article, the energy band structure for a one-dimensional periodic square-well potential is obtained in terms of the well depth for the whole range of possible ratios of well width to hill width.
Abstract: The energy band structure for a one-dimensional periodic square-well potential is obtained in terms of the well depth for the whole range of possible ratios of well width to hill width. This model bears a closer resemblance to a real crystal since, as potential depth is varied for a fixed ratio of well width to hill width, the curves bounding distinct bands cross while in the case of a delta-function potential no such crossings occur. The location of these crossings is derived. The number of times that a given pair of boundary curves can cross is considered. For the set of boundary curves that belong to a given ratio of well-to-hill widths, this number is unbounded.

39 citations