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Journal ArticleDOI

Symmetry criterion for surface states in solids.

J. Zak
- 15 Aug 1985 - 
- Vol. 32, Iss: 4, pp 2218-2226
TLDR
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.

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Citations
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Lasing in topological edge states of a one-dimensional lattice

TL;DR: In this article, topologically protected lasing is reported in a one-dimensional lattice of polariton micropillars that implements an orbital version of the Su-Schrieffer-Heeger Hamiltonian, which offers new opportunities for robust trapping of light in nano-and micrometre-scale systems subject to fabrication imperfections and environmentally induced deformations.
Journal ArticleDOI

Geometric phase and band inversion in periodic acoustic systems

TL;DR: The behavior of sound waves in phononic crystals is similar to that of electrons in solids as mentioned in this paper, and phononic band inversion and Zak phases have been measured for a 1D phononic system.
Journal ArticleDOI

Topological states on the gold surface

TL;DR: This work shows that these Shockley surface states can be reinterpreted as topologically derived surface states (TDSSs) of a topological insulator (TI), a recently discovered quantum state.
Journal ArticleDOI

Lasing in topological edge states of a 1D lattice

TL;DR: In this paper, topological edge states of a one-dimensional lattice of polariton micropillars that implements an orbital version of the Su-Schrieffer-Heeger Hamiltonian were shown to persist under local deformations of the lattice.
Journal ArticleDOI

Light propagation and localization in modulated photonic lattices and waveguides

TL;DR: In this article, the authors review both theoretical and experimental advances in the recently emerged field of modulated photonic lattices and highlight a new type of modulation-induced light localization based on the defect-free surface waves.
References
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Journal ArticleDOI

On the Surface States Associated with a Periodic Potential

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.
Journal ArticleDOI

Analytic Properties of Bloch Waves and Wannier Functions

TL;DR: In this article, the one-dimensional Schr\"odinger equation with a periodic and symmetric potential is considered, under the assumption that the energy bands do not intersect, and it is shown that for each band there exists one and only one Wannier function which is real, symmetric or antisymmetric under an appropriate reflection.
Journal ArticleDOI

Surface electronic structure

TL;DR: The theory of the electronic structure of clean metal and semiconductor surfaces is reviewed, starting from an effective one-electron Schrodinger equation, and the effects of the surface on the electronic wavefunctions are discussed using simple models as mentioned in this paper.
Journal ArticleDOI

Electronic states at the surfaces of crystals: I. The approximation of nearly free electrons

E. T. Goodwin
TL;DR: In this article, the wave functions and energies of these states are calculated, on the nearly free electron approximation, in terms of the constants of the crystalline potential field, which is represented by a triple Fourier series having the periodicity of the lattice.
Journal ArticleDOI

Die Oberflächenwellen in der Elektronentheorie der Metalle

TL;DR: An der Begrenzungsflache eines Kristalls konnen sich Oberflachenelektronenwellen ausbilden as discussed by the authors, und ihr Beitrag zur i Leitfahigkeit in Metallen wird untersucht.
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