Journal ArticleDOI
Symmetry criterion for surface states in solids.
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.read more
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Lasing in topological edge states of a one-dimensional lattice
P. St-Jean,V. Goblot,Elisabeth Galopin,Aristide Lemaître,Tomoki Ozawa,L. Le Gratiet,Isabelle Sagnes,Jacqueline Bloch,Alberto Amo +8 more
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
Binghai Yan,Benjamin Stadtmüller,Norman Haag,S. Jakobs,Johannes Seidel,Dominik Jungkenn,Stefan Mathias,Mirko Cinchetti,Martin Aeschlimann,Claudia Felser +9 more
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
P. St-Jean,V. Goblot,Elisabeth Galopin,Aristide Lemaître,Tomoki Ozawa,L. Le Gratiet,Isabelle Sagnes,Jacqueline Bloch,Alberto Amo +8 more
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.
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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.
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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.
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Electronic states at the surfaces of crystals: I. The approximation of nearly free electrons
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.