Dietz, Barbara ; Iachello, Francesco ; Macek, Michal (2017)
Algebraic Theory of Crystal Vibrations: Localization Properties of Wave Functions in Two-Dimensional Lattices.
In: Crystals, 2017, 7 (8)
doi: 10.3390/cryst7080246
Artikel, Zweitveröffentlichung
Kurzbeschreibung (Abstract)
The localization properties of the wave functions of vibrations in two-dimensional (2D) crystals are studied numerically for square and hexagonal lattices within the framework of an algebraic model. The wave functions of 2D lattices have remarkable localization properties, especially at the van Hove singularities (vHs). Finite-size sheets with a hexagonal lattice (graphene-like materials), in addition, exhibit at zero energy a localization of the wave functions at zigzag edges, so-called edge states. The striped structure of the wave functions at a vHs is particularly noteworthy. We have investigated its stability and that of the edge states with respect to perturbations in the lattice structure, and the effect of the boundary shape on the localization properties. We find that the stripes disappear instantaneously at the vHs in a square lattice when turning on the perturbation, whereas they broaden but persist at the vHss in a hexagonal lattice. For one of them, they eventually merge into edge states with increasing coupling, which, in contrast to the zero-energy edge states, are localized at armchair edges. The results are corroborated based on participation ratios, obtained under various conditions.
| Typ des Eintrags: | Artikel |
|---|---|
| Erschienen: | 2017 |
| Autor(en): | Dietz, Barbara ; Iachello, Francesco ; Macek, Michal |
| Art des Eintrags: | Zweitveröffentlichung |
| Titel: | Algebraic Theory of Crystal Vibrations: Localization Properties of Wave Functions in Two-Dimensional Lattices |
| Sprache: | Englisch |
| Publikationsjahr: | 2017 |
| Publikationsdatum der Erstveröffentlichung: | 2017 |
| Verlag: | MDPI |
| Titel der Zeitschrift, Zeitung oder Schriftenreihe: | Crystals |
| Jahrgang/Volume einer Zeitschrift: | 7 |
| (Heft-)Nummer: | 8 |
| DOI: | 10.3390/cryst7080246 |
| URL / URN: | https://doi.org/10.3390/cryst7080246 |
| Herkunft: | Zweitveröffentlichung aus gefördertem Golden Open Access |
| Kurzbeschreibung (Abstract): | The localization properties of the wave functions of vibrations in two-dimensional (2D) crystals are studied numerically for square and hexagonal lattices within the framework of an algebraic model. The wave functions of 2D lattices have remarkable localization properties, especially at the van Hove singularities (vHs). Finite-size sheets with a hexagonal lattice (graphene-like materials), in addition, exhibit at zero energy a localization of the wave functions at zigzag edges, so-called edge states. The striped structure of the wave functions at a vHs is particularly noteworthy. We have investigated its stability and that of the edge states with respect to perturbations in the lattice structure, and the effect of the boundary shape on the localization properties. We find that the stripes disappear instantaneously at the vHs in a square lattice when turning on the perturbation, whereas they broaden but persist at the vHss in a hexagonal lattice. For one of them, they eventually merge into edge states with increasing coupling, which, in contrast to the zero-energy edge states, are localized at armchair edges. The results are corroborated based on participation ratios, obtained under various conditions. |
| URN: | urn:nbn:de:tuda-tuprints-69326 |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 530 Physik |
| Fachbereich(e)/-gebiet(e): | 05 Fachbereich Physik > Institut für Kernphysik 05 Fachbereich Physik |
| Hinterlegungsdatum: | 24 Dez 2017 20:55 |
| Letzte Änderung: | 24 Dez 2017 20:55 |
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