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Title: Algebraic Theory of Crystal Vibrations: Localization Properties of Wave Functions in Two-Dimensional Lattices

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.

Authors:
 [1];  [2]; ORCiD logo [3]
  1. Lanzhou Univ. (China). School of Physical Science and Technology. Key Lab. for Magnetism and Magnetic Materials of MOE
  2. Yale Univ., New Haven, CT (United States). Center for Theoretical Physics. Sloane Physics Lab.
  3. The Czech Academy of Sciences, Brno (Czech Republic). Inst. of Scientific Instruments
Publication Date:
Research Org.:
Yale Univ., New Haven, CT (United States); The Czech Academy of Sciences, Brno (Czech Republic); Lanzhou Univ. (China)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26); Czech Science Foundation; Ministry of Education, Youth and Sports of the Czech Republic
OSTI Identifier:
1425398
Grant/Contract Number:  
FG02-91ER40608; P203-13-07117S; LO1212
Resource Type:
Accepted Manuscript
Journal Name:
Crystals
Additional Journal Information:
Journal Volume: 7; Journal Issue: 8; Journal ID: ISSN 2073-4352
Publisher:
MDPI
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; 97 MATHEMATICS AND COMPUTING; algebraic models; graphene-like materials; striped structures; photonic crystals

Citation Formats

Dietz, Barbara, Iachello, Francesco, and Macek, Michal. Algebraic Theory of Crystal Vibrations: Localization Properties of Wave Functions in Two-Dimensional Lattices. United States: N. p., 2017. Web. doi:10.3390/cryst7080246.
Dietz, Barbara, Iachello, Francesco, & Macek, Michal. Algebraic Theory of Crystal Vibrations: Localization Properties of Wave Functions in Two-Dimensional Lattices. United States. doi:10.3390/cryst7080246.
Dietz, Barbara, Iachello, Francesco, and Macek, Michal. Mon . "Algebraic Theory of Crystal Vibrations: Localization Properties of Wave Functions in Two-Dimensional Lattices". United States. doi:10.3390/cryst7080246. https://www.osti.gov/servlets/purl/1425398.
@article{osti_1425398,
title = {Algebraic Theory of Crystal Vibrations: Localization Properties of Wave Functions in Two-Dimensional Lattices},
author = {Dietz, Barbara and Iachello, Francesco and Macek, Michal},
abstractNote = {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.},
doi = {10.3390/cryst7080246},
journal = {Crystals},
number = 8,
volume = 7,
place = {United States},
year = {2017},
month = {8}
}

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