Algebraic Theory of Crystal Vibrations: Localization Properties of Wave Functions in TwoDimensional Lattices
The localization properties of the wave functions of vibrations in twodimensional (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). Finitesize sheets with a hexagonal lattice (graphenelike materials), in addition, exhibit at zero energy a localization of the wave functions at zigzag edges, socalled 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 zeroenergy edge states, are localized at armchair edges. The results are corroborated based on participation ratios, obtained under various conditions.
 Authors:

^{[1]};
^{[2]};
^{[3]}
 Lanzhou Univ. (China). School of Physical Science and Technology. Key Lab. for Magnetism and Magnetic Materials of MOE
 Yale Univ., New Haven, CT (United States). Center for Theoretical Physics. Sloane Physics Lab.
 The Czech Academy of Sciences, Brno (Czech Republic). Inst. of Scientific Instruments
 Publication Date:
 Grant/Contract Number:
 FG0291ER40608; P2031307117S; LO1212
 Type:
 Accepted Manuscript
 Journal Name:
 Crystals
 Additional Journal Information:
 Journal Volume: 7; Journal Issue: 8; Journal ID: ISSN 20734352
 Publisher:
 MDPI
 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) (SC26); Czech Science Foundation; Ministry of Education, Youth and Sports of the Czech Republic
 Country of Publication:
 United States
 Language:
 English
 Subject:
 36 MATERIALS SCIENCE; 97 MATHEMATICS AND COMPUTING; algebraic models; graphenelike materials; striped structures; photonic crystals
 OSTI Identifier:
 1425398
Dietz, Barbara, Iachello, Francesco, and Macek, Michal. Algebraic Theory of Crystal Vibrations: Localization Properties of Wave Functions in TwoDimensional Lattices. United States: N. p.,
Web. doi:10.3390/cryst7080246.
Dietz, Barbara, Iachello, Francesco, & Macek, Michal. Algebraic Theory of Crystal Vibrations: Localization Properties of Wave Functions in TwoDimensional Lattices. United States. doi:10.3390/cryst7080246.
Dietz, Barbara, Iachello, Francesco, and Macek, Michal. 2017.
"Algebraic Theory of Crystal Vibrations: Localization Properties of Wave Functions in TwoDimensional 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 TwoDimensional Lattices},
author = {Dietz, Barbara and Iachello, Francesco and Macek, Michal},
abstractNote = {The localization properties of the wave functions of vibrations in twodimensional (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). Finitesize sheets with a hexagonal lattice (graphenelike materials), in addition, exhibit at zero energy a localization of the wave functions at zigzag edges, socalled 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 zeroenergy 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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