Lattice vibrations in the Frenkel-Kontorova model. I. Phonon dispersion, number density, and energy
Abstract
We studied the lattice vibrations of two inter-penetrating atomic sublattices via the Frenkel-Kontorova (FK) model of a linear chain of harmonically interacting atoms subjected to an on-site potential, using the technique of thermodynamic Green's functions based on quantum field-theoretical methods. General expressions were deduced for the phonon frequency-wave-vector dispersion relations, number density, and energy of the FK model system. In addition, as the application of the theory, we investigated in detail cases of linear chains with various periods of the on-site potential of the FK model. Some unusual but interesting features for different amplitudes of the on-site potential of the FK model are discussed. In the commensurate structure, the phonon spectrum always starts at a finite frequency, and the gaps of the spectrum are true ones with a zero density of modes. In the incommensurate structure, the phonon spectrum starts from zero frequency, but at a non-zero wave vector; there are some modes inside these gap regions, but their density is very low. In our approximation, the energy of a higher-order commensurate state of the one-dimensional system at a finite temperature may become indefinitely close to the energy of an incommensurate state. This finding implies that the higher-order incommensurate-commensurate transitionsmore »
- Authors:
-
- Brookhaven National Lab. (BNL), Upton, NY (United States)
- Publication Date:
- Research Org.:
- Brookhaven National Laboratory (BNL), Upton, NY (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1193218
- Alternate Identifier(s):
- OSTI ID: 1185135
- Report Number(s):
- BNL-108038-2015-JA
Journal ID: ISSN 1098-0121; PRBMDO; R&D Project: MA015MACA; KC0201010
- Grant/Contract Number:
- SC00112704; AC02-98CH10886
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B, Condensed Matter and Materials Physics
- Additional Journal Information:
- Journal Volume: 91; Journal Issue: 22; Journal ID: ISSN 1098-0121
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Citation Formats
Meng, Qingping, Wu, Lijun, Welch, David O., and Zhu, Yimei. Lattice vibrations in the Frenkel-Kontorova model. I. Phonon dispersion, number density, and energy. United States: N. p., 2015.
Web. doi:10.1103/PhysRevB.91.224305.
Meng, Qingping, Wu, Lijun, Welch, David O., & Zhu, Yimei. Lattice vibrations in the Frenkel-Kontorova model. I. Phonon dispersion, number density, and energy. United States. https://doi.org/10.1103/PhysRevB.91.224305
Meng, Qingping, Wu, Lijun, Welch, David O., and Zhu, Yimei. Wed .
"Lattice vibrations in the Frenkel-Kontorova model. I. Phonon dispersion, number density, and energy". United States. https://doi.org/10.1103/PhysRevB.91.224305. https://www.osti.gov/servlets/purl/1193218.
@article{osti_1193218,
title = {Lattice vibrations in the Frenkel-Kontorova model. I. Phonon dispersion, number density, and energy},
author = {Meng, Qingping and Wu, Lijun and Welch, David O. and Zhu, Yimei},
abstractNote = {We studied the lattice vibrations of two inter-penetrating atomic sublattices via the Frenkel-Kontorova (FK) model of a linear chain of harmonically interacting atoms subjected to an on-site potential, using the technique of thermodynamic Green's functions based on quantum field-theoretical methods. General expressions were deduced for the phonon frequency-wave-vector dispersion relations, number density, and energy of the FK model system. In addition, as the application of the theory, we investigated in detail cases of linear chains with various periods of the on-site potential of the FK model. Some unusual but interesting features for different amplitudes of the on-site potential of the FK model are discussed. In the commensurate structure, the phonon spectrum always starts at a finite frequency, and the gaps of the spectrum are true ones with a zero density of modes. In the incommensurate structure, the phonon spectrum starts from zero frequency, but at a non-zero wave vector; there are some modes inside these gap regions, but their density is very low. In our approximation, the energy of a higher-order commensurate state of the one-dimensional system at a finite temperature may become indefinitely close to the energy of an incommensurate state. This finding implies that the higher-order incommensurate-commensurate transitions are continuous ones and that the phase transition may exhibit a “devil's staircase” behavior at a finite temperature.},
doi = {10.1103/PhysRevB.91.224305},
journal = {Physical Review. B, Condensed Matter and Materials Physics},
number = 22,
volume = 91,
place = {United States},
year = {Wed Jun 17 00:00:00 EDT 2015},
month = {Wed Jun 17 00:00:00 EDT 2015}
}
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Works referencing / citing this record:
Theory of Electron-Phonon-Dislon Interacting System - Toward a Quantized Theory of Dislocations
text, January 2017
- Li, Mingda; Tsurimaki, Yoichiro; Meng, Qingping
- arXiv
Theory of electron–phonon–dislon interacting system—toward a quantized theory of dislocations
journal, February 2018
- Li, Mingda; Tsurimaki, Yoichiro; Meng, Qingping
- New Journal of Physics, Vol. 20, Issue 2