Lattice vibrations in the Frenkel-Kontorova model. I. Phonon dispersion, number density, and energy [electronic resource].
- Washington, D.C. : United States. Dept. of Energy. Office of Basic Energy Sciences, 2015. and Oak Ridge, Tenn. : Distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy
- Physical Description:
- Article numbers 224,305 : digital, PDF file
- Additional Creators:
- Brookhaven National Laboratory, United States. Department of Energy. Office of Basic Energy Sciences, and United States. Department of Energy. Office of Scientific and Technical Information
- Restrictions on Access:
- Free-to-read Unrestricted online access
- 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.
- Published through SciTech Connect., 06/17/2015., "bnl--108038-2015-ja", "KC0201010", Physical Review. B, Condensed Matter and Materials Physics 91 22 ISSN 1098-0121; PRBMDO AM, and Meng, Qingping; Wu, Lijun; Welch, David; Zhu, Yimei.
- Funding Information:
- SC00112704 and MA015MACA
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