### Abstract

A detailed account is given of the matching procedure devised to calculate surface phonon and resonance dispersion curves. Each kind of phonon symmetry is studied separately. A secular equation is first derived which is shown to contain in particular all the information on the dispersion curves and density of states of the bulk phonons along the reciprocal space direction not contained in the two-dimensional subspace associated with the surface. The dispersion curves of the surface phonons and resonances are obtained within a single framework by matching the evanescent and travelling solutions, respectively, of the secular equation, satisfying the boundary conditions brought about by the surface. A surface phonon is found to be the sum of evanescent waves. Bulk phonons of the same frequency travelling to and away from the surface are related to one another by reflection coefficients, for which sum rules are derived. An initial condition describing the scattering of an incoming bulk wave by the surface is introduced. The resonance frequency and the behaviour of the surface displacement spectral density in the vicinity of a bulk Van Hove singularity are shown to depend upon this initial condition.

Original language | English |
---|---|

Pages (from-to) | 4725-4736 |

Number of pages | 12 |

Journal | Journal of Physics C: Solid State Physics |

Volume | 20 |

Issue number | 29 |

DOIs | |

Publication status | Published - 20 Oct 1987 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Condensed Matter Physics

### Cite this

*Journal of Physics C: Solid State Physics*,

*20*(29), 4725-4736. https://doi.org/10.1088/0022-3719/20/29/010

**Calculation of surface phonons and resonances : The matching procedure revisited: I.** / Szeftel, J.; Khater, A.

Research output: Contribution to journal › Article

*Journal of Physics C: Solid State Physics*, vol. 20, no. 29, pp. 4725-4736. https://doi.org/10.1088/0022-3719/20/29/010

}

TY - JOUR

T1 - Calculation of surface phonons and resonances

T2 - The matching procedure revisited: I

AU - Szeftel, J.

AU - Khater, A.

PY - 1987/10/20

Y1 - 1987/10/20

N2 - A detailed account is given of the matching procedure devised to calculate surface phonon and resonance dispersion curves. Each kind of phonon symmetry is studied separately. A secular equation is first derived which is shown to contain in particular all the information on the dispersion curves and density of states of the bulk phonons along the reciprocal space direction not contained in the two-dimensional subspace associated with the surface. The dispersion curves of the surface phonons and resonances are obtained within a single framework by matching the evanescent and travelling solutions, respectively, of the secular equation, satisfying the boundary conditions brought about by the surface. A surface phonon is found to be the sum of evanescent waves. Bulk phonons of the same frequency travelling to and away from the surface are related to one another by reflection coefficients, for which sum rules are derived. An initial condition describing the scattering of an incoming bulk wave by the surface is introduced. The resonance frequency and the behaviour of the surface displacement spectral density in the vicinity of a bulk Van Hove singularity are shown to depend upon this initial condition.

AB - A detailed account is given of the matching procedure devised to calculate surface phonon and resonance dispersion curves. Each kind of phonon symmetry is studied separately. A secular equation is first derived which is shown to contain in particular all the information on the dispersion curves and density of states of the bulk phonons along the reciprocal space direction not contained in the two-dimensional subspace associated with the surface. The dispersion curves of the surface phonons and resonances are obtained within a single framework by matching the evanescent and travelling solutions, respectively, of the secular equation, satisfying the boundary conditions brought about by the surface. A surface phonon is found to be the sum of evanescent waves. Bulk phonons of the same frequency travelling to and away from the surface are related to one another by reflection coefficients, for which sum rules are derived. An initial condition describing the scattering of an incoming bulk wave by the surface is introduced. The resonance frequency and the behaviour of the surface displacement spectral density in the vicinity of a bulk Van Hove singularity are shown to depend upon this initial condition.

UR - http://www.scopus.com/inward/record.url?scp=0010483594&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0010483594&partnerID=8YFLogxK

U2 - 10.1088/0022-3719/20/29/010

DO - 10.1088/0022-3719/20/29/010

M3 - Article

VL - 20

SP - 4725

EP - 4736

JO - Journal of Physics Condensed Matter

JF - Journal of Physics Condensed Matter

SN - 0953-8984

IS - 29

ER -