The reason for existence of discrete breathers in 2D and 3D morse crystals

Abstract

It is known that crystals can support discrete breathers (DBs) — periodic in time and spatially localized vibrational modes. DB does not radiate energy, as its frequency does not lie within the spectrum of small-amplitude traveling waves (phonons). DB frequency can leave the spectrum of low-amplitude oscillations due to the nonlinearity of the interatomic potentials, as it is well known that the frequency of a nonlinear oscillator depends on the amplitude. Theoretically, it was shown that DB cannot exist in a one-dimensional chain of identical point masses interacting with each other through the Toda, Born-Mayer, Lennard-Jones or Morse potential. The reason of non-existence of DB is the softness of the considered potentials, which does not allow to form a spatially localized mode with frequency above the phonon spectrum. On the basis of this rigorous result, it was concluded that because of the softness of the interatomic interactions in crystals with a simple structure (e.g., in pure metals) existence of DB is very unlikely. Attention should be paid to crystals with a gap in phonon spectrum. In such crystals localized vibrational modes may have frequencies decreasing with amplitude and entering the gap of the phonon spectrum. The first successful attempt to excite a gap DB in alkali halide NaI crystal dates back to 1997, for this purpose, the method of molecular dynamics was used. However, in 2011 DBs with frequencies higher than the phonon spectrum were discovered in pure metals, which poses the question about the conditions of the existence of DBs in crystals with realistic interatomic potentials. In this paper we show that the dimension of the crystal is important, and the Morse crystals of dimension higher than one can support DBs with frequencies above the phonon spectrum.