In a one-dimensional monatomic lattice with both positive quadratic and quartic nearest-neighbor interaction potential the intrinsic odd-parity [1] and even parity [2] local modes appear above the top of the plane wave spectrum. When a cubic term is added to the interatomic potential, with increasing amplitude, the frequency of a stationary local mode decreases until it approaches the cutoff plane wave frequency, where the mode becomes unstable.

Examination of 1-D lattices with the Toda, Born-Mayer, Lennard-Jones or Morse two-body interatomic potentials demonstrates that intrinsic local modes do not appear above the top of plane wave spectrum [3]; however, diatomic lattices with the same interparticle interaction potentials do possess anharmonic gap modes with frequencies between acoustic and optic bands [4]. Both stationary and moving intrinsic anharmonic gap modes can be generated in diatomic lattices.

[1] A.J.Sievers and S.Takeno, Phys. Rev. Lett.

[2] J. B. Page, Phys. Rev. B

[3] S. R. Bickham, S. A. Kiselev, and A. J. Sievers, Physics Review B,

[4] S. A. Kiselev, S. R. Bickham, and A. J. Sievers, Physics Review B,

Last modified: August 12, 1997