Introduction
It has been proposed [1,2] and numerically
demonstrated [3] that a large amplitude vibration in a
perfect 1-D lattice can localize because of anharmonicity. More
detailed analytical and numerical investigations of classical 1-D
anharmonic chains made possible by simple eigenvalue generating
recursion relations have revealed a variety of stable intrinsic
localized modes with frequencies outside of the plane wave
bands [3-8].
Recently quantum mechanical aspects of ILMs (Intrinsic Localized
Modes) have been considered [9,10]. Some progress
also has been reported for higher dimensional classical crystal
lattices with simple nearest-neighbor model
interactions [11,12]. Particularly important has been
the recognition that diatomic crystal potentials like the
Born-Mayer-Coulomb in 1-D produces an intrinsic gap mode (IGM)
between the optic and acoustic branches instead of an ILM above the
plane wave spectrum [13]. The possibility of IGMs in 3-D
anharmonic lattices with realistic potentials has remained elusive.
One approach has been to focus on crystal surfaces and edges where
harmonic localization already plays an important
role [14-16].
In this paper we demonstrate with molecular dynamics simulations
that, for sufficiently large vibrational amplitude, anharmonicity can
stabilize an IGM in a 3-D uniform diatomic crystal with rigid ion NaI
potential arranged in either the fcc or zinc blende structure. By
developing a self-consistent numerical technique for finding an
intrinsic localized mode eigenvector, we have been able to show that
for a given gap mode amplitude with the same potential that the
localization is much stronger for a Td
symmetry site when compared
to an Oh one.
[1] A.S.Dolgov, Sov. Phys. Solid State 28, 907 (1986).
[2] A.J.Sievers and S.Takeno, Phys. Rev. Lett. 61, 970 (1988).
[3] V.M.Burlakov, S.A.Kiselev, and V.N.Pyrkov,
Phys. Rev. B 42, 4921 (1990).
[4] J.B.Page, Phys. Rev. B 41, 7835 (1990).
[5] K.W.Sandusky, J.B.Page, and K.E.Schmidt,
Phys. Rev. B 46, 6161 (1992).
[6] Y.S.Kivshar and N.Flytzanis, Phys. Rev. A 46, 7972 (1992).
[7] S.A.Kiselev, S.R.Bickham, and A.J.Sievers, Comm. Cond. Mat.
Phys. 17, 135 (1995).
[8] A.Franchini, V.Bortolani, and R.F.Wallis,
Phys. Rev. B 53, 5420 (1996).
[9] T.Rossler and J.B.Page,
Phys. Rev. B 51, 11382 (1995).
[10] W.Z.Wang, J.Tinka Gammel, A.R.Bishop, and M.I.Salkola,
Phys. Rev. Lett. 76, 3598 (1996).
[11] S.Takeno, J. Phys. Soc. Jpn. 58, 3899 (1990).
[12] S.Flach, K.Kladko, and C.R.Willis,
Phys. Rev. E 50, 2293 (1994).
[13] S.A.Kiselev, S.R.Bickham, and A.J.Sievers, Phys. Rev. B
48, 13508 (1993).
[14] J.N.Teixeira and A.A.Maradudin,
Phys. Lett. A 205, 349 (1995).
[15] D.Bonart, A.P.Mayer, and U.Schroder,
Phys. Rev. Lett. 75, 870 (1995).
[16] D.Bonart, A.P.Mayer, and U.Schroder,
Phys. Rev. B 51, 13739 (1995).
Last modified: April 3, 1997