Nonlinear Gap Modes in a 1D Alternating Bond Monatomic Lattice with Anharmonicity

We analytically study the nonlinear localized gap modes in a one-dimensional atomic chain with uniform atomic mass but two periodically alternating force constants between the nearest neighbors by means of a quasi-continuum approximation. This model simulates a row of atoms in the <111> direction of a diamond-structure type of crystals or molecular crystals with alternating double and single bonds. For this lattice system, we find that the harmonic plus quartic anharmonic terms of inter-site potential produce a new type of nonlinear localized gap modes with a slightly asymmetry distribution of atomic displacements. These localized gap modes are somewhat different from widely studied localized gap modes with a symmetry atomic displacement distribution in diatomic ion lattices.