Phonon spectrum and gap quasi-breathers in B2 (CsCl) structure

Discrete breathers can exist in nonlinear lattices as exact time-periodic solutions only in the absence of perturbations. In reality, long-lived spatially localized vibrational modes, called quasi-breathers (QBs), are of interest because they contribute to the macroscopic properties of crystals. Crystals with complex structure may have a gap in the phonon spectrum, and gap QBs may exist, vibrating at frequencies in the gap. Here, a binary crystal with B2 (CsCl) structure is analyzed taking into account interactions up to the fourth neighbor. The atoms of two spices have masses $m_1$ and $m_2$. The pairwise interatomic interactions with hard or soft cubic anharmonicity are considered. The conditions on the mass ratio $m_2/m_1$ and the stiffness of the interatomic bonds are derived under which the gap appears in the phonon spectrum and short- or long-lived gap QBs can exist. Short-lived QBs have the main frequency in the gap, but higher harmonics fall in the optical band of the phonon spectrum. Long-lived QBs have the main frequency and all higher harmonics outside the phonon spectrum. Examples of numerically found gap QBs are given. Our results provide a theoretical background for finding gap QBs in B2 crystals with components whose difference in atomic mass is large enough to open a gap in the phonon spectrum; examples of such crystals are given.