Vibration spectra of soliton boundaries separating nanostructured 2D hexagonal lattice domains

We investigate the vibration spectra at domain boundaries called heavy and superheavy solitons that separate phase domains in hexagonal two dimensional lattices. The breakdown of translation symmetry in the 2D plane, normal to a soliton domain boundary, gives rise to localized vibration effects. The matching method is used to calculate the characteristic vibration Green functions, spectral densities, and densities of states, for the vibration components of the individual atomic sites that constitute a complete representation of the heavy and superheavy soliton domain boundaries. The variations of these vibration spectra due to changes in the homogeneous elastic constraints in the soliton domain boundary are calculated. It is shown that the calculated vibration spectra are sensitive and explicit signatures for the softening and hardening effects. The theoretical results yield criteria under certain experimental conditions, as regards the interpretation of the measurements of the elastic constraints in the domain boundaries.