Vibrational band structure of nanoscale phononic crystals

The vibrational properties of two-dimensional phononic crystals are studied with large-scale molecular dynamics simulations and finite element method calculation. The vibrational band structure derived from the molecular dynamics simulations shows the existence of partial acoustic band gaps along the $\Gamma$-M direction. The band structure is in excellent agreement with the results from the finite element model, proving that molecular dynamics simulations can be used to study the vibrational properties of such complex systems. An analysis of the structure of the vibrational modes reveals how the acoustic modes deviate from the homogeneous bulk behaviour for shorter wavelengths and hints towards a decoupling of vibrations in the phononic crystal.