Phonon transport through a three-dimensional abrupt junction

By using the scattering matrix method, the authors investigate the transmission coefficient and thermal conductance of acoustic phonon through a three-dimensional abrupt junction at low temperatures. It is found that the transmission coefficient of long-wavelength phonon strongly depends on the geometrical parameters of the structure as the incident frequency omega -> 0, and there exist some dips in the transmission spectrum with an increase of incident frequency omega. In the meantime, as the temperature T -> 0, the thermal conductance is strongly influenced by the abrupt junction structure. These results are not in agreement with previous theoretical studies for the case of two-dimensional structure and can be used as a guideline for the thermal management of the various nanostructures.