Acoustic phonon transport through a quantum waveguide with two stubs

Using the scattering matrix method, we investigate the acoustic phonon transmission and thermal conductance in a quantum waveguide with two stubs at low temperatures. It is found that the threshold frequency of the onset of each phonon mode travelling through the quantum waveguide depends on the stub heights. The thermal conductance exhibits oscillatory decaying behaviour with the width between the two stubs due to the coupling effects between them. In addition, the transmission coefficient and thermal conductance are also sensitive to the widths and heights of the stubs. It is suggested that changing the geometric parameters of the stubs could provide an efficient way to control the thermal conductance of the proposed micro-structures artificially.