Heat transport in a four-perpendicularity-bend quantum waveguide

Using the scattering matrix method, we investigate acoustic phonon transmission and thermal conductance in a four-perpendicularity-bend quantum waveguide at low temperatures. The transmission spectrum of the quantum waveguide displays a series of resonant peaks and dips; and when one of the bend heights is larger than or equal to the minimum of the dimensions of the phonon channel in the quantum waveguide, a stop-frequency gap will appear; and some single four-perpendicularity-bend quantum waveguides with larger bend heights exhibit narrower width or smaller number of the stop-frequency gaps than that with smaller bend heights. The thermal conductivity is much sensitive to the change of the smaller heights and longitudinal lengths of the bend section; and the thermal conductivity decreases with the increasing of the temperature first, then increases after it reaches a minimum. The investigations of multiple four-perpendicularity-bend waveguides connected in series indicate that the first additional waveguide suppresses the transmission coefficient and forms the stop-frequency gap; and two additional resonance peaks will be formed when each four-perpendicularity-bend waveguide is added in the series. The results could be useful for controlling thermal conductance artificially and the design of phonon devices.