Acoustic phonon transport and thermal conductance in a periodically modulated quantum wire

We investigate acoustic phonon transport and thermal conductance at low temperatures in a quantum wire with rectangle scatters periodically placed in the quantum channel. It is found that the transmission spectra of zero mode exhibits a series of resonant peaks-valleys structures, and the transport valley gradually develops into stop-frequency gap by increasing the number of the period. The number of resonant peaks or valleys between two nearest gaps is just twice as large as the number of the period. The result also indicates that the thermal conductance is sensitive to the number of the period and structural parameters, and the change is more pronounced in the structure with smaller number of period.