  We report a theoretical model for a thermal transistor in dielectric
four-terminal nanostructures based on mesoscopic ballistic phonon transport, in
which a steady thermal flow condition of system is obtained to set up the
temperature field effect of gate. In the environment, thermal flow shows the
transisting behaviors at low temperatures: saturation, asymmetry, and
rectification. The phenomena can be explained reasonably by the nonlinear
variation of the temperature dependence of propagating phonon modes in
terminals. The results suggest the possibility of the novel nano-thermal
transistor fabrication.
