Dynamic response of a thermal transistor to time-varying signals

Thermal transistor, the thermal analog of an electronic transistor, is one of the most important thermal devices for microscopic-scale heat manipulating. It is a three-terminal device, and the heat current flowing through two terminals can be largely controlled by the temperature of the third one. Dynamic response plays an important role in the application of electric devices and also thermal devices, which represents the devices' ability to treat fast varying inputs. In this paper, we systematically study two typical dynamic responses of a thermal transistor, i.e., the response to a step-function input (a switching process) and the response to a square-wave input. The role of the length L of the control segment is carefully studied. It is revealed that when L is increased, the performance of the thermal transistor worsens badly. Both the relaxation time for the former process and the cutoff frequency for the latter one follow the power-law dependence on L quite well, which agrees with our analytical expectation. However, the detailed power exponents deviate from the expected values noticeably. This implies the violation of the conventional assumptions that we adopt.