Thermal transistor utilizing gas-liquid transition

We propose a simple thermal transistor, a device to control heat current. In order to effectively change the current, we utilize the gas-liquid transition of the heat-conducting medium (fluid) because the gas region can act as a good thermal insulator. The three terminals of the transistor are located at both ends and the center of the system, and are put into contact with distinct heat baths. The key idea is a special arrangement of the three terminals. The temperature at one end (the gate temperature) is used as an input signal to control the heat current between the center (source, hot) and another end (drain, cold). Simulating the nanoscale systems of this transistor, control of heat current is demonstrated. The heat current is effectively cut off when the gate temperature is cold and it flows normally when it is hot. By using an extended version of this transistor, we also simulate a primitive application for an inverter.

Figure 1

(a) Arrangement of terminals in a standard transistor. The gate (G), which controls the current from the source (S) to the drain (D), is located in the middle between S and D. (b) Arrangement of terminals in the present thermal transistor. G, which controls the current from S to D, is located behind S.

Figure 2

Schematics of the system. $N$ particles are enclosed in the rectangular box ($L_x\times L_y\times L_z$). They can move all over the box and interact with each other through the LJ potential. Three gray rectangular regions (Gate, Source, and Drain) inside the box are set up as the areas of contact with the heat baths (at temperatures $T_{\mathrm{G}}$, $T_{\mathrm{S}},$ and $T_{\mathrm{D}}$). Only when the particles are inside these regions are they subjected to Langevin thermal forces. In most simulations, we used $L_x=60$, $L_y=L_z=48$, and $h=6$ locating the source region just in the center of the system. The wall conditions are applied on both ends along the $x$ direction and the periodic boundary conditions are applied along the other directions ($y,z$).

Figure 3

Heat currents (energy per unit time) ($J_{\mathrm{G}},J_{\mathrm{S}}$, and $J_{\mathrm{D}}$ averaged during $4000⩽t⩽5000$) from the three terminals (Gate, Source, and Drain) into the system for various gate temperature $T_{\mathrm{G}}$. The parameters $N/(L_x{L}_y{L}_z)=0.5(N=69120)$, $L_x=60,L_y=L_z=48,T_{\mathrm{S}}=1.2,$ and $T_{\mathrm{D}}=0.6$ were used. The ratio of $\left|J_{\mathrm{D}}\right|$ between the ON ($T_{\mathrm{G}}=1.2$) and OFF ($T_{\mathrm{G}}=0.6$) states is about $20$. For $T_{\mathrm{G}}=1.2$, random initial configurations were used (dependence on the initial condition is negligible for this state). For $T_{\mathrm{G}}<1.2$, initial configurations were taken from that at $t=5000$ for the gate temperature $T_{\mathrm{G}}+\Delta T$ ($\Delta T=0.05$).

Figure 4

Response of heat currents to the square wave input of $T_{\mathrm{G}}$ alternating between $1.2$ and $0.6$ with the period $5000$. Starting from the ON state, $T_{\mathrm{G}}$ was kept at $1.2$ (ON), and was switched to $0.6$ (OFF) at $t=5000$, and then switched back to $1.2$ (ON) at $t=10,000$, and so forth. Heat currents averaged during each $100$ time unit are plotted. The parameters, except $T_{\mathrm{G}}$, are the same as those in Fig. 3. Overshoot currents just after the switching are transient heat currents due to the formation/destruction of the liquid bridge between the source and the gate.

Figure 5

(a) Density profiles $\rho (x)$ and (b) temperature profiles $T(x)$ in the heat-conducting nonequilibrium steady states (ON and OFF states in Fig. 3).

Figure 6

Density dependence of heat currents for two typical gate temperatures: (a) $T_{\mathrm{G}}=0.6$, (b) $T_{\mathrm{G}}=1.2$. The parameters, except $N$, are the same as those in Fig. 3. For $T_{\mathrm{G}}=1.2$, random initial configurations were used. For $T_{\mathrm{G}}=0.6$, initial configurations were taken from the configurations at $t=5000$ for $T_{\mathrm{G}}=1.2$.

Figure 7

Schematics of the extended model. In the three rectangular regions (Gate, Source, Drain) inside the system, particles interact with the distinct Langevin heat baths. Assuming that these baths have finite heat capacities ($C_{\mathrm{G}},C_{\mathrm{S}}$,$C_{\mathrm{D}}$), the temperatures ($T_{\mathrm{G}},T_{\mathrm{S}}$,$T_{\mathrm{D}}$) of the Langevin baths are allowed to vary in time depending on energy exchange from the particles and that from the external baths of constant temperatures ($T_{\mathrm{G}}^{\mathrm{ext}},T_{\mathrm{S}}^{\mathrm{ext}}$,$T_{\mathrm{D}}^{\mathrm{ext}}$) attached via the constant heat conductivities ($K_{\mathrm{G}},K_{\mathrm{S}}$,$K_{\mathrm{D}}$).

Figure 8

Time developments of the terminal temperatures in the extended model (see Fig. 7) for applied square wave of $T_{\mathrm{G}}^{\mathrm{ext}}$ alternating between $0.6$ and $1.2$ with the period $10,000$. The initial condition was taken from the configuration in the steady state for $T_{\mathrm{G}}=1.2$ (obtained after a transient run starting from a random initial configuration). The parameters $N/L_x{L}_y{L}_z=0.4$, $K_{\mathrm{S}}=150$, $K_{\mathrm{G}}=K_{\mathrm{D}}={10}^5$, $C_{\mathrm{G}}=C_{\mathrm{S}}=C_{\mathrm{D}}=20,000$, $T_{\mathrm{S}}^{\mathrm{ext}}=1.2$, and $T_{\mathrm{D}}^{\mathrm{ext}}=0.6$ were used.