Thermal Logic Gates: Computation with Phonons

Logic gates are basic digital elements for computers. We build up thermal logic gates that can perform similar operations as their electronic counterparts. The thermal logic gates are based on nonlinear lattices, which exhibit very intriguing phenomena due to their temperature dependent power spectra. We demonstrate that phonons, the heat carriers, can also be used to carry information and processed accordingly. The possibility of nanoscale experiments is discussed.

Figure 1

(a) Configuration of the thermal transistor. (b) Heat currents through three terminals $D$, $S$, and $G$ versus temperature $T_G$. The NDTR is clearly seen in a wide region, namely, $J_D$ increases when temperature $T_G$ is increased. At $T_G=T_{\mathrm{on}}$ and $T_{\mathrm{off}}$, $J_G$ is exactly zero. Insets: power spectra of particles $O$ and $O^{\prime }$ near off and on states. Power spectrum of $O$ depends sensitively on temperature. It matches that of $O^{\prime }$ much better at the on state than at the off state, thus making much higher $J_D$ at the on state although the temperature difference between terminal $D$ and particle $O$ is much larger at the off state.

Figure 2

(a) $T_O-T_G$ versus $T_G$. Notice the super response that in the central region, $T_O-T_G$ increases when $T_G$ increases; namely, $T_O$ increases even greater than $T_G$. (b) $T_{O^{\prime }}$ versus $T_G$. Notice the negative response that $T_{O^{\prime }}$ decreases as $T_G$ increases.

Figure 3

(a) Structure of a thermal repeater. (b) Function of a thermal repeater that contains six thermal transistors. The outputs are better and better as the number of transistors is increased. The final output from the 6th transistor is very close to that of an ideal repeater.

Figure 4

(a) Structure of the thermal NOT gate. Through the $G$ segment, the signal is transferred to the $O$ point of the transistor. The output of the transistor (from the $O^{\prime }$ point) is transferred to the temperature divider. Plug the output of the temperature divider into a repeater; the final output is shown in (b) Function of the thermal NOT gate. It is very close to an ideal NOT gate. Inset: Structure of a two-resistor voltage divider, the counterpart of a temperature divider, which supplies a voltage lower than that of the battery. Without load, the output of the voltage divider is $V_{\mathrm{out}}=V{R}_2/(R_1+R_2)$.

Figure 5

(a) Structure of thermal AND and OR gates. Two inputs (after being standardized by repeaters) are transferred to a same repeater. (b) Function of thermal AND gate. We plot $T_{\mathrm{output}}$ versus $T_{\mathrm{input}1}$ while $T_{\mathrm{input}2}$ is fixed to $T_{\mathrm{on}}$. (c) Function of thermal OR gate. We plot $T_{\mathrm{output}}$ versus $T_{\mathrm{input}1}$ while $T_{\mathrm{input}2}$ is fixed to $T_{\mathrm{off}}$.