Radiative Bistability and Thermal Memory

We predict the existence of a thermal bistability in many-body systems out of thermal equilibrium which exchange heat by thermal radiation using insulator-metal transition materials. We propose a writing-reading procedure and demonstrate the possibility to exploit the thermal bistability to make a volatile thermal memory. We show that this thermal memory can be used to store heat and thermal information (via an encoding temperature) for arbitrary long times. The radiative thermal bistability could find broad applications in the domains of thermal management, information processing, and energy storage.

Figure 1

Sketch of a radiative thermal memory. A membrane made of an IMT material is placed at a distance $d$ from a dielectric layer. The system is surrounded by two thermal baths at different temperatures $T_L$ and $T_R$. The temperature $T_2$ can be increased or reduced either by Joule heating by applying a voltage difference through a couple of electrodes or by using Peltier elements.

Figure 2

(a) Reflectance and (b) transmittance at normal incidence of a $1\mu \mathrm{m}$ thick ${\mathrm{VO}}_2$ membrane in its amorphous (metallic) and crystalline (dielectric) phases. This information is taken from the data of Barker et al. [17].

Figure 3

(a) Trajectories of temperatures (pink and turquoise lines) for different initial conditions in the plane ($T_1,T_2$) in a two-membrane ${\mathrm{SiO}}_2/{\mathrm{VO}}_2$ system with ${\delta }_1={\delta }_2=1\mu \mathrm{m}$. The dashed blue and solid red lines represent the local equilibrium conditions ${\mathrm{\Phi }}_1=0$ and ${\mathrm{\Phi }}_2=0$ of each membrane. The green (red) points denote the stable (unstable) global steady-state temperatures $(T_1^{(1)},T_2^{(1)})=(328.03\mathrm{K},337.77\mathrm{K})$, $(T_1^{(2)},T_2^{(2)})=(328.06\mathrm{K},338.51\mathrm{K})$, and $(T_1^{(3)},T_2^{(3)})=(324.45\mathrm{K},341.97\mathrm{K})$. The red arrows in the background represent the vector field $\mathbf{\Phi }$. The temperatures of thermal reservoirs are $T_L=320\mathrm{K}$ and $T_R=358\mathrm{K}$. (b) Temperature trajectories as in (a) but for a two-membrane ${\mathrm{SiO}}_2/{\mathrm{VO}}_2$ system with ${\delta }_1=1\mathrm{mm}$ and ${\delta }_2=1\mu \mathrm{m}$, choosing $T_L=320\mathrm{K}$ and $T_R=355\mathrm{K}$. In both configurations, the separation distance $d$ is much larger than the thermal wavelengths.

Figure 4

(a) Hysteresis of the ${\mathrm{VO}}_2$ membrane temperature during a transition between the thermal states 0 and 1 inside a two-membrane ${\mathrm{SiO}}_2/{\mathrm{VO}}_2$ system with ${\delta }_1={\delta }_2=1\mu \mathrm{m}$. The volumic powers supplied and extracted from the ${\mathrm{VO}}_2$ layer during time intervals $\mathrm{\Delta }{t}_1=0.4\mathrm{s}$ and $\mathrm{\Delta }{t}_2=1.5\mathrm{s}$ are $Q_2={10}^{-2}\mathrm{W}{\mathrm{mm}}^{-3}$ and $Q_2=-2.5\times {10}^{-2}\mathrm{W}{\mathrm{mm}}^{-3}$, respectively. The writing time of state 1 (0) from state 0 (1) is $\mathrm{\Delta }t(0\to 1)=4\mathrm{s}$ [$\mathrm{\Delta }t(1\to 0)=8\mathrm{s}$]. (b) Time evolution $T_1(t)$ and $T_2(t)$ of ${\mathrm{SiO}}_2$ and ${\mathrm{VO}}_2$ membrane temperatures. The thermal states 0 and 1 can be maintained for an arbitrarily long time, provided that the thermostats ($T_L=320\mathrm{K}$ and $T_R=358\mathrm{K}$) remain switched on.