Figure 1

(a) Conventional device geometry for thermal rectification between two bodies consisting of two parallel plates. (b) The red solid and blue dashed lines denote the temperature dependence of a resonance of each body, respectively. The vertical dashed lines mark the operating temperatures $T_h$ and $T_l$. The red circles and the blue rings mark the resonance frequencies of two bodies at the operating temperatures, respectively. (c) The (overlapping) resonance frequencies of two bodies in the forward bias scenario in the conventional mechanism. (d) The (nonoverlapping) resonance frequencies of two bodies in the reverse bias scenario in the conventional mechanism. (e) Our device geometry for thermal rectification. For our representative implementation in our paper, two spheres have the radii of 96 and 10 nm, respectively, and the sphere-sphere distance is 26 nm. (f)–(g) Illustration of our mechanism for thermal rectification. The symbols have the same meaning as (b)–(d). Notice that the two bodies are on resonance in both the forward and reverse bias scenarios.Reuse & Permissions

Figure 2

(a) The solid black lines denote the temperature dependence of resonance frequencies of $m=0$ modes with different $L$ for a deep-subwavelength 3$C$-SiC sphere. At a given temperature, the resonance frequencies increase with $L$. We show here modes from $L=1$ to 9. The vertical dashed lines mark the operating temperatures $T_h$ and $T_l$. (b)–(c) The electric field $E_z$ distribution of $L=1$ and 2 modes, with $m=0$, in x-z plane with $y=0$. The $z$ axis is the horizontal direction. The radii of the spheres are 96 nm in (b) and 10 nm in (c).Reuse & Permissions

Figure 3

(a) The field distribution $E_z$ of ${|2\rangle }_{\mathrm{large}}$ and ${|1\rangle }_{\mathrm{small}}$. (b) The field distribution ($E_z$) of ${|1\rangle }_{\mathrm{large}}$ and ${|2\rangle }_{\mathrm{small}}$. In (a) and (b), for the mode of the small sphere, we only show the field inside the small sphere. (c) Coupling constants between the four lowest order modes of the two spheres in the $m=0$ channel. $L_1$ and $L_2$ are the total angular momenta of the modes of the large and the small spheres, respectively. (a)–(c) use the same parameters of the representative device implementation [Fig. 1e].Reuse & Permissions

Figure 4

(a) Net heat transfer magnitude as a function of the larger sphere temperature $T_1$ and the small sphere temperature $T_2$. (b) Rectification contrast ratio for different sets of $T_h$ and $T_l$. (a) and (b) use the same parameters of the representative device implementation [see Fig. 1e]. (c) Maximum rectification contrast ratio as a function of the contrast between the radii of the spheres ($r_{\mathrm{large}}/r_{\mathrm{small}}$), as the sphere-sphere distance is varied, for a temperature bias $T_h=700$ K and $T_l=200$ K. The small sphere has a radius of 10 nm. (d) The net heat transfer between two spheres as a function of the large sphere temperature $T_1$, where the small sphere is maintained at $T_2=500$ K, using the same parameters of the representative device implementation [see Fig. 1e].Reuse & Permissions

Figure 5

(a) Net heat transfer spectra in forward bias scenario (blue line), and reverse bias scenario (magenta line), for a bias condition $T_h=700$ K, $T_l=200$ K. (b) The net heat transfer spectrum (blue line), far-field radiation spectra of the large sphere (green dashed line) and the small sphere (red dash-dotted line) in the forward bias scenarios. (c) The net heat transfer spectrum (magenta line), far-field radiation spectra of the large sphere (green dashed line) and the small sphere (red dash-dotted line) in the reverse bias scenarios. (a)–(c) use the same parameters of the representative device implementation [see Fig. 1e].Reuse & Permissions

Figure 6

(a) Wave forms for the temperatures of the contacts ${\tau }_1$ and ${\tau }_2$, the temperatures of two spheres $T_1$ and $T_2$, and net heat transfer, in three frequencies, i.e., 10, 100, and 500 MHz, as denoted by the circles in (b). The first row shows wave forms of the temperatures of the contacts ${\tau }_1$ (blue line) and ${\tau }_2$ (green dashed line). The second row shows wave forms of the temperatures of the two spheres $T_1$ (blue line) and $T_2$ (green dashed line). The third row shows wave forms of net heat transfer $Q(T_1,T_2)$ (red line). The contact conductances are $h_1=4512$ nW, $h_2=5.1$ nW. (b) Frequency dependence of rectification contrast ratio for $A=250$ K. (a) and (b) use the same parameters of the representative device implementation [see Fig. 1e].Reuse & Permissions