Deep-Subwavelength Thermal Switch via Resonant Coupling in Monolayer Hexagonal Boron Nitride

Unlike the electrical conductance that can be widely modulated within the same material even in deep-subwavelength devices, tuning the thermal conductance within a single material system or nanostructure is extremely challenging and requires a large-scale device. This prohibits the realization of robust on/off states in switching the flow of thermal currents. Here, we present the theory of a thermal switch based on resonant coupling of three photonic resonators, in analogy to the field-effect electronic transistor composed of a source, a gate, and a drain. As a material platform, we capitalize on the extreme tunability and low-loss resonances observed in the dielectric function of monolayer hexagonal boron nitride ($h$-BN) under controlled strain. We derive the dielectric function of $h$-BN from first principles, including the phonon-polariton line widths computed by considering phonon-isotope and anharmonic phonon-phonon scattering. Subsequently, we propose a strain-controlled $h$-BN–based thermal switch that modulates the thermal conductance by more than an order of magnitude, corresponding to a contrast ratio in the thermal conductance of $98\mathrm{\%}$, in a deep-subwavelength nanostructure.

Figure 1

The concept of a photonic thermal switch based on resonant coupling between thermally excited modes. Resonator $S$ represents the source, resonator $G$ the gate, and resonator $D$ the drain.

Figure 2

The concept of the mechanism that leads to a large on/off ratio in the thermal-switch configuration described in Fig. 1: (a),(b) pertaining to on and off states for a symmetric switch with small loss rate ${\gamma }_{\mathrm{small}}$; (c),(d) corresponding to the same symmetric switch with the same $\mathrm{\Delta }\omega$, for a large loss rate ${\gamma }_{\mathrm{large}}=20{\gamma }_{\mathrm{small}}$.

Figure 3

(a) The resonance frequency ${\omega }_{\mathrm{LO}}$ and (b) the linewidth, ${\mathrm{\Gamma }}_{\mathrm{LO}}$, of the longitudinal-optical phonon of monolayer $h$-BN as a function of strain, computed ab initio [ [45]; see the discussion around Eq. (8)]. (c) The real part of the dielectric function of monolayer $h$-BN, ${ϵ}_{h\text{−}\mathrm{BN}}(\omega ,X)$, as a function of the frequency for different strains, $X$.

Figure 4

(a) A schematic of the $h$-BN–based thermal switch composed of three $h$-BN monolayers at different strains $X_S$, $X_G$, and $X_D$. (b) The spectral heat flux to the drain [$J_D(\omega )$] for $X_S=0\mathrm{\%}$, $X_G=0.5\mathrm{\%}$, and $X_D=1\mathrm{\%}$, calculated from coupled-mode theory (circles) and fluctuational electrodynamics (solid curve). The triplet of resonances near 0.17 eV and near 0.1925 eV correspond to the symmetric and antisymmetric SPhP modes, respectively, which dominate the near-field heat transfer. The temperatures are set to $T_S=500$ K, $T_D=300$ K, and $T_G=430$ K.

Figure 5

The thermal currents $J_D$ and $J_G$ as a function of the strain in the gate, $X_G$: (a) for the symmetric structure for $T_G=430$ K, which minimizes $J_G$; (b) for the asymmetric structure for a floating $T_G$ (inset) that minimizes $J_G$; (c) for the asymmetric structure for $T_G=430$ K. (d) The thermal conductance $\rho$ as a function of the strain in the gate for the cases in the following panels: (a) black, near $T=430$ K, (b) blue, near $T=T_G$ [see inset in (b)], and (c) green near $T=430$ K , respectively.

Figure 6

(a) The real part of the dielectric function of monolayer $h$-BN for different strains. (b),(c) The spectral heat flux to the drain [$J_D(\omega )$] for the symmetric and asymmetric thermal switches, respectively, for $T_S=500$ K, $T_D=300$ K, and $T_G=430$ K. The black curves pertain to $X_G=0\mathrm{\%}$, the cyan curves pertain to $X_G=0.5\mathrm{\%}$, and the red curves pertain to $X_G=1\mathrm{\%}$.

Figure 7

(a) The thermal currents $J_D$ and $J_G$ as a function of the strain in the gate, for the photonic thermal switch with tungsten substrates on the source and the drain. (b) The corresponding thermal conductance $\rho$ near $T=885$ K. (c) The spectral heat flux to the drain [$J_D(\omega )$], for $T_S=1000$ K and $T_D=800$ K. The black curve pertains to $X_G=0\mathrm{\%}$, the cyan curve pertains to $X_G=0.5\mathrm{\%}$, and the red curve pertains to $X_G=1\mathrm{\%}$. The temperature of the gate, $T_G$, floats such that $J_G=0$.

Figure 8

The summarized results of all the cases considered. The relative change in the thermal conductance, as defined in Eq. (12), with respect to its value at $X_G=0\mathrm{\%}$. The black curve corresponds to the results of Fig. 5, the symmetric configuration of the free-standing $h$-BN monolayers, whereas the blue curve corresponds to the results of Fig. 5, the asymmetric configuration of free-standing $h$-BN monolayers, both for a floating temperature of the gate. The green curve pertains to the results of Fig. 5, the same asymmetric configuration for a fixed $T_G$. Finally, the red curve corresponds to the results of Fig. 7, in which case a tungsten substrate is considered adjacent to the source and drain $h$-BN monolayers.