Unlike the electrical conductance that can be widely modulated within the same material even in deep nanoscale 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, gate, and 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 (hBN) under controlled strain. We derive the dielectric function of hBN from first principles, including the phonon-polariton linewidths computed by considering phonon isotope and anharmonic phonon-phonon scattering. Subsequently, we propose a strain-controlled hBN-based thermal switch that modulates thermal conductance by more than an order of magnitude, corresponding to an ON/OFF contrast ratio of 98%, in a deep subwavelength nanostructure.
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