Strong suppression of near-field thermal transport between twisted bilayer graphene near the magic angle

Twisted bilayer graphene (TBLG) has recently emerged as a versatile platform for studying a variety of exotic transport phenomena. Here, we present a theoretical study of near-field thermal radiation between suspended TBLG with a focus on the magic angle. Within the chirally symmetric continuum model, we observe a suppressed heat flow when approaching the magic angle owing to a reduced Drude weight, with greater suppressions at lower temperatures and larger gap sizes. When the chemical potential lies in the energy gap near the charge neutrality point, more than 100-fold heat-flow variation can be achieved at 50 K within 0.25{\deg}of twist. By reducing the electron scattering rate, the radiation spectrum near the magic angle dramatically narrows, leading to over 10,000-fold of suppression. In addition, supported TBLG is briefly considered to facilitate experimental measurement. With rationally tailored substrates, the heat-flow contrast can still exceed 1000. We also discuss lattice relaxation effect in terms of the interlayer coupling energy, finding that a stronger coupling leads to a smaller heat-flow contrast and more prominent multiband transport. Our results highlight the great potential of magic-angle TBLG in thermal transport, especially for controlling thermal radiation.