Quantized Heat Flow in the Hofstadter Butterfly.

While the Hofstadter butterfly is commonly observed in moiré superlattices, its thermal properties have not been investigated, particularly the quantized heat flow expected for Chern insulators. Here we report the first thermal transport measurements in a graphene and hexagonal boron nitride moiré superlattice under high magnetic field. We observe a quantized heat flow, uniquely set by the topological invariant, for all investigated states of the Hofstadter butterfly: quantum Hall states, Chern insulators, and even symmetry-broken Chern insulators emerging from strong electronic interactions. Our work firmly establishes the universality of the quantization of heat transport and its intimate link with topology.