Quantized heat flow in moiré chern bands of bilayer graphene

When electrons are subjected simultaneously to a magnetic field and a periodic potential, they form the fractal Hofstadter spectrum, whose topological gaps host quantum Hall and Chern insulating states with distinct Chern numbers. While electrical transport has established the topology of these states, whether their heat transport is likewise universal has remained unexplored. Here, we measure the thermal conductance of quantum Hall, Chern insulator, and interaction-driven symmetry-broken Chern insulator states in a bilayer graphene-hexagonal boron nitride moir\'e superlattice with a moir\`e wavelength of $\sim$14 nm using Johnson-noise thermometry. We find that the thermal conductance ($G_Q$) is quantized in units of the thermal conductance quantum ($G_Q = t\kappa_0T$) and is determined solely by the Chern number ($t$), independent of the microscopic origin of the topological state. By directly revealing universal topological heat transport in Hofstadter bands, our work establishes thermal conductance as a stringent probe of moir\'e topological matter and provides a route to investigating more exotic phases, including fractional Chern insulators.