Entropy plateaus, combinatorial degeneracy, local moments, and heavy-fermion mass renormalization in magic-angle...

Heavy-fermion behavior, driven by the interaction-induced enhancement of electronic mass, underpins exotic states ranging from unconventional superconductivity to quantum criticality. Long restricted to complex three-dimensional f-electron compounds, these phenomena are now predicted to emerge within the flat bands of magic-angle twisted bilayer graphene. Here, we use high-resolution planar tunneling spectroscopy to perform inverse-compressibility and entropy measurements, providing direct evidence for topological heavy-fermion behavior in magic-angle graphene. Our inverse-compressibility data reveal strong, filling-dependent mass renormalization, consistent with the hybridization between localized and itinerant electrons within a Kondo-lattice framework. Furthermore, entropy spectroscopy reveals two plateau structures whose degeneracies directly encode the combinatorial structure of local moment states. This 8-to-4-fold degeneracy reduction is an  entropic signature of strain-mediated symmetry breaking, consistent with the topological heavy-fermion model.