Kondo phase in twist bilayer graphene

While the gapped phases in magic-angle twisted bilayer graphene (MATBG) are believed to be symmetry-breaking states described by mean-field theories, the gapless phases exhibit features beyond the mean field. This work, based on the recently proposed topological heavy fermion model for MATBG, combining poor man's scaling, numerical renormalization group, and dynamic mean-field theory, demonstrates that the gapless phases are the heavy Fermi liquid state with some symmetries broken and the others preserved. At zero temperature and most non-integer fillings, the ground states are found to be heavy Fermi liquids with the Kondo temperature $T_K$ at the order of 1meV. A higher temperature than $T_K$ drives the system into a metallic LM phase where disordered local moments and a Fermi liquid coexist. At integer fillings ±1,±2, $T_K$ is suppressed to zero or a value weaker than RKKY interaction, leading to Mott insulators or symmetry-breaking states. This theory explains experimental observations, including zero-energy peaks and quantum-dot-like behaviors in STM, the Pomeranchuk effect, the saw-tooth feature of inverse compressibility, etc. We predict that the Fermi surface in the gapless phase will shrink upon heating. We also conjecture that the heavy Fermi liquid is the parent state of the observed unconventional superconductivity since the Kondo screening effectively reduces the Coulomb interaction (~60meV) to a small value (~1meV) comparable to possible weak attractive interactions.