Kondo phase in twisted bilayer graphene

A number of interesting physical phenomena have been discovered in magic-angle twisted bilayer graphene (MATBG), such as superconductivity, correlated gapped and gapless phases, etc. The gapped phases are believed to be symmetry-breaking states described by mean-field theories, whereas gapless phases exhibit features not explained by mean-field theories. This work, using a combination of poor man's scaling, numerical renormalization group, and dynamic mean-field theory, demonstrates that the gapless phases are the heavy-Fermi-liquid state, where some symmetries might be broken while the others are preserved. We adopt the recently proposed topological heavy-fermion model for MATBG, where effective local orbitals around AA-stacking regions and Dirac fermions surrounding them play the roles of local moments (LM's) and itinerant electrons, respectively. At zero temperature and most noninteger fillings, the ground states are found to be heavy Fermi liquids and exhibit Kondo resonance peaks. The Kondo temperature T₊ is found at the order of 1 meV. A higher temperature than T₊ will drive the system into a metallic LM phase where disordered LM's, obeying Curie's law, and a Fermi liquid formed by itinerant electrons coexist. At integer fillings 1, 2, T₊ is suppressed to zero or a value weaker than the Ruderman-Kittel-Kasuya-Yoshida interaction, leading to Mott insulators or symmetry-breaking states. Remarkably, this theory offers a unified explanation for several experimental observations, such as zero-energy peaks and quantum-dot-like behaviors in STM, the so-called Pomeranchuk effect, and the sawtooth feature of inverse compressibility, etc. For future experimental verification, we predict that the Fermi surface in the gapless phase will shrink upon heating, as a characteristic of the heavy Fermi liquid. We also conjecture that the heavy Fermi liquid is the parent state of the observed unconventional superconductivity because the Kondo screening reduces the overwhelming Coulomb interaction (U600. 28em{0ex}meV) to a rather small residual effective interaction (U^*10. 28em{0ex}meV) that is comparable to possible weak attractive interactions.