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 beyond mean field. This work, 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. We adopt the recently proposed
topological heavy fermion model for MATBG with effective local orbitals around
AA-stacking regions and Dirac fermions surrounding them. At zero temperature
and most non-integer fillings, the ground states are found to be heavy Fermi
liquids and exhibit Kondo resonance peaks. The Kondo temperature TK​ is found
at the order of 1meV. A higher temperature than TK​ will drive the system
into a metallic LM phase where disordered LM's and a Fermi liquid coexist. At
integer fillings ±1,±2, TK​ is suppressed to zero or a value weaker
than RKKY interaction, leading to Mott insulators or symmetry-breaking states.
This theory offers a unified explanation for several experimental observations,
such as zero-energy peaks and quantum-dot-like behaviors in STM, the
Pomeranchuk effect, and the saw-tooth 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 (~60meV) to a rather small
effective interaction (~1meV) comparable to possible weak attractive
interactions.Comment: DMFT calculations for the THF model and discussions on possible
symmetry-breaking states are adde