Kondo Phase in Twisted Bilayer Graphene -- A Unified Theory for Distinct Experiments

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 $T_K$ is found at the order of 1meV. A higher temperature than $T_K$ will drive the system into a metallic LM phase where disordered LM's and a Fermi liquid coexist. At integer fillings $\pm1,\pm2$, $T_K$ 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

Hierarchical Liouville-space approach for accurate and universal characterization of quantum impurity systems

A hierarchical equations of motion (HEOM) based numerical approach is developed for accurate and efficient evaluation of dynamical observables of strongly correlated quantum impurity systems. This approach is capable of describing quantitatively Kondo resonance and Fermi liquid characteristics, achieving the accuracy of latest high-level numerical renormalization group approach, as demonstrated on single-impurity Anderson model systems. Its application to a two-impurity Anderson model results in differential conductance versus external bias, which correctly reproduces the continuous transition from Kondo states of individual impurity to singlet spin-states formed between two impurities. The outstanding performance on characterizing both equilibrium and nonequilibrium properties of quantum impurity systems makes the HEOM approach potentially useful for addressing strongly correlated lattice systems in the frame work of dynamical mean field theory.Comment: 5 pages, 4 figures, to appear in PR