A narrow magic window for ultraflat bands and emergent heavy fermions near the magic angle in twisted bilayer graphene

The notion of a single "magic angle" in twisted bilayer graphene has evolved into a fascinating array of magic angles and ranges each describing different facets of the material's behavior.  While the original continuum model predicted a nominal magic angle, its simplicity ignored the intricate interplay of different physical phenomena.  For example, lattice relaxation [1] near the magic angle shifts its value upward, only to be counteracted by pseudomagnetic fields.  Including a symmetry allowed relaxation parameter changes this magic angle to a magic range.  Yet another magic angle emerges from the coupling to phonons when the Fermi velocity equals the phonon sound velocity.  Building upon this rich tapestry of magical effects, we will discuss our recent work on the convergence of lattice relaxation and Hartree interaction near the magic angle [2]. We unveil a previously unreported Lifshitz transition to a Fermi surface topology that supports a "heavy fermion" pocket and an ultraflat band pinned to the Fermi energy. Analytical and numerical insights shed light on the narrow "magic angle range" where the “heavy fermion” is stable and make predictions for its experimental observation.  We believe that the bands presented here are accurate  at high temperature and provide a good starting point to understand the myriad of complex behavior observed in this system.
 
[1] “Analytical Model for Atomic Relaxation in Twisted Moiré Materials” by MMA Ezzi, GN Pallewela, C De Beule, EJ Mele, and S Adam, arXiv:2401.00498 (2024)
[2]  “A self-consistent Hartree theory for lattice-relaxed magic-angle twisted bilayer graphene” by MMA Ezzi, L Peng, Z Liu, JHZ Chao, GN Pallewela, D Foo, and S Adam arXiv:2404.17638 (2024)