  The unexpected discovery of superconductivity and strong electron correlation
in twisted bilayer graphene (TBG), a system containing only sp electrons, is
considered as one of the most intriguing developments in two-dimensional
materials in recent years. The key feature is the emergent flat energy bands
near the Fermi level, a favorable condition for novel many-body phases, at the
so-called "magic angles". The physical origin of these interesting flat bands
has been elusive to date, hindering the construction of an effective theory for
the unconventional electron correlation. In this work, we have identified the
importance of charge accumulation in the AA region of the moire supercell and
the most critical role of the Fermi ring in AA-stacked bilayer graphene. We
show that the magic angles can be predicted by the moire periodicity determined
by the size of this Fermi ring. The resonant criterion in momentum space makes
it possible to coherently combine states on the Fermi ring through scattering
by the moire potential, leading to flat bands near the Fermi level. We thus
establish the physical origin of the magic angles in TBG and identify the
characteristics of one-particle states associated with the flat bands for
further many-body investigations.

Mesoscale and Nanoscale Physics;Materials Science