  When two graphene layers are rotated from AA or AB configuration by a small
angle, the band structure changes dramatically. Numerical calculations have
shown that, at certain discrete angles called magic angles, the low energy
bands become flat leading to localization of electrons. The origin of this
strange behavior, however, is not well understood. Here, I propose a theory
that offers an understanding of the phenomenon, focusing on the first magic
angle. It is shown that coupling between the layers, in addition to
renormalizing the Dirac velocity, introduces higher order momentum terms in the
energy dispersion that are not all of the same sign. Partial cancellation among
these terms leads to the flatness of the low energy bands. Also, while there is
modulation of electron density in real space, there is no localization---the
modulation arises due to the superposition of plane wave states with different
momenta in the two layers. In addition, it is conjectured that there is an
underlying geometric reason for the appearance of more than one magic angle
which can be exploited to predict higher magic angles approximately without
computing the band structure.
