Band Degeneracy and Normal State Properties of Twisted Bilayer Graphene at the Magic Angle

Recently, superconductivity is discovered in twisted bilayer graphene at a small twist angle. Associated this superconducting state is a whole host of unusual normal state properties:
(i) that the band degeneracy between charge neutrality and the insulating phase is 4, instead of the expected 8-fold degeneracy by counting all the relevant quantum numbers (valley indices, two layers and two spins),
(ii) the appearance of an insulating phase at a finite chemical potential below charge neutrality,
(iii) that the insulating phase is destroyed by an in-plane magnetic field,
(iv) a further reduction of the band degeneracy from 4 to 2 on at chemical potential away from the insulating phase,
(v) a large asymmetry of the size of Fermi surfaces on different sides of the insulating phase as reveal by quantum oscillation measurements.

In this talk, we show how (i) can come about through coupling of Dirac cones of the opposite valley index in different layers.
This reduction of degeneracy immediately provides a natural explanation for all other phenomena (ii) to (v); and that the insulating phase is associated with a spin density wave. Our picture also has implications on light scattering and Raman absorption experiments.