  The low-energy bands of twisted bilayer graphene form Dirac cones with
approximate electron-hole symmetry at small rotation angles. These crossings
are protected by the emergent symmetries of moir\'e patterns, conferring a
topological character to the bands. Strain accumulated between layers
(heterostrain) shifts the Dirac points both in energy and momentum. The overlap
of conduction and valence bands favors an excitonic instability of the Fermi
surface close to the neutrality point. The spontaneous condensation of
electron-hole pairs breaks time reversal symmetry and the separate conservation
of charge within each valley sector. The order parameter describes interlayer
circulating currents in a Kekul\'e-like orbital magnetization density wave.
Vortices in this order parameter carry fermion numbers owing to the underlying
topology of the bands. This mechanism may explain the occurrence of insulating
states at neutrality in the most homogenous samples, where uniform strain
fields contribute both to stabilizing the relative orientation between layers
and to the formation of an excitonic gap.
