  When two graphene sheets are twisted relative to each other by a small angle,
enhanced correlations lead to superconductivity whose origin remains under
debate. Here, we derive some general constraints on superconductivity in
twisted bilayer graphene (TBG), independent of its underlying mechanism.
Neglecting weak coupling between valleys, the global symmetry group of TBG
consists of independent spin rotations in each valley in addition to valley
charge rotations, $ {\rm SU}(2) \times {\rm SU}(2) \times {\rm U}_V(1) $. This
symmetry is further enhanced to a full ${\rm SU}(4)$ in the idealized chiral
limit. In both cases, we show that any charge $2e$ pairing must break the
global symmetry. Additionally, if the pairing is unitary the resulting
superconductor admits fractional vortices. This leads to the following general
statement: Any superconducting condensate in either symmetry class has to
satisfy one of three possibilities: (i) the superconducting pairing is
non-unitary, (ii) the superconducting condensate has charge $2e$ but admits at
least half quantum vortices which carry a flux of $h/4e$, or (iii) the
superconducting condensate has charge $2me$, $m>1$, with vortices carrying
$h/2me$ flux. The latter possibility can be realized by a symmetric charge $4e$
superconductor ($m=2$). Non-unitary pairing (i) is expected in TBG for
superconductors observed in the vicinity of flavor polarized states. On the
other hand, in the absence of flavor polarization, e.g. in the vicinity of
charge neutrality, one of the two exotic possibilities (ii) and (iii) is
expected. We sketch how all three scenarios can be realized in different limits
within a strong coupling theory of superconductivity based on skyrmions.
Finally we discuss the effect of symmetry lowering anisotropies and
experimental implications of these scenarios.
