  Electrons on honeycomb or pi-flux lattices obey effective massless Dirac
equation at low energies and at the neutrality point, and should suffer quantum
phase transitions into various Mott insulators and superconductors at strong
two-body interactions. We show that 35 out of 36 such order parameters that
provide Lorentz-invariant mass-gaps to Dirac fermions can be organized into a
single irreducible tensor representation of the $SO(8)$ symmetry of the
two-dimensional Dirac Hamiltonian for the spin-1/2 lattice fermions. The
minimal interacting Lagrangian away from the neutrality point has the $SO(8)$
symmetry reduced to $U(1) \times SU(4)$ by finite chemical potential, and it
allows only two independent interaction terms. When the Lagrangian is nearly
$SO(8)$-symmetric and the ground state insulating at the neutrality point, we
argue it turns superconducting at the critical value of the chemical potential
through a ``flop" between the tensor components. The theory is exactly solvable
when the $SU(4)$ is generalized to $SU(N)$ and $N$ taken large. A lattice
Hamiltonian that may exhibit this transition, parallels with the Gross-Neveu
model, and applicability to related electronic systems are briefly discussed.
