  Many systems exhibit boundary law scaling for entanglement entropy in more
than one spatial dimension. Here I describe three systems in 3+1 dimensions
that violate the boundary law for entanglement entropy. The first is free Weyl
fermions in a magnetic field, the second is a holographic strong coupling
generalization of the Weyl fermion system, and the third is a strong
topological insulator in the presence of dislocations. These systems are
unified by the presence of a low energy description that includes many gapless
1+1 dimensional modes. I conclude with some comments on the search for highly
entangled states of quantum matter and some potential experimental signatures.
