  We investigate the entanglement entropy (EE) and charge fluctuations in
models where the low energy physics is governed by massless Dirac fermions. We
focus on the response to flux insertion which, for the EE, is widely assumed to
be universal, i.e., independent of the microscopic details. We provide an
analytical derivation of the EE and charge fluctuations for the seminal example
of graphene, using the dimensional reduction of its tight-binding model to the
one-dimensional Su-Schrieffer-Heeger model. Our asymptotic expression for the
EE matches the conformal field theory prediction. We show that the charge
variance has the same asymptotic behavior, up to a constant prefactor. To check
the validity of universality arguments, we numerically consider several models,
with different geometries and number of Dirac cones, and either for strictly
two-dimensional models or for gapless surface mode of three-dimensional
topological insulators. We also show that the flux response does not depend on
the entangling surface geometry as long as it encloses the flux. Finally we
consider the universal corner contributions to the EE. We show that in the
presence of corners, the Kitaev-Preskill subtraction scheme provides
non-universal, geometry dependent results.
