  Anomalous electric currents, first predicted to emerge during large heavy ion
collision experiments, were also observed a few years ago in condensed matter
environments, exploring the fact that charge carriers in Dirac/Weyl semi-metals
exhibit a relativistic-like behavior. The mechanism through which such currents
are generated relies on an imbalance in the chirality of systems immersed in a
magnetic background, leading to the so-called chiral magnetic effect. While
chiral magnetic currents have been observed in materials in three space
dimensions, in this work we propose that a neat analog of the chiral magnetic
effect can be constructed in two space dimensions, corresponding to a novel
type of intrinsic half-integer Quantum Hall effect, thereby also offering a
topological protection mechanism for the current. The underlying mechanism can
occur in disturbed honeycomb lattices where both spin degeneracy and time
reversal symmetry are broken. These configurations harbor two distinct
gap-opening mechanisms that, when occurring simultaneously, drive slightly
different gaps in each valley, establishing an analog of the necessary chiral
imbalance. Some examples of promising material setups that fulfill the
prerequisites of our proposal are also listed.
