Non-dissipative anomalous currents in 2D materials: the parity magnetic effect as an analog of the chiral magnetic effect

Anomalous electric currents along a magnetic field, 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 (CME). While chiral magnetic currents have been observed in materials in three space dimensions, in this work we propose that an 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. While the 3D chiral anomaly underpins the CME, its 2D cousin is emerging from the 2D parity anomaly, we thence call it the parity magnetic effect (PME). It 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.