  An interaction-driven nonzero quantum Hall conductivity is shown to occur in
time-reversal symmetric massive Dirac materials, in the absence of any external
agent. The effect is produced through the dynamical breakdown of time-reversal
symmetry, which is generated by quantum fluctuations, when the full dynamical
electromagnetic interaction among the electrons is taken into account. The
manifestation of this emergent parity anomaly should be observed in materials
such as silicene, stanene, germanene and transition metal dichalcogenides, at
low enough temperatures.
