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We analyze the magneto-optical conductivity (and related magnitudes liketransmittance and Faraday rotation of the irradiated polarized light) of someelemental two-dimensional Dirac materials of group IV (graphene analogues,buckled honeycomb lattices, like silicene, germanene, stannane, etc.), group V(phosphorene), and zincblende heterostructures (like HgTe/CdTe quantum wells)near the Dirac and gamma points, under out-of-plane magnetic and electricfields, to characterize topological-band insulator phase transitions and theircritical points. We provide plots of the Faraday angle and transmittance as afunction of the polarized light frequency, for different external electric andmagnetic fields, chemical potential, HgTe layer thickness and temperature, totune the material magneto-optical properties. We have shown thatabsortance/transmittance acquires extremal values at the critical point, wherethe Faraday angle changes sign, thus providing fine markers of the topologicalphase transition. In the case of non-topological materials as phosphorene, aminimum of the transmittance is also observed due to the energy gap closing byan external electric field.

Faraday rotation and transmittance as markers of topological phase transitions in 2D materials