Magneto-optical Transport in Haldane Model Materials

We present a theoretical study of quantum magneto-transport in Haldane materials, focusing on the interplay of symmetry breaking, Landau quantization, and topological phases. In two-dimensional hexagonal lattices, including graphene, buckled Xenes, and transition-metal dichalcogenides, time-reversal and inversion symmetries govern the emergence of spin and valley degrees of freedom. Breaking these symmetries generates a topological mass gap and enables nontrivial band topology. Under a perpendicular magnetic field, the electronic spectrum quantizes into Landau levels whose structure reflects the underlying phase. By tuning sublattice asymmetry and next-nearest-neighbour hopping, we demonstrate transitions between quantum spin Hall, valley-spin–polarized metallic, and trivial insulating phases. The resulting spin- and valley-polarized Landau levels produce distinct signatures in the density of states and magneto-optical conductivities. Using the Kubo formalism, we identify clear optical fingerprints of topological phase transitions in Haldane materials.