Floquet-driven thermal transport in topological Haldane lattice systems

In this paper, we employ a modified Haldane lattice model to investigate the light-driven, spin- and valley-dependent anomalous Nernst effect in two-dimensional hexagonal topological systems. We demonstrate that two-dimensional buckled materials exhibit a hierarchy of electrically and optically tunable topological phases when subjected to off-resonant circularly polarized light in the presence of intrinsic spin-orbit coupling and a staggered sublattice potential. Within a Berry-curvature-driven transport framework, we systematically analyze charge-, spin-, and valley-resolved anomalous Nernst responses and identify their correspondence with distinct topological regimes. A finite charge Nernst conductivity arises under optical driving combined with spin-orbit coupling, whereas the generation of a pure valley Nernst current requires the simultaneous presence of sublattice asymmetry and off-resonant light. Substrate-induced inversion asymmetry further enables thermally driven valley currents with tunable magnitude and sign. We find that single-spin and single-valley Nernst responses occur in selected insulating and metallic phases, while the valley Nernst signal is suppressed in spin-polarized and anomalous quantum Hall phases. Extending our analysis to monolayer MoS$_2$, we show that strong spin-orbit coupling and broken inversion symmetry allow fully spin- and valley-polarized Nernst currents over a broad energy window. The temperature dependence of the Nernst response exhibits characteristic signatures of topological phase transitions, establishing the anomalous Nernst effect as a sensitive probe of field-engineered band topology in two-dimensional Dirac materials.