Interplay of Spin–Orbit and Exchange Couplings in the Pseudospin-1 Dice Lattice: Effects of Staggered Potentials

The Dice lattice is a two-dimensional Dirac semimetal featuring three energy bands—two dispersive bands forming Dirac cones at low energy, similar to the honeycomb lattice, and a non-dispersive flat band at zero energy. Owing to its three sublattices, its low-energy excitations are described by pseudospin-1 matrices, placing it among pseudospin-1 systems such as the Lieb and kagome lattices. The presence of the flat band allows additional low-energy states to participate in the system’s response to spin–orbit interactions. Here, we investigate the interplay between Rashba spin–orbit coupling and ferromagnetic exchange interaction in the pseudospin-1 Dice lattice. Drawing parallels with Dirac-semimetallic honeycomb-based systems such as graphene and silicene - where such couplings induce quantum anomalous Hall (QAH) phases, we show that the Dice lattice develops a QAH phase with a quantized Hall conductivity of 2e²/h, accompanied by the dispersion of the originally flat band. Introducing a staggered potential further modifies the topological phase boundaries and band topology, leading to behaviors distinct from those of the pseudospin-1/2 honeycomb lattice.