Phase Driven Topological Exotic States Based On The Correlated Haldane Model In Honeycomb Lattice

In 1988,Haldane proposed a lattice model which exhibits topological ground state without external magnetic field.The Haldane model describes noninteracting spinless electrons on a honeycomb lattice with nearest neighbor(NN),next-nearest-neighbor(NNN)hoppings and inversion symmetry breaking staggered potential.Complex hopping t’eiφij breaks the time-reversal symmetry and opens an energy gap at the Dirac points.There has a competition between complex hopping t’eiφij and staggered potential,resulting in the Haldane model in topological phase or non-topological phase.Recently,researchers have studied the correlated Haldane model with different methods to explore the interaction-driven topological quantum phases,but the phase φ of the complex hopping is often assigned to(π/2).However,in Haldane model,we all know that the change of phase φ will also cause topological phase transition.Furthermore,while some researchers have also studied the case with arbitrary phase φ in Haldane-Hubbard model,they generally set the staggered potential ε to be zero in the model.An interesting question naturally arises:whether the change of phase φ will cause richer topological phase transition and induce topological nontrivial states in the correlated Haldane model in the presence of staggered potential.Motivated by above interesting questions,in this work we studied the phase of complex hopping t’eiφij driven topological exotic states based on the correlated Haldane model on honeycomb lattice by mean field method and random phase approximation.We observe a spontaneous SU(2)symmetry breaking.It is manifested as one spin component remaining topological,whereas the other turns trivial upon the changing of phase of complex hopping t’eiφij,resulting in a non-trivial phase with Chern number C=1.We note that while previous studies have also found the C=1 topological quantum state,it is driven by the interaction rather than the phase.Therefore,the phase can induce topological phase transitions,resulting in topological exotic states with different topological properties,including Chern number,edge state and Hall conductivity.We obtain different topological states:Chern number C=2 topological spin density waves(TSDW),C=1 TSDW and trivial antiferromagnetic(AF)spin density waves(SDW).Our work provides a new insight for topological phase transitions in correlated quantum anomalous Hall insulators.