The Study Of Quantum Anomalous Hall Effect In α-T₃ Lattice

Quantum anomalous Hall insulator,also called Chen insulator,has the characteristics of internal insulation but edge conductivity.These conductive edge states have the characteristics of spin-momentum locking,so backscattering is strongly suppressed,and these transport characteristics make it have the potential to become a new generation of electronic devices.As a hot-spot material in physics,the topological states of graphene have received extensive attention and research,such as the realization of the quantum anomalous Hall effect.However,it is difficult to achieve the magnetic moment necessary for the quantum anomalous Hall effect in graphene,and the dice lattice,which is similar to graphene,has spontaneous ferromagnetism because it has a flat band at the Dirac point.However,α-T₃ lattice,as a transition between graphene and dice lattice,is expected to provide an effective way to realize quantum anomalous Hall effect.This paper aims to extend the quantum anomalous Hall effect model in graphene to theα-T₃ lattice,and realize the quantum anomalous Hall effect with the flat band spontaneous magnetism of theα-T₃ lattice.The specific research contents of this paper are as follows:（1）The quantum anomalous Hall phase of theα-T₃ lattice under two types of Rashba spin-orbit coupling（RSOC）as well as the exchange field is studied.By analyzing the phase diagram,band structure,edge states,and topological invariants,we show that the system provides a platform for achieving rich topological phases,including the semimetal phases and the quantum anomalous Hall phases with Chern numbers-1 and 2.It is also found that the edge channel of the quantum anomalous Hall phase with Chern number-1 is mainly concentrated in an energy valley,characterized by valley polarization,called valley polarized quantum anomalous Hall phase.100%valley polarization can be formed when Chern number C and valley Chern number C_V satisfy C=C_V=-1.This provides an effective platform for the design of dissipation-free valley electronic devices.（2）The quantum anomalous Hall phase of theα-T₃ lattice is studied under the two types of RSOC as well as the electron-electron interactions.We work,by analyzing the RSOC and electronic interaction-driven phase diagram,band structure,edge states and topological invariants,to show that the system can achieve richer topological phases,including the semimetal phases and the valley polarized quantum anomalous Hall phases with C=±1 and the quantum anomalous Hall phases with C=±2,where the valley polarized quantum anomalous Hall phase only exist at 0<α<1 and the onsite energy of the B lattice point is not zero.100%valley polarization can be formed when the Chern number and valley Chern number satisfy C=C_V=±1.Our results demonstrate the potential of interacting systems in realizing topological phases,especially quantum anomalous Hall phases,and their potential applications in valley electronic devices.