Research On Goos-hanchen And Imbert-fedorov Shifts Of Topological Quantum System

Quantum anomalous Hall effect is a typical type of topological phase.It has an insulated bulk state,but its edge state has a non-dissipative unidirectional conductive channel without an externally strengthened magnetic field,so it has broad application prospects.However,the preparation conditions of quantum anomaly Hall effect are rigorous,so we hope produce quantum anomalous Hall effect from quantum spin Hall effect.The quantum spin Hall effect can be regarded as the superposition of two quantum anomalous Hall effects.If the time inversion symmetry of the quantum spin Hall system can be broken,it is possible to obtain quantum anomalous Hall sffect.The two-dimensional honeycomb lattice quantum system was the first to be predicted to obtain quantum spin Hall effect.Some twodimensional honeycomb lattice materials such as silene and germane have large spin-orbit coupling strength and can form quantum spin Hall effect,and this type of two-dimensional honeycomb lattice system can be described by the same Hamiltonian.The Goos–H(?)nchen shift and Imbert–Fedorov shift(referred as GH shift and IF shift)have attracted people’s attention for a long time.These phenomena do not conform to the conclusion of geometric optics,so people have aroused great interest in them.Nowadays,with the development of weak measurement amplification technology,we can more easily observe the GH shift and IF shift.Therefore,it is hoped that the GH shift and IF shift can be used to detect the topological states of materials effectively and conveniently,especially quantum spin Hall state and quantum anomalous Hall state.The main research content of this subject is to use the Goos–H(?)nchen shift and Imbert-Fedorov shift to detect the topological phase of a two-dimensional honeycomb lattice system.Firstly,we study the different quantum states of the twodimensional honeycomb lattice quantum system under the influence of intrinsic spin-orbit coupling,electron-electron repulsive potential and exchange field interaction,and calculate the energy band structure and topological properties of different quantum states.Next we simply deduces Kubo formula under the condition of non-interacting electronic system,and uses Kubo formula to calculate the optical conductivity of the two-dimensional quantum system under different quantum state conditions.Then we assume that the two-dimensional honeycomb lattice quantum system is tiled on a semi-infinite uniform medium.The linearly polarized Gaussian beam and the circularly polarized Gaussian beam are obliquely incident and the GH shift and IF shift of the reflected beam are calculated.And the difference between the GH shift and IF shift for different topological quantum states are explored.It is found that GH shift and IF shift can be used to distinguish quantum spin Hall state and quantum anomalous Hall state.