Disorder Effects In Floquet Topological Insulator

This thesis contains two parts,the first part briefly introduces the quantum topo-logical states in quantum systems.The second part of the thesis is focused on disorder effects at the surfaces of a photon-dressed thin film three dimensional topological in-sulator.To investigate the impurity effects on the surfaces of a thin film topological insu-lator(TI),one possible way is to apply a off-resonant circular polarized light.It is dis-covered that the off-resonant driving induces a quantized total Hall conductivity,when the driving strength is larger than a critical value and the Fermi level lies in the band gap,indicating that the system is converted into the topological phase.Meanwhile,if we continuely increase the disorder strength,the Dirac masses of top and bottom sur-faces are renormalized and then fixed to half of their initial values,respectively,which will shrink the widths of half-integer plateau of anomalous Hall conductivities.