Floquet topological properties in the non-Hermitian long-range system with complex hopping amplitudes

Non-equilibrium phases of matter have attracted much attention in recent years, among which the Floquet phase is a hot point. In this work, based on the periodic driving non-Hermitian model, we reveal that the winding number calculated in the framework of the Bloch band theory has a direct connection with the number of edge states even though the non-Hermiticity is present. Further, we find that the change of the phase of the hopping amplitude can induce the topological phase transitions. Precisely speaking, the increase in the value of the phase can bring the system into a topological phase with a large topological number. Moreover, it can be unveiled that the introduction of the purely imaginary hopping term brings an extremely rich phase diagram. In addition, we can select the even topological invariant exactly from the unlimited winding numbers if we only consider the next-nearest neighbor hopping term. Here, the results obtained may be useful for understanding the periodic driving non-Hermitian theory.