Floquet $\pi$ Exceptional Points

We report a new kind of exceptional points in periodically driven system, called Floquet $\pi$ exceptional points, whose eigenvectors rotate on Bloch sphere and accumulate $\pi$ geometric phase in one time period. The merging of two such kind exceptional points are constrained by their dynamical structure, meaning two order-1/2 exceptional points with same dynamical structure can merge to one order-1 one while those with opposite dynamical structure can not. We show they exist in Floquet bipartite lattices, and the order-1 Floquet $\pi$ exceptional points appear at the phase transition point between quasimomentum gap phases and quasienergy gap phases. The scattering properties around the order-1 Floquet $\pi$ exceptional points is quite novel, which is perfect transparency but detectable in reflection for one of two sides.