  We study the Floquet-surface bound states embedded in the continuum (BICs)
and bound states out the continuum (BOCs)in a resonantly driven 1D tilted
defect-free lattice. In contrast to fragile single-particle BICs assisted by
specially tailored potentials, we find that Floquet-surface BICs, stable
against structural perturbations, can exist in a wide range of parameter space.
By using a multiple-time-scale asymptotic analysis in the high-frequency limit,
the appearance of Floquet-surface bound states can be analytically explained by
effective Tamm-type defects at boundaries induced by the resonance between the
periodic driving and tilt. The phase boundary of existing Floquet-surface
states is also analytically given. Based on the repulsion effect of surface
states, we propose to detect transition points and measure the number of
Floquet-surface bound states by quantum walk. Our work opens a new door to
experimental realization of BICs in quantum system.
