  Electronic bands featuring nontrivial bulk topological invariant manifest
through robust gapless modes at the boundaries, e.g., edges and surfaces. As
such this bulk-boundary correspondence is also operative in driven quantum
materials. For example, a suitable periodic drive can convert a trivial
insulator into a Floquet topological insulator (FTI) that accommodates
nondissipative dynamic gapless modes at the interfaces with vacuum. Here we
theoretically demonstrate that dislocations, ubiquitous lattice defects in
crystals, can probe FTIs as well as unconventional $\pi$-trivial insulator in
the bulk of driven quantum systems by supporting normal and anomalous modes,
localized near the defect core. Respectively, normal and anomalous dislocation
modes reside at the Floquet zone center and boundaries. We exemplify these
outcomes specifically for two-dimensional (2D) Floquet Chern insulator and
$p_x+ip_y$ superconductor, where the dislocation modes are respectively
constituted by charged and neutral Majorana fermions. Our findings should be
therefore instrumental in probing Floquet topological phases in the
state-of-the-art experiments in driven quantum crystals, cold atomic setups,
and photonic and phononic metamaterials through bulk topological lattice
defects.
