Dispersive nodal fermions along grain boundaries in Floquet topological crystals

Driven quantum materials often feature emergent topology, otherwise absent in static crystals. Dynamic bulk-boundary correspondence, encoded by nondissipative gapless modes residing near the Floquet zone center and/or boundaries, is its most prominent example. Here we show that topologically robust gapless dispersive modes appear along the grain boundaries, embedded in the interior of Floquet topological crystals, when the Floquet-Bloch band inversion occurring at a finite momentum (${\mathbf{K}}_{\mathrm{i}\mathrm{n}\mathrm{v}}^{\mathrm{F}\mathrm{l}\mathrm{q}}$) and the Burgers vector ($\mathbf{b}$) of the constituting array of dislocations satisfy ${\mathbf{K}}_{\mathrm{i}\mathrm{n}\mathrm{v}}^{\mathrm{F}\mathrm{l}\mathrm{q}}\cdot \mathbf{b}=\pi$ (modulo $2\pi$). Such nondissipative gapless states can be found near the center and/or edges of the Floquet Brillouin zone, irrespective of the drive protocol. We showcase these general outcomes for two-dimensional driven time-reversal symmetry breaking insulators. Promising experimental platforms hosting such dynamic topological dispersive bands in real materials are discussed.