Topological Floquet engineering of a three-band optical lattice with dual-mode resonant driving

We present a Floquet framework for controlling topological features of a one-dimensional optical lattice system with dual-mode resonant driving, in which both the amplitude and phase of the lattice potential are modulated simultaneously. We investigate a three-band model consisting of the three lowest orbitals and elucidate the formation of a cross-linked two-leg ladder through an indirect interband coupling via an off-resonant band. We numerically demonstrate the emergence of topologically nontrivial bands within the driven system, and a topological charge pumping phenomenon with cyclic parameter changes in the dual-mode resonant driving. Finally, we show that the band topology in the driven three-band system is protected by parity-time reversal symmetry.