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Abstract

Using two-frequency driving in two dimensions opens up new possibilities for Floquet engineering, which range from controlling specific symmetries to tuning the properties of resonant gaps. In this work, we study two-band lattice models subject to two-tone Floquet driving and analyze the resulting effective Floquet band structures both numerically and analytically. On the one hand, we extend the methodology of Sandholzer et al. [Phys. Rev. Res. 4, 013056 (2022)] from one to two dimensions and find competing topological phases in a simple Bravais lattice when the two resonant drives at 1ω and 2ω interfere. On the other hand, we explore driving-induced symmetry breaking in the hexagonal lattice, in which the breaking of either inversion or time-reversal symmetry can be tuned independently via the Floquet modulation. Possible applications of our work include a simpler generation of topological bands for ultracold atoms and the realisation of nonlinear Hall effects as well as Haldane's parity anomaly in inversion-symmetric parent lattices.