Topological Floquet engineering using two frequencies in two dimensions

Abstract

Using two-frequency driving in two dimensions opens up new possibilites 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 analyse the resulting effective Floquet bandstructures both numerically and analytically. On the one hand, we extend the methodology of Sandholzer et al. [10.1103/PhysRevResearch.4.013056] from one to two dimensions and find competing topological phases in a simple Bravais lattice when the two resonant drives at $1\omega$ and $2\omega$ 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 non-linear Hall effects as well as Haldane's parity anomaly in inversion-symmetric parent lattices.

References in corpus (12)

• Photovoltaic Hall effect in graphene
• Periodically-driven quantum systems: Effective Hamiltonians and engineered gauge fields
• Tunable gauge potential for neutral and spinless particles in driven lattices
• Non-Abelian gauge fields and topological insulators in shaken optical lattices
• Light-Induced Valleytronics in Pristine Graphene
• Terahertz driven extremely nonlinear bulk photogalvanic currents in non-resonant conditions
• Shaping topological properties of the band structures in a shaken optical lattice
• Generation of Circularly-Polarised High-Harmonics with Identical Helicity in Two-Dimensional Materials
• Observation of Floquet topological phases with large Chern numbers
• Excitation of atoms in an optical lattice driven by polychromatic amplitude modulation
• Evidence of ac-Stark-shifted resonances in intense two-color circularly polarized laser fields
• Topological Floquet engineering of a 1D optical lattice via resonantly shaking with two harmonic frequencies