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.

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Cited by in corpus (10)

• Photocurrent induced by a bicircular light drive in centrosymmetric systems
• Suppression of Heating by Multi-color Driving Protocols in Floquet Engineered Strongly Correlated Systems
• Controllable photocurrent generation in Dirac systems with two frequency drives
• Two-color laser control of photocurrent and high harmonics in graphene
• Steering spin fluctuations in lattice systems via two-tone Floquet engineering
• Monolayer transition metal dichalcogenides under finite-pulse polarized radiation
• Localization and topological signatures under periodic twisting
• Optical control of electrons in a Floquet topological insulator
• Floquet engineering with spatially non-uniform driving fields
• Topological energy pumping in a quasi-periodically driven four-level system