Floquet topological states

Topology is a key concept in modern condensed matter physics. It is robust against perturbations and has generally been believed to be determined once a material is synthesized. We discovered a way to dynamically alter the topology of a material, proposing theoretical models in which the Berry curvature, Chern number, and chiral edge states can be controlled by applying a time-periodic external field such as a laser. The key idea is that electrons enter a photon-dressed state. Such states can be described as Floquet states, and the topology of the resulting Floquet bands can be tuned as a function of the laser intensity, polarization, frequency, and other parameters.

In recent years, these Floquet states and the models we proposed have begun to be observed experimentally, and the field continues to grow rapidly.

Relativistic Floquet engineering of Dirac electrons

In this work, we analyzed how the electronic states of quantum materials, including Dirac electron systems, are modified when driven by a traveling wave V(Qx−ωt) characterized by a wave vector and a frequency. Such traveling waves include laser light, polaritons, surface acoustic waves, and sliding density waves. Because their wave vectors and frequencies can be externally controlled, and because of their characteristic periodicity in both time and space, they give rise to Floquet-Bloch states. As a model, we considered three-dimensional (3D) Dirac electrons driven by a circularly polarized laser and classified the traveling waves into three categories—temporal, lightlike, and spatial—according to their velocity, revealing a distinctive electronic state in each regime. We further found that the modification of the electronic Floquet bands leads to the emergence of Floquet-Weyl bands. In addition, as the wave velocity approaches the Fermi velocity, the Lorentz contraction is maximized, enhancing the effect of Floquet band engineering. We also discuss the geometric properties of the response current.

Floquet Driving of Enzymatic Reactions: Counting Statistics and Long-Time Currents

Technologies for artificially controlling chemical reaction systems, such as optogenetics, are rapidly advancing, making it increasingly important to understand reaction dynamics under time-dependent control.
This study focuses on chemical reaction systems with time-dependent rates, constructing a Floquet theory for classical stochastic processes that includes counting fields, and clarifying how steady-state currents are generated after long times. In particular, we derive analytical expressions for the current in both high- and low-frequency regimes under periodic rate modulation.

Additionally, inspired by the enzymatic reaction of cAMP production, which is activated and inhibited by G-proteins, we consider a Michaelis--Menten-type reaction model as a concrete example of discrete Floquet driving, where the rates change non-perturbatively and piecewise constantly, obtaining analytical expressions and numerical results. In particular, we show that in the high-frequency regime, the effect of periodic driving can be interpreted as an effective change in the chemical reaction rates.
These results provide a foundation for Floquet analysis of periodically driven chemical reactions.