Floquet engineering, the control of quantum systems using periodic driving, is an old concept in condensed matter physics, dating back to ideas such as the inverse Faraday effect. There is a renewed interest in this concept owing to the rapid developments in laser and ultrafast spectroscopy techniques and discovery and understanding of various "quantum materials" hosting interesting exotic quantum properties. Here, starting from a nontechnical introduction with emphasis on the Floquet picture and effective Hamiltonians, we review the recent applications of Floquet engineering in ultrafast, nonlinear phenomena in the solid state. In particular, Floquet topological states, application to ultrafast spintronics, and to strongly correlated electron systems are overviewed.
Floquet engineering is a powerful tool that drives materials with periodic light. Traditionally, the light is monochromatic, with amplitude, frequency, and polarization varied. We introduce Floquet engineering via unpolarized light built from quasi-monochromatic light, and show how it can modify strongly correlated systems, while preserving the original symmetries. Different types of unpolarized light can realize different strongly correlated phases As an example, we treat insulating magnetic materials on a triangular lattice and show how unpolarized light can induce a Dirac spin liquid.
Floquet Engineering Magnetism and Superconductivity in the Square-Lattice Hubbard Model
RWTH Aachen University（亚琛工业大学）；Columbia University（哥伦比亚大学）；Max Planck Institute for the Structure and Dynamics of Matter（物质结构与动力学马普研究所）；Technische Universität Braunschweig（布伦瑞克工业大学）
In recent years, there has been an intense search for materials realizing the Kitaev quantum spin liquid model. A number of edge-shared compounds with strong spin-orbit coupling, such as RuCl$_3$ and iridates, have been proposed to realize this model. Nevertheless, an effective spin Hamiltonian derived from the microscopic model relevant to these compounds generally contains terms that are antagonistic toward the quantum spin liquid. This is consistent with the fact the zero magnetic field ground state of these materials is generally magnetically ordered. It is a pressing issue to identify pro…
We present a new scheme to control the spin exchange interactions between two magnetic ions by manipulating the orbital degrees of freedom using a periodic drive. We discuss two different protocols for orbital Floquet engineering. In one case, we modify the properties of the ligand orbitals which mediate magnetic interactions between two transition metal ions. While in the other case, we mix the d orbitals on each magnetic ion. In contrast to previous works on Floquet engineering of magnetic properties, the present scheme makes use of the AC Stark shift of the states involved in the exchange p…
Intense time-periodic laser fields can transform the electronic structure of a solid into strongly modified Floquet-Bloch bands. While this suggests multiple pathways to induce electronic orders such as superconductivity or charge density waves, the possibility of preparing low-energy phases of Floquet Hamiltonians remains unclear because of the energy absorption at typical experimentally accessible driving frequencies. Here we investigate a realistic pathway towards laser control of electronic orders, which is the transient enhancement of fluctuating orders. Using a conserving Keldysh Green's…
Magnetic exchange couplings can be tuned by coupling to periodic light, where the frequency and amplitude are typically varied: a process known as Floquet engineering. The polarization of the light is also important, and in this paper, we show how different polarizations, including several types of unpolarized light, can tune the exchange couplings in distinct ways. Using unpolarized light, for example, it is possible to tune the material without breaking either time-reversal or any lattice symmetries. To illustrate these effects generically, we consider single-band Hubbard models at half-fill…
Light-matter coupling involving classical and quantum light offers a wide range of possibilities to tune the electronic properties of correlated quantum materials. Two paradigmatic results are the dynamical localization of electrons and the ultrafast control of spin dynamics, which have been discussed within classical Floquet engineering and in the deep quantum regime where vacuum fluctuations modify the properties of materials. Here we discuss how these two extreme limits are interpolated by a cavity which is driven to the excited states. In particular, this is achieved by formulating a Schri…
What happens to the QCD vacuum when a time-periodic circularly polarized laser field with a sufficiently large intensity and frequency is applied? Based on the Floquet formalism for periodically driven systems and the systematic low-energy effective theory of QCD, we show that for a sufficiently large frequency and above a critical intensity, the QCD vacuum is unstable against the chiral soliton lattice of pions; a crystalline structure of topological solitons that spontaneously breaks parity and continuous translational symmetries. Our work would pave the way for novel "Floquet vacuum enginee…
The coupling of monochromatic light fields and solids introduces nonequilibrium Floquet states, offering opportunities to create and explore new topological phenomena. Using combined first-principles and Floquet analysis we show that one can freely engineer Floquet-Dirac fermions (FDFs) in graphene by tuning the frequency and intensity of linearly polarized light. Not only type-II FDFs are created, but they also coexist with type-I FDFs near the Fermi level. Intriguingly, novel topologically nontrivial edge states connecting type-I and type-II Floquet-Dirac points emerge in photodriven graphen…
Electric polarization is a geometric phenomenon in solids and has a close relationship to the symmetry of the system. Here we propose a mechanism to dynamically induce and manipulate electric polarization by using an external light field. Specifically, we show that application of bicircular lights (BCLs) control the rotational symmetry of the system and can generate electric polarization. To this end, we use Floquet theory to study a system subjected to a two-frequency drive. We derive an effective Hamiltonian with high frequency expansions, for which the electric polarization is computed with…
We consider driving multi-orbital Mott insulators using laser radiation. We derive general expressions for periodically driven spin-orbital models using time-dependent perturbation theory in the strong interaction limit. We show that the effective exchange interactions of the Floquet spin-orbital Hamiltonian are highly tunable via variations of the frequency, amplitude, and polarization of the laser. We also take the effect of finite bandwidth of excitations into account and study possible heating effects. We further apply our formalism to orthorhombic titanates YTiO$_3$ and LaTiO$_3$ based on…
It is generally believed that non-Hermiticity can transform Weyl semimetals into Weyl-exceptional-ring semimetals. However, this belief is from the systems without skin effect. We investigate the non-Hermitian Weyl semimental and its Floquet engineering in a system with skin effect, which breaks the bulk-boundary correspondence in its Hermitian counterpart. It is found in both the static and periodically driven cases that the skin effect makes this general belief no longer valid. We discover that exotic non-Hermitian topological matters, e.g., a composite phase of Weyl semimetal and topologica…
We analyze, analytically and numerically, a periodically driven Rashba nanowire proximity coupled to an $s$-wave superconductor using bosonization and renormalization group analysis in the regime of strong electron-electron interactions. Due to the repulsive interactions, the superconducting gap is suppressed, whereas the Floquet Zeeman gap is enhanced, resulting in a higher effective value of $g$-factor compared to the non-interacting case. The flow equations for different coupling constants, velocities, and Luttinger-liquid parameters explicitly establish that even for small initial values o…
We investigate the topological properties of Floquet-engineered twisted bilayer graphene above the magic angle driven by circularly polarized laser pulses. Employing a full Moiré-unit-cell tight-binding Hamiltonian based on first-principles electronic structure we show that the band topology in the bilayer, at twisting angles above 1.05$^\circ$, essentially corresponds to the one of single-layer graphene. However, the ability to open topologically trivial gaps in this system by a bias voltage between the layers enables the full topological phase diagram to be explored, which is not possible in…
We propose a method for controlling the exchange interactions of Mott insulators with strong spin-orbit coupling. We consider a multiorbital system with strong spin-orbit coupling and a circularly polarized light field and derive its effective Hamiltonian in the strong-interaction limit. Applying this theory to a minimal model of $α$-RuCl$_{3}$, we show that the magnitudes and signs of three exchange interactions, $J$, $K$, and $Γ$, can be changed simultaneously. Then, considering another case in which one of the hopping integrals has a different value and the other parameters are the same as …
We propose a mechanism for light-induced unconventional superconductivity in a two-valley semiconductor with a massive Dirac type band structure. The superconducting phase results from the out-of-equilibrium excitation of carriers in the presence of Coulomb repulsion and is stabilized by coupling the driven semiconductor to a bosonic or fermionic thermal bath. We consider a circularly-polarized light pump and show that by controlling the detuning of the pump frequency relative to the band gap, different types of chiral superconductivity would be induced. The emergence of novel superconducting …
We develop the Floquet-Magnus expansion for a classical equation of motion under a periodic drive that is applicable to both isolated and open systems. For classical systems, known approaches based on the Floquet theorem fail due to the nonlinearity and the stochasticity of their equations of motion (EOMs) in contrast to quantum ones. Here, employing their master equation, we successfully extend the Floquet methodology to classical EOMs to obtain their Floquet-Magnus expansions, thereby overcoming this difficulty. Our method has a wide range of application from classical to quantum as long as …
Recent experimental advances enable the manipulation of quantum matter by exploiting the quantum nature of light. However, paradigmatic exactly solvable models, such as the Dicke, Rabi or Jaynes-Cummings models for quantum-optical systems, are scarce in the corresponding solid-state, quantum materials context. Focusing on the long-wavelength limit for the light, here, we provide such an exactly solvable model given by a tight-binding chain coupled to a single cavity mode via a quantized version of the Peierls substitution. We show that perturbative expansions in the light-matter coupling have …
Higher-order topological~(HOT) states,~hosting topologically protected modes on lower-dimensional boundaries,~such as hinges and corners, have recently extended the realm of the static topological phases.~Here we demonstrate the possibility of realizing a two-dimensional \emph{Floquet} second-order topological insulator, featuring corner-localized zero quasienergy modes and characterized by quantized Floquet qudrupolar moment $Q^{\rm Flq}_{xy}=0.5$, by periodically kicking a quantum spin Hall insulator (QSHI) with a discrete fourfold ($C_4$) and time-reversal (${\mathcal T}$) symmetry breaking…
Strong periodic driving with light offers the potential to coherently manipulate the properties of quantum materials on ultrafast timescales. Recently, strategies have emerged to drastically alter electronic and magnetic properties by optically inducing non-trivial band topologies, emergent spin interactions and even superconductivity. However, the prospects and methods of coherently engineering optical properties on demand are far less understood. Here we demonstrate coherent control and giant modulation of optical nonlinearity in a van der Waals layered magnetic insulator, manganese phosphor…
The realization of synthetic gauge fields has attracted a lot of attention recently in relation with periodically driven systems and the Floquet theory. In ultra-cold atom systems in optical lattices and photonic networks, this allows to simulate exotic phases of matter such as quantum Hall phases, anomalous quantum Hall phases and analogs of topological insulators. In this paper, we apply the Floquet theory to engineer anisotropic Haldane models on the honeycomb lattice and two-leg ladder systems. We show that these anisotropic Haldane models still possess a topologically non-trivial band str…
