Within the Floquet theory of periodically driven quantum systems, we developed the theory of light-induced modification of electronic states in semiconductor materials described by the Luttinger Hamiltonian (the electronic term $Γ_8$). Particularly, exact solutions of the Floquet problem are found for the band edge in the cases of linearly and circularly polarized irradiation. It is shown that the irradiation changes electron effective masses near the band edge, induces anisotropy of the electron dispersion and splits the bands. It is demonstrated that the light-induced band splitting strongly depends on the light polarization. Namely, the circularly polarized light acts similarly to a stationary magnetic field and lifts the spin degeneracy of electron branches, whereas a linearly polarized light does not affect the spin degeneracy and only splits the bands in the center of the Brillouin zone. The present theory can be applied to describe electronic properties of various semiconductor structures irradiated by an electromagnetic field in the broad frequency range.
$α$-Sn is well known as a typical Luttinger semimetal with a quadratic band touching at the $Γ$ point. Based on the effective $k\cdot p$ analysis as well as first-principles calculations, we demonstrate that multiple topological phases with a rich diagram, including topological insulator, Dirac semimetal, and Weyl semimetal phases, can be induced and engineered in $α$-Sn by external strains, magnetic fields, and circularly polarized light (CPL). Intriguingly, not only the conventional type-I Weyl nodes, but also type-II Weyl nodes and double-Weyl nodes can be generated directly from the quadra…
Within the Floquet theory of periodically driven quantum systems, we demonstrate that a high-frequency electromagnetic field can be used as an effective tool to control excitonic properties of semiconductor quantum dots (QDs). It is shown, particularly, that the field both decreases the exciton binding energy and dynamically stabilizes the exciton, increasing its radiative lifetime. The developed theory can serve as a basis for the ultrafast method to tune spectral characteristics of the QD-based photon emitters by a high-frequency field.
Magnetism and Topology from Circularly Polarized Phonon Floquet Engineering
RIKEN Center for Emergent Matter Science (CEMS)（RIKEN 涌现物质科学中心）；Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）；The Institute for Solid State Physics, The University of Tokyo（东京大学固体物理研究所）；Department of Physics, Institute of Science Tokyo（东京科学大学物理系）
Floquet engineering, modulating quantum systems in a time periodic way, lies at the central part for realizing novel topological dynamical states. Thanks to the Floquet engineering, various new realms on experimentally simulating topological materials have emerged. Conventional Floquet engineering, however, only applies to time periodic non-dissipative Hermitian systems, and for the quantum systems in reality, non-Hermitian process with dissipation usually occurs. So far, it remains unclear how to characterize topological phases of periodically driven non-Hermitian systems via the frequency sp…
We consider asymmetric and symmetric dimerized two-leg ladders, comprising of four different lattice points per unit cell, illuminated by circularly polarized light. In the asymmetric dimerized ladder case, rungs are not perpendicular to the ladder's legs whereas the rungs are perpendicular to the legs for the symmetric one. Using the Floquet theory, we obtain an effective Hamiltonian to study topological properties of the systems. Depending on the dimerization strength and driving amplitude, it is shown that topologically protected edge states manifest themselves not only as a zero-energy ban…
Floquet engineering is an important way to manipulate the electronic states of condensed matter physics. Recently, the discovery of the magnetic topological insulator MnBi$_2$Te$_4$ and its family provided a valuable platform to study magnetic topological phenomena, such as, the quantum anomalous Hall effect, the axion insulator state and the topological magnetoelectric effect. In this work, based on the effective model and first-principles calculations in combination with the Floquet theory, we reveal that the circularly polarized light (CPL) induces the sign reversal of the Chern number of o…
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…
We introduce the concept of Floquet odd-frequency superconducting pairs and establish their emergence in time-periodic conventional superconductors, where the continuous time-translation invariance is broken. We show that these exotic Cooper pairs are possible because the Floquet modes in time-periodic systems provide an additional index (a Floquet index) that broadens the classification of pair symmetries, with no analog in the static regime. Our results thus put forward a different route for odd-frequency superconducting pairs and pave the way for Floquet engineered dynamical superconducting…
We propose to Floquet-engineer Dirac cones at the surface of a three-dimensional topological insulator. We show that a large tunability of the Fermi velocity can be achieved as a function of the polarization, direction and amplitude of the driving field. Using this external control, the Dirac cones in the quasienergy spectrum may become elliptic or massive, in accordance to experimental evidences. These results help us to understand the interplay of surface states and external ac driving fields in topological insulators. In our work we use the full Hamiltonian for the three-dimensional system …
In this paper, we theoretically study the Floquet engineering of two dimensional photonic waveguide arrays in three types of lattices: honeycomb lattice with Kekule distortion, breathing square lattice and breathing Kagome lattice. The Kekule distortion factor or the breathing factor in the corresponding lattice is periodically changed along the axial direction of the photonic waveguide with frequency $ω$. Within certain ranges of $ω$, the Floquet corner states in the Floquet band gap of quasi-energy spectrum are found, which are localized at the corner of the finite two-dimensional arrays. Du…
Floquet engineering of topological bands in semiconductor van der Waals heterobilayers
Universidad Nacional Autónoma de México（墨西哥国立自治大学）；Universidad Distrital Francisco José de Caldas（弗朗西斯科·何塞·德卡尔德斯地区大学）；Kennesaw State University（肯尼索州立大学）
We introduce a new approach that allows one complete control over the modulation of the effective twist angle change in few-layer van der Waals heterostructures by irradiating them with longitudinal waves of light at the end of a waveguide. As a specific application, we consider twisted bilayer graphene and show that one can tune the magic angles to be either larger or smaller, allowing in-situ experimental control of the phase diagram of this and other related materials. A waveguide allows one to circumvent the free-space constraints on the absence of longitudinal electric field components of…
Floquet engineering is the concept of tailoring a system by a periodic drive. It has been very successful in opening new classes of Hamiltonians to the study with ultracold atoms in optical lattices, such as artificial gauge fields, topological band structures and density-dependent tunneling. Furthermore, driven systems provide new physics without static counterpart such as anomalous Floquet topological insulators. In this review article, we provide an overview of the exciting developments in the field and discuss the current challenges and perspectives.
We review recent work on low-frequency Floquet engineering and its application to quantum materials driven by light, emphasizing van der Waals systems hosting Moiré superlattices. These non-equilibrium systems combine the twist-angle sensitivity of the band structures with the flexibility of light drives. The frequency, amplitude, and polarization of light can be easily tuned in experimental setups, leading to platforms with on-demand properties. First, we review recent theoretical developments to derive effective Floquet Hamiltonians in different frequency regimes. We apply some of these theo…
We demonstrate the emergence of a non-equilibrium superradiant phase in the dissipative Rabi-Dicke model. This phase is characterized by a photonic steady state that oscillates with a frequency close to the cavity frequency, in contrast to the constant photonic steady state of the equilibrium superradiant phase in the Dicke model. We relate this superradiant phase to the population inversion of Floquet states by introducing a Schwinger representation of the driven two-level systems in the cavity. This inversion is depleted near Floquet energies that are resonant with the cavity frequency to su…
Dynamic manipulation of magnetism in topological materials is demonstrated here via a Floquet engineering approach using circularly polarized light. Increasing the strength of the laser field, besides the expected topological phase transition, the magnetically doped topological insulator thin film also undergoes a magnetic phase transition from ferromagnetism to paramagnetism, whose critical behavior strongly depends on the quantum quenching. In sharp contrast to the equilibrium case, the non-equilibrium Curie temperatures vary for different time scale and experimental setup, not all relying o…
Using Floquet theory, we investigate the effect of light on triple fold fermions. We study a low energy model as well as a simplified tight binding model under illumination. We find that the three fold degeneracy remains symmetry protected even after applying light if the original band structure is rotationally symmetric around the degeneracy. Otherwise, light can lift the degeneracy and open up a gap. We further investigate the effect of light on the topological Fermi arcs by means of numerical computations. The changes caused by illumination are reflected in experimentally detectable signatu…
Prethermalization, where quasi-steady states are realized in the intermediate long time regime (prethermal regime), in periodically driven (Floquet) systems is an important phenomenon since it provides a platform of nontrivial Floquet many-body physics. In this Letter, we consider Floquet systems with dual energy scales: the Hamiltonian consists of two different terms whose amplitude is either comparable or much smaller than the frequency. As a result, when the larger-amplitude drive induces a $\mathbb{Z}_N$ symmetry operation, we obtain the effective static Hamiltonian respecting a new emerge…
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…
In Hermitian topological systems, the bulk-boundary correspondence strictly constraints boundary transport to values determined by the topological properties of the bulk. We demonstrate that this constraint can be lifted in non-Hermitian Floquet insulators. Provided that the insulator supports an anomalous topological phase, non-Hermiticity allows us to modify the boundary states independently of the bulk, without sacrificing their topological nature. We explore the ensuing possibilities for a Floquet topological insulator with non-Hermitian time-reversal symmetry, where the helical transport …
Floquet engineering is one of the most vigorous fields in periodically driven (Floquet) systems, with which we can control phases of matter usually by high-frequency drives. In this paper, with Floquet engineering by a combination of high-frequency drives and resonant drives, we propose a way to realize nontrivial topological phases protected by a $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry only in the presence of a $\mathbb{Z}_2$ symmetry, using a robust emergent $\mathbb{Z}_2$ symmetry induced by the resonant drives. Moreover, the symmetry protected topological (SPT) phases are switchable be…
Floquet engineering provides a toolbox for the realization of novel quantum phases without static counterparts, while conventionally the realization may rely on the manipulation of complex temporal evolution. Here we propose a systematic and high-precision scheme to realize unconventional Floquet topological phases by engineering local band structures in particular momentum subspace called band inversion surfaces (BISs). This scheme is based on a new bulk-boundary correspondence that for a class of generic $d$-dimensional periodically driven systems, the local topological structure formed in e…
We present an experimental proposal to tune the effective lattice structure in twisted transition metal dichalcogenide (TMD) heterobilayers with time-periodic Floquet drive. We show that elliptically polarized light with sub-terahertz frequencies $\hbarω\sim 1$ meV and moderate electric fields $E\sim0.2$~MV/cm allows tuning between the native triangular lattice and a square lattice, while linearly polarized light enables dimensional reduction to a quasi-one-dimensional geometry. Without drive, these twisted TMDs simulate the single band Fermi-Hubbard model; we show that this approximation stil…
Time-periodic driving in the form of coherent radiation provides powerful tool for the manipulation of topological materials or synthetic quantum matter. In this paper we propose a scheme to realize non-Hermitian semimetals exhibiting exceptional rings in the spectra through Floquet engineering. A transition from a concentric pair of the rings to a dipolar pair is observed. The concentric pair carries only a quantized Berry phase while the dipolar pair possesses opposite Chern numbers in addition, signaling a topological Lifshitz transition of the Fermi surface. The transport properties of the…
This work provides a convenient and powerful means towards the engineering of Floquet bands via Bloch oscillations, by adding a tilted linear potential to periodically driven lattice systems. The added linear field not only restricts the spreading of a time-evolving wavepacket but also, depending on the ratio between the Bloch oscillation frequency and the modulation frequency of the periodic driving, dramatically modifies the band profile and topology. Specifically, we consider a driven Aubry-André-Harper model as a working example, in the presence of a linear field. Almost flat Floquet bands…
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…
Here we present a theoretical investigation of the Floquet spectrum in multiterminal quantum dot Josephson junctions biased with commensurate voltages. We first draw an analogy between the electronic band theory and superconductivity which enlightens the time-periodic dynamics of the Andreev bound states. We then show that the equivalent of the Wannier-Stark ladders observed in semiconducting superlattices via photocurrent measurements, appears as specific peaks in the finite frequency current fluctuations of superconducting multiterminal quantum dots. In order to probe the Floquet-Wannier-Sta…
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 study the current produced in a Tomonaga-Luttinger liquid by an applied bias and by weak, point-like impurity potentials which are oscillating in time. We use bosonization to perturbatively calculate the current up to second order in the impurity potentials. In the regime of small bias and low pumping frequency, both the DC and AC components of the current have power law dependences on the bias and pumping frequencies with an exponent 2K - 1 for spinless electrons, where K is the interaction parameter. For K < 1/2, the current becomes large for special values of the bias. For non-interactin…
We discuss Floquet engineering of dissipative molecular systems through periodic driving of an infrared-active vibrational transition, either directly or via a cavity mode. Following a polaron quantum Langevin equations approach, we derive correlation functions and stationary quantities showing strongly modified optical response of the infrared-dressed molecule. The coherent excitation of molecular vibrational modes, in combination with the modulation of electronic degrees of freedom due to vibronic coupling can lead to both enhanced vibronic coherence as well as control over vibrational sideb…
The quest to realize novel phases of matter with topological order is an important pursuit with implications for strongly correlated physics and quantum information. Utilizing ideas from state-of-the-art coherent control of artificial quantum systems such as superconducting circuits, we present a proposal to realize bosonic fractional quantum Hall physics on small lattices by creating nearly flat topological bands using staggered flux patterns. Fingerprints of fractionalization through charge pumping can be observed with nearly perfect quantization using as few as 24 lattice sites (two photons…
Motivated by the recent experimental realization of twisted double bilayer graphene (TDBG) samples we study, both analytically and numerically, the effects of circularly polarized light propagating in free space and confined into a waveguide on the band structure and topological properties of these systems. These two complementary Floquet protocols allow us to selectively tune different parameters of the system by varying the intensity and the frequency of the light. For the drive protocol in free space, in the high-frequency regime, we find that in TDBG with AB/BA stacking, we can selectively…
It is of theoretical and experimental interest to engineer topological phases with very large topological invariants via periodic driving. As advocated by this work, such Floquet engineering can be elegantly achieved by the particle swarm optimization (PSO) technique from the swarm intelligence family. With the recognition that conventional gradient-based optimization approaches are not suitable for directly optimizing topological invariants as integers, the highly effective PSO route yields new promises in the search for exotic topological phases, requiring limited physical resource. Our resu…
We derive a theory for the generation of arbitrary spin-spin interactions in superconducting circuits via periodic time modulation of the individual qubits or the qubit-qubit interactions. The modulation frequencies in our approach are in the microwave or radio frequency regime so that the required fields can be generated with standard generators. Among others, our approach is suitable for generating spin lattices that exhibit quantum spin liquid behavior such as Kitaev's honeycomb model.
Quantum simulators based on atoms or molecules often have long-range interactions due to dipolar or Coulomb interactions. We present a method based on Floquet engineering to turn a long-range interaction into a short-range one. By modulating a magnetic-field gradient with one or a few frequencies, one reshapes the interaction profile, such that the system behaves as if it only had nearest-neighbor interactions. Our approach works in both one and two dimensions and for both spin-1/2 and spin-1 systems. It does not require individual addressing, and is applicable to all experimental systems with…
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…
The insertion of a local magnetic flux, as the one created by a thin solenoid, plays an important role in gedanken experiments of quantum Hall physics. By combining Floquet engineering of artificial magnetic fields with the ability of single-site addressing in quantum-gas microscopes, we propose a scheme for the realization of such local solenoid-type magnetic fields in optical lattices. We show that it can be employed to manipulate and probe elementary excitations of a topological Chern insulator. This includes quantized adiabatic charge pumping along tailored paths inside the bulk, as well a…
Floquet engineering is a convenient strategy to induce nonequilibrium phenomena in molecular and solid-state systems, or to dramatically alter the physicochemical properties of matter, bypassing costly and time-consuming synthetic modifications. In this article, we investigate theoretically some interesting consequences of the fact that an originally achiral molecular system can exhibit nonzero circular dichroism (CD) when it is driven with elliptically polarized light. More specifically, we consider an isotropic ensemble of small cyclic molecular aggregates in solution whose local low-frequen…
We review methods for using time-periodic fields (e.g., laser or microwave fields) to induce non-equilibrium topological phenomena in quantum many-body systems. We discuss how such fields can be used to change the topological properties of the single particle spectrum, and key experimental demonstrations in solid state, cold atomic, and photonic systems. The single particle Floquet band structure provides a stage on which the system's dynamics play out; the crucial question is then how to obtain robust topological behaviour in the many-particle setting. In the regime of mesoscopic transport, w…
