Theory of Floquet band formation and local pseudospin textures in pump-probe photoemission of graphene

Light-Induced Topological Phase Transition with Tunable Layer Hall Effect in Axion Antiferromagnets

The intricate interplay between light and matter provides effective tools for manipulating topological phenomena. Here, we theoretically propose and computationally show that circularly polarized light holds the potential to transform the axion insulating phase into a quantum anomalous Hall state in MnBi2Te4 thin films, featuring tunable Chern numbers (ranging up to ±2). In particular, we reveal the spatial rearrangement of the hidden layer-resolved anomalous Hall effect under light-driven Floquet engineering. Notably, upon Bi2Te3 layer intercalation, the anomalous Hall conductance predominantly localizes in the nonmagnetic Bi2Te3 layers that hold zero Berry curvature in the intact state, suggesting a significant magnetic proximity effect. Additionally, we estimate variations in the magneto-optical Kerr effect, giving a contactless method for detecting topological transitions. Our work not only presents a strategy to investigate emergent topological phases but also sheds light on the possible applications of the layer Hall effect in topological antiferromagnetic spintronics.

Floquet engineering of the orbital Hall effect and valleytronics in two-dimensional topological magnets

We show that circularly polarized light is a versatile way to manipulate both the orbital Hall effect and band topology in two-dimensional ferromagnets. Employing the hexagonal lattice, we proposed that interactions between light and matter allow for the modulation of the valley polarization effect, and then band inversions, accompanied by the band gap closing and reopening processes, can be achieved subsequently at two valleys. Remarkably, the distribution of orbital angular momentum can be controlled by the band inversions, leading to the Floquet engineering of the orbital Hall effect, as well as the topological phase transition from a second-order topological insulator to a Chern insulator with in-plane magnetization, and then to a normal insulator. Furthermore, first-principles calculations validate the feasibility with the 2H-ScI2 monolayer as a candidate material, paving a technological avenue to bridge the orbitronics and nontrivial topology using Floquet engineering.

Reversible Ultrafast Chiroptical Responses in Planar Plasmonic Nano-Oligomer

Ultracompact chiral plasmonic nanostructures with unique chiral light-matter interactions are vital for future photonic technologies. However, previous studies are limited to reporting their steady-state performance, presenting a fundamental obstacle to the development of high-speed optical devices with polarization sensitivity. Here, a comprehensive analysis of ultrafast chiroptical response of chiral gold nano-oligomers using time-resolved polarimetric measurements is provided. Significant differences are observed in terms of the absorption intensity, thus hot electron generation, and hot carrier decay time upon polarized photopumping, which are explained by a phenomenological model of the helicity-resolved optical transitions. Moreover, the chiroptical signal is switchable by reversing the direction of the pump pulse, demonstrating the versatile modulation of polarization selection in a single device. The results offer fundamental insights into the helicity-resolved optical transitions in photoexcited chiral plasmonics and can facilitate the development of high-speed polarization-sensitive flat optics with potential applications in nanophotonics and quantum optics.

Circular dichroism in Floquet Chern insulator via high-order harmonics spectroscopy

High-order harmonics (HOHs) spectroscopy is attracting the attention of the condensed matter community, mostly because the HOHs spectrum encode the material property. Topological materials are of interest for both basic research and advanced technologies because of their robust properties against dissipation and perturbations. Floquet engineering technique have been demonstrated to be a unique tool to manipulate topological phase. In this paper, we apply HOH spectroscopy to characterize the Floquet state via the circular dichroism (CD). We find that the CD of the co-rotating harmonics is sensitive to Floquet topological states.

Build-up and dephasing of Floquet-Bloch bands on subcycle timescales

Strong light fields have created opportunities to tailor novel functionalities of solids1-5. Floquet-Bloch states can form under periodic driving of electrons and enable exotic quantum phases6-15. On subcycle timescales, lightwaves can simultaneously drive intraband currents16-29 and interband transitions18,19,30,31, which enable high-harmonic generation16,18,19,21,22,25,28-30 and pave the way towards ultrafast electronics. Yet, the interplay of intraband and interband excitations and their relation to Floquet physics have been key open questions as dynamical aspects of Floquet states have remained elusive. Here we provide this link by visualizing the ultrafast build-up of Floquet-Bloch bands with time-resolved and angle-resolved photoemission spectroscopy. We drive surface states on a topological insulator32,33 with mid-infrared fields-strong enough for high-harmonic generation-and directly monitor the transient band structure with subcycle time resolution. Starting with strong intraband currents, we observe how Floquet sidebands emerge within a single optical cycle; intraband acceleration simultaneously proceeds in multiple sidebands until high-energy electrons scatter into bulk states and dissipation destroys the Floquet bands. Quantum non-equilibrium calculations explain the simultaneous occurrence of Floquet states with intraband and interband dynamics. Our joint experiment and theory study provides a direct time-domain view of Floquet physics and explores the fundamental frontiers of ultrafast band-structure engineering.

Growth of Mesoscale Ordered Two-Dimensional Hydrogen-Bond Organic Framework with the Observation of Flat Band

Flat bands (FBs), presenting a strongly interacting quantum system, have drawn increasing interest recently. However, experimental growth and synthesis of FB materials have been challenging and have remained elusive for the ideal form of monolayer materials where the FB arises from destructive quantum interference as predicted in 2D lattice models. Here, we report surface growth of a self-assembled monolayer of 2D hydrogen-bond (H-bond) organic frameworks (HOFs) of 1,3,5-tris(4-hydroxyphenyl)benzene (THPB) on Au(111) substrate and the observation of FB. High-resolution scanning tunneling microscopy or spectroscopy shows mesoscale, highly ordered, and uniform THPB HOF domains, while angle-resolved photoemission spectroscopy highlights a FB over the whole Brillouin zone. Density-functional-theory calculations and analyses reveal that the observed topological FB arises from a hidden electronic breathing-kagome lattice without atomically breathing bonds. Our findings demonstrate that self-assembly of HOFs provides a viable approach for synthesis of 2D organic topological materials, paving the way to explore many-body quantum states of topological FBs.

Light driven magnetic transitions in transition metal dichalcogenide heterobilayers

Motivated by the recent excitement around the physics of twisted transition metal dichalcogenide (TMD) multilayer systems, we study strongly correlated phases of TMD heterobilayers under the influence of light. We consider both waveguide light and circularly polarized light. The former allows for longitudinally polarized light, which in the high frequency limit can be used to selectively modify interlayer hoppings in a tight-binding model. We argue based on quasi-degenerate perturbation theory that changes to the interlayer hoppings can be captured as a modulation to the strength of the moiré potential in a continuum model. As a consequence, waveguide light can be used to drive transitions between a myriad of different magnetic phases, including a transition from a 120^∘Neel phase to a stripe ordered magnetic phase, or from a spin density wave phase to a paramagnetic phase, among others. When the system is subjected to circularly polarized light we find that the effective mass of the active TMD layer is modified by an applied electromagnetic field. By simultaneously applying waveguide light and circularly polarized light to a system, one has a high level of control in moving through the phase diagram in-situ. Lastly, we comment on the experimental feasibility of Floquet state preparation and argue that it is within reach of available techniques when the system is coupled to a judiciously chosen bath.

Floquet engineering of tilted and gapped Dirac bandstructure in 1T[Formula: see text]-MoS[Formula: see text]

We have developed a rigorous theoretical formalism for Floquet engineering, investigating, and subsequently tailoring most crucial electronic properties of 1T[Formula: see text]-MoS[Formula: see text] by applying an external high-frequency dressing field within the off-resonance regime. It was recently demonstrated that monolayer semiconducting 1T[Formula: see text]-MoS[Formula: see text] exhibits tunable and gapped spin- and valley-polarized tilted Dirac bands. The electron-photon dressed states depend strongly on the polarization of the applied irradiation and reflect a full complexity of the low-energy Hamiltonian for non-irradiated material. We have calculated and analyzed the properties of the electron dressed states corresponding to linear and circular polarization of a dressing field by focusing on their symmetry, anisotropy, tilting, direct and indirect band gaps. Circularly polarized dressing field is known for transition into a new electronic state with broken time-reversal symmetry and a non-zero Chern number, and therefore, the combination of these topologically non-trivial phases and transitions between them could reveal some truly unique and previously unknown phenomena and applications. We have also computed and discussed the density of states for various types of 1T[Formula: see text]-MoS[Formula: see text] materials and its modification in the presence of a dressing field.

Controlling Floquet states on ultrashort time scales

The advent of ultrafast laser science offers the unique opportunity to combine Floquet engineering with extreme time resolution, further pushing the optical control of matter into the petahertz domain. However, what is the shortest driving pulse for which Floquet states can be realised remains an unsolved matter, thus limiting the application of Floquet theory to pulses composed by many optical cycles. Here we ionized Ne atoms with few-femtosecond pulses of selected time duration and show that a Floquet state can be observed already with a driving field that lasts for only 10 cycles. For shorter pulses, down to 2 cycles, the finite lifetime of the driven state can still be explained using an analytical model based on Floquet theory. By demonstrating that the amplitude and number of Floquet-like sidebands in the photoelectron spectrum can be controlled not only with the driving laser pulse intensity and frequency, but also by its duration, our results add a new lever to the toolbox of Floquet engineering.

Dynamical Phase Transitions in the Photodriven Charge-Ordered Dirac-Electron System

We study photoinduced phase transitions and charge dynamics in the interacting Dirac-electron system with a charge-ordered ground state theoretically by taking an organic salt α-(BEDT-TTF)_{2}I_{3}. By analyzing the extended Hubbard model for this compound using a combined method of numerical simulations based on the time-dependent Schrödinger equation and the Floquet theory, we observe successive dynamical phase transitions from the charge-ordered insulator to a gapless Dirac semimetal and, eventually, to a Chern insulator phase under irradiation with circularly polarized light. These phase transitions occur as a consequence of two major effects of circularly polarized light, i.e., closing of the charge gap through melting the charge order and opening of the topological gap by breaking the time-reversal symmetry at the Dirac points. We demonstrate that these photoinduced phenomena are governed by charge dynamics of driven correlated Dirac electrons.

Through the Lens of a Momentum Microscope: Viewing Light-Induced Quantum Phenomena in 2D Materials

Van der Waals (vdW) materials at their 2D limit are diverse, flexible, and unique laboratories to study fundamental quantum phenomena and their future applications. Their novel properties rely on their pronounced Coulomb interactions, variety of crystal symmetries and spin-physics, and the ease of incorporation of different vdW materials to form sophisticated heterostructures. In particular, the excited state properties of many 2D semiconductors and semi-metals are relevant for their technological applications, particularly those that can be induced by light. In this paper, the recent advances made in studying out-of-equilibrium, light-induced, phenomena in these materials are reviewed using powerful, surface-sensitive, time-resolved photoemission-based techniques, with a particular emphasis on the emerging multi-dimensional photoemission spectroscopy technique of time-resolved momentum microscopy. The advances this technique has enabled in studying the nature and dynamics of occupied excited states in these materials are discussed. Then, the future research directions opened by these scientific and instrumental advancements are projected for studying the physics of 2D materials and the opportunities to engineer their band-structure and band-topology by laser fields.

Low-Energy Excitations of Skyrmion Crystals in a Centrosymmetric Kondo-Lattice Magnet: Decoupled Spin-Charge Excitations and Nonreciprocity

We theoretically study spin and charge excitations of skyrmion crystals stabilized by conduction-electron-mediated magnetic interactions via spin-charge coupling in a centrosymmetric Kondo-lattice model by large-scale spin-dynamics simulations combined with the kernel polynomial method. We reveal clear segregation of spin and charge excitation channels and nonreciprocal nature of the spin excitations governed by the Fermi-surface geometry, which are unique to the skyrmion crystals in centrosymmetric itinerant hosts and can be a source of novel physical phenomena.

Shortcut to Self-Consistent Light-Matter Interaction and Realistic Spectra from First Principles

We introduce a simple approach to how an electromagnetic environment can be efficiently embedded into state-of-the-art electronic structure methods, taking the form of radiation-reaction forces. We demonstrate that this self-consistently provides access to radiative emission, natural linewidth, Lamb shifts, strong coupling, electromagnetically induced transparency, Purcell-enhanced and superradiant emission. As an example, we illustrate its seamless integration into time-dependent density-functional theory with virtually no additional cost, presenting a convenient shortcut to light-matter interactions.

Laser induced enhanced coupling between photons and squeezed magnons in antiferromagnets

In this paper we consider a honeycomb antiferromagnet subject to an external laser field. Obtaining a time-independent effective Hamiltonian, we find that the external laser renormalizes the exchange interaction between the in-plane components of the spin-operators, and induces a synthetic Dzyaloshinskii-Moria interaction (DMI) between second neighbors. The former allows the control of the magnon dispersion's bandwidth and the latter breaks time-reversal symmetry inducing non-reciprocity in momentum space. The eigen-excitations of the system correspond to squeezed magnons whose squeezing parameters depend on the properties of the laser. When studying how these spin excitations couple with cavity photons, we obtain a coupling strength which can be enhanced by an order of magnitude via careful tuning of the laser's intensity, when compared to the case where the laser is absent. The transmission plots through the cavity are presented, allowing the mapping of the magnons' dispersion relation.

All-optical control of excitons in semiconductor quantum wells

Applying the Floquet theory, we developed the method to control excitonic properties of semiconductor quantum wells (QWs) by a high-frequency electromagnetic field. It is demonstrated, particularly, that the field induces the blue shift of exciton emission from the QWs and narrows width of the corresponding spectral line. As a consequence, the field strongly modifies optical properties of the QWs and, therefore, can be used to tune characteristics of the optoelectronic devices based on them.

Steady Floquet-Andreev states in graphene Josephson junctions

Engineering quantum states through light-matter interaction has created a paradigm in condensed-matter physics. A representative example is the Floquet-Bloch state, which is generated by time-periodically driving the Bloch wavefunctions in crystals. Previous attempts to realize such states in condensed-matter systems have been limited by the transient nature of the Floquet states produced by optical pulses^1-3, which masks the universal properties of non-equilibrium physics. Here we report the generation of steady Floquet-Andreev states in graphene Josephson junctions by continuous microwave application and direct measurement of their spectra by superconducting tunnelling spectroscopy. We present quantitative analysis of the spectral characteristics of the Floquet-Andreev states while varying the phase difference of the superconductors, the temperature, the microwave frequency and the power. The oscillations of the Floquet-Andreev-state spectrum with phase difference agreed with our theoretical calculations. Moreover, we confirmed the steady nature of the Floquet-Andreev states by establishing a sum rule of tunnelling conductance⁴, and analysed the spectral density of Floquet states depending on Floquet interaction strength. This study provides a basis for understanding and engineering non-equilibrium quantum states in nanodevices.

Optically induced Kondo effect in semiconductor quantum wells

It is demonstrated theoretically that the circularly polarized irradiation of two-dimensional electron systems can induce the localized electron states which antiferromagnetically interact with conduction electrons, resulting in the Kondo effect. Conditions of experimental observation of the effect are discussed for semiconductor quantum wells.

Dynamic Spin-Triplet Order Induced by Alternating Electric Fields in Superconductor-Ferromagnet-Superconductor Josephson Junctions

Dynamic states offer extended possibilities to control the properties of quantum matter. Recent efforts are focused on studying the ordered states which appear exclusively under the time-dependent drives. Here, we demonstrate a class of systems which feature dynamic spin-triplet superconducting order stimulated by the alternating electric field. The effect is based on the interplay of ferromagnetism, interfacial spin-orbital coupling, and the condensate motion driven by the field, which converts hidden static p-wave order, produced by the joint action of the ferromagnetism and the spin-orbital coupling, into dynamic s-wave equal-spin-triplet correlations. We demonstrate that the critical current of Josephson junctions hosting these states is proportional to the electromagnetic power, supplied either by the external irradiation or by the ac current source. Based on these unusual properties we propose the scheme of a Josephson transistor which can be switched by the ac voltage and demonstrates an even-numbered sequence of Shapiro steps. Combining the photoactive Josephson junctions with recently discovered Josephson phase batteries we find photomagnetic SQUID devices which can generate spontaneous magnetic fields while being exposed to irradiation.

Coherence in the Ferroelectric A3ClO (A = Li, Na) Family of Electrolytes

Coherence is a major caveat in quantum computing. While phonons and electrons are weakly coupled in a glass, topological insulators strongly depend on the electron-phonon coupling. Knowledge of the electron−phonon interaction at conducting surfaces is relevant from a fundamental point of view as well as for various applications, such as two-dimensional and quasi-1D superconductivity in nanotechnology. Similarly, the electron−phonon interaction plays a relevant role in other transport properties e.g., thermoelectricity, low-dimensional systems as layered Bi and Sb chalcogenides, and quasi-crystalline materials. Glass-electrolyte ferroelectric energy storage cells exhibit self-charge and self-cycling related to topological superconductivity and electron-phonon coupling; phonon coherence is therefore important. By recurring to ab initio molecular dynamics, it was demonstrated the tendency of the Li₃ClO, Li_2.92Ba_0.04ClO, Na₃ClO, and Na_2.92Ba_0.04ClO ferroelectric-electrolytes to keep phonon oscillation coherence for a short lapse of time in ps. Double-well energy potentials were obtained while the electrolyte systems were thermostatted in a heat bath at a constant temperature. The latter occurrences indicate ferroelectric type behavior but do not justify the coherent self-oscillations observed in all types of cells containing these families of electrolytes and, therefore, an emergent type phenomenon where the full cell works as a feedback system allowing oscillations coherence must be realized. A comparison with amorphous SiO₂ was performed and the specific heats for the various species were calculated.

Floquet-Dirac fermions in monolayer graphene by Wannier functions

Wannier functions have been widely applied in the study of topological properties and Floquet-Bloch bands of materials. Usually, the real-space Wannier functions are linked to thek-space Hamiltonian by two types of Fourier transform (FT), namely lattice-gauge FT (LGFT) and atomic-gauge FT (AGFT), but the differences between these two FTs on Floquet-Bloch bands have rarely been addressed. Taking monolayer graphene as an example, we demonstrate that LGFT gives different topological descriptions on the Floquet-Bloch bands for the structurally equivalent directions which are obviously unphysical, while AGFT is immune to this dilemma. We introduce the atomic-laser periodic effect to explain the different Floquet-Bloch bands between the LGFT and AGFT. Using AGFT, we showed that linearly polarized laser could effectively manipulate the properties of the Dirac fermions in graphene, such as the location, generation and annihilation of Dirac points. This proposal offers not only deeper understanding on the role of Wannier functions in solving the Floquet systems, but also a promising platform to study the interaction between the time-periodic laser field and materials.

Revealing Hidden Orbital Pseudospin Texture with Time-Reversal Dichroism in Photoelectron Angular Distributions

We performed angle-resolved photoemission spectroscopy (ARPES) of bulk 2H-WSe_{2} for different crystal orientations linked to each other by time-reversal symmetry. We introduce a new observable called time-reversal dichroism in photoelectron angular distributions (TRDAD), which quantifies the modulation of the photoemission intensity upon effective time-reversal operation. We demonstrate that the hidden orbital pseudospin texture leaves its imprint on TRDAD, due to multiple orbital interference effects in photoemission. Our experimental results are in quantitative agreement with both the tight-binding model and state-of-the-art fully relativistic calculations performed using the one-step model of photoemission. While spin-resolved ARPES probes the spin component of entangled spin-orbital texture in multiorbital systems, we unambiguously demonstrate that TRDAD reveals its orbital pseudospin texture counterpart.

Topological Switch for Non-Hermitian Skin Effect in Cold-Atom Systems with Loss

We propose a realistic cold-atom quantum setting where topological localization induces nonreciprocal pumping. This is an intriguing non-Hermitian phenomenon that illustrates how topology, when assisted with atom loss, can act as a "switch" for the non-Hermitian skin effect (NHSE), rather than as a passive property that is modified by the NHSE. In particular, we present a lattice-shaking scenario to realize a two-dimensional cold-atom platform, where nonreciprocity is switched on only in the presence of both atom loss and topological localization due to time-reversal symmetry breaking. The resultant nonreciprocal pumping is manifested by asymmetric dynamical evolution, detectable by atomic populations along the system edges. Our setup may trigger possible applications in nonreciprocal atomtronics, where loss and topological mechanisms conspire to control atomic transport. Its quantum nature will also facilitate future studies on the interplay between non-Hermiticity and many-body physics.

Floquet Engineering Topological Many-Body Localized Systems

We show how second-order Floquet engineering can be employed to realize systems in which many-body localization coexists with topological properties in a driven system. This allows one to implement and dynamically control a symmetry protected topologically ordered qubit even at high energies, overcoming the roadblock that the respective states cannot be prepared as ground states of nearest-neighbor Hamiltonians. Floquet engineering-the idea that a periodically driven nonequilibrium system can effectively emulate the physics of a different Hamiltonian-is exploited to approximate an effective three-body interaction among spins in one dimension, using time-dependent two-body interactions only. In the effective system, emulated topology and disorder coexist, which provides an intriguing insight into the interplay of many-body localization that defies our standard understanding of thermodynamics and into the topological phases of matter, which are of fundamental and technological importance. We demonstrate explicitly how combining Floquet engineering, topology, and many-body localization allows one to harvest the advantages (time-dependent control, topological protection, and reduction of heating, respectively) of each of these subfields while protecting them from their disadvantages (heating, static control parameters, and strong disorder).

Periodically Driven Sachdev-Ye-Kitaev Models

Periodically driven quantum matter can realize exotic dynamical phases. In order to understand how ubiquitous and robust these phases are, it is pertinent to investigate the heating dynamics of generic interacting quantum systems. Here we study the thermalization in a periodically driven generalized Sachdev-Ye-Kitaev (SYK) model, which realizes a crossover from a heavy Fermi liquid (FL) to a non-Fermi liquid (NFL) at a tunable energy scale. Developing an exact field theoretic approach, we determine two distinct regimes in the heating dynamics. While the NFL heats exponentially and thermalizes rapidly, we report that the presence of quasiparticles in the heavy FL obstructs heating and thermalization over comparatively long timescales. Prethermal high-frequency dynamics and possible experimental realizations of nonequilibrium SYK physics are discussed as well.

Local Berry curvature signatures in dichroic angle-resolved photoelectron spectroscopy from two-dimensional materials

Topologically nontrivial two-dimensional materials hold great promise for next-generation optoelectronic applications. However, measuring the Hall or spin-Hall response is often a challenge and practically limited to the ground state. An experimental technique for tracing the topological character in a differential fashion would provide useful insights. In this work, we show that circular dichroism angle-resolved photoelectron spectroscopy provides a powerful tool that can resolve the topological and quantum-geometrical character in momentum space. In particular, we investigate how to map out the signatures of the momentum-resolved Berry curvature in two-dimensional materials by exploiting its intimate connection to the orbital polarization. A spin-resolved detection of the photoelectrons allows one to extend the approach to spin-Chern insulators. The present proposal can be extended to address topological properties in materials out of equilibrium in a time-resolved fashion.

Light-induced anomalous Hall effect in graphene

Many non-equilibrium phenomena have been discovered or predicted in optically-driven quantum solids¹. Examples include light-induced superconductivity^2,3 and Floquet-engineered topological phases^4-8. These are short lived effects that should lead to measurable changes in electrical transport, which can be characterized using an ultrafast device architecture based on photoconductive switches⁹. Here, we report the observation of a light-induced anomalous Hall effect in monolayer graphene driven by a femtosecond pulse of circularly polarized light. The dependence of the effect on a gate potential used to tune the Fermi level reveals multiple features that reflect a Floquet-engineered topological band structure^4,5, similar to the band structure originally proposed by Haldane¹⁰. This includes an approximately 60 meV wide conductance plateau centered at the Dirac point, where a gap of equal magnitude is predicted to open. We find that when the Fermi level lies within this plateau, the estimated anomalous Hall conductance saturates around 1.8±0.4 e²/h.

Photon-Induced Weyl Half-Metal Phase and Spin Filter Effect from Topological Dirac Semimetals

Recently discovered Dirac semimetals (DSMs) with two Dirac nodes, such as Na_{3}Bi and Cd_{2}As_{3}, are regarded as carrying the Z_{2} topological charge in addition to the chiral charge. We study the Floquet phase transition of Z_{2} topological DSMs subjected to a beam of circularly polarized light. Owing to the resulting interplay of the chiral and Z_{2} charges, the Weyl nodes are not only chirality dependent but also spin dependent, which constrains the behavior in creation and annihilation of the pair of Weyl nodes. Interestingly, we find a novel phase: One spin band is in the Weyl semimetal phase while the other is in the insulator phase, and we dub it the Weyl half-metal (WHM) phase. We further study the spin-dependent transport in a Dirac-Weyl semimetal junction and find a spin filter effect as a fingerprint of the existence of the WHM phase. The proposed spin filter effect, based on the WHM bulk band, is highly tunable in a broad parameter regime and robust against magnetic disorder, which is expected to overcome the shortcomings of the previously proposed spin filter based on the topological edge or surface states. Our results offer a unique opportunity to explore the potential applications of topological DSMs in spintronics.

Behavior of Floquet Topological Quantum States in Optically Driven Semiconductors

Spatially uniform optical excitations can induce Floquet topological band structures within insulators which can develop similar or equal characteristics as are known from three-dimensional topological insulators. We derive in this article theoretically the development of Floquet topological quantum states for electromagnetically driven semiconductor bulk matter and we present results for the lifetime of these states and their occupation in the non-equilibrium. The direct physical impact of the mathematical precision of the Floquet-Keldysh theory is evident when we solve the driven system of a generalized Hubbard model with our framework of dynamical mean field theory (DMFT) in the non-equilibrium for a case of ZnO. The physical consequences of the topological non-equilibrium effects in our results for correlated systems are explained with their impact on optoelectronic applications.

Charge Density Wave Melting in One-Dimensional Wires with Femtosecond Subgap Excitation

Charge density waves (CDWs) are symmetry-broken ground states that commonly occur in low-dimensional metals due to strong electron-electron and/or electron-phonon coupling. The nonequilibrium carrier distribution established via photodoping with femtosecond laser pulses readily quenches these ground states and induces an ultrafast insulator-to-metal phase transition. To date, CDW melting has been mainly investigated in the single-photon regime with pump photon energies bigger than the gap size. The recent development of strong-field midinfrared sources now enables the investigation of CDW dynamics following subgap excitation. Here we excite prototypical one-dimensional indium wires with a CDW gap of ∼300  meV with midinfrared pulses at ℏω=190  meV with MV/cm field strength and probe the transient electronic structure with time- and angle-resolved photoemission spectroscopy. We find that the CDW gap is filled on a timescale short compared to our temporal resolution of 300 fs and that the band structure changes are completed within ∼1  ps. Supported by a minimal theoretical model we attribute our findings to multiphoton absorption across the CDW gap.

Photon-mediated electronic correlation effects in irradiated two-dimensional Dirac systems

Periodically driven systems can host many interesting phenomena. Two-dimensional Dirac systems irradiated by circularly polarized light are especially attractive thanks to the special absorption and emission of photons near Dirac cones. Here, letting the light travel in the two-dimensional plane, we treat the light-driven Dirac systems by using a unitary transformation, instead of usual Floquet theory, to capture the photon-mediated electronic correlation effects. In this approach, the direct electron-photon interaction terms can be removed and the resulting effective electron-electron interactions can produce important effects. The effective interactions can produce topological band structure in the case of irradiated 2D Dirac fermion system, and can lift the energy degeneracy of the Dirac cones for irradiated graphene. This method can be applied to other light-driven Dirac systems to investigate their photon-mediated electronic effects. These phenomena would be observed with ultraviolet light in some effective two-dimensional Dirac systems of honeycomb long-period superstructures.

Positivity of the Spectral Densities of Retarded Floquet Green Functions

Periodically driven nonequilibrium many-body systems are interesting because they have quasi-energy spectra, which can be tailored by controlling the external driving fields. We derive the general spectral representation of retarded Green functions in the Floquet regime, thereby generalizing the well-known Lehmann representation from equilibrium many-body physics. The derived spectral Floquet representation allows us to prove the non-negativity of spectral densities and to determine exact spectral sum rules, which can be employed to benchmark the accuracy of approximations to the exact Floquet many-body Green functions.

Unraveling materials Berry curvature and Chern numbers from real-time evolution of Bloch states

It was established by Thouless, Kohmoto, Nightingale, and den Nijs in 1982 that the topology of the solid-state wavefunctions leads to quantization of transverse electrical conductivity of an insulator. This recognition has led to the development of the new field of topological materials characterized by symmetry-protected quantum numbers. Here, we propose a general and computationally efficient framework enabling one to unveil and predict materials-topological invariants in terms of physical observables, such as the bulk time-dependent current. We show how the quantized charge and spin Hall effect appears even for materials with a non-Abelian Berry phase. This dynamical approach is not necessarily restricted to density functional theory, but can be extended to other schemes and to other methods dealing with correlations explicitly.

Materials can be classified by the topological character of their electronic structure and, in this perspective, global attributes immune to local deformations have been discussed in terms of Berry curvature and Chern numbers. Except for instructional simple models, linear response theories have been ubiquitously used in calculations of topological properties of real materials. Here we propose a completely different and versatile approach to obtain the topological characteristics of materials by calculating physical observables from the real-time evolving Bloch states: The cell-averaged current density reveals the anomalous velocities that lead to the conductivity quantum. Results for prototypical cases are shown, including a spin-frozen valley Hall and a quantum anomalous Hall insulator. The advantage of this method is best illustrated by the example of a quantum spin Hall insulator: The quantized spin Hall conductivity is straightforwardly obtained irrespective of the non-Abelian nature in its Berry curvature. Moreover, the method can be extended to the description of real observables in nonequilibrium states of topological materials.

Optically pumped Floquet states of magnetization in ferromagnets

Floquet states have been the subject of great research interest since Zel'dovich's pioneering work on the quasienergy of a quantum system influenced by a temporally periodic action. Nowadays, periodic modulation of the system Hamiltonian is achieved mostly by microwaves, leading to novel exciting phenomena in condensed matter physics. On the other hand, nonthermal optical control of magnetization at picosecond time scales is currently a highly appealing research topic for potential applications in magnetic data storage. Here we combine these two concepts to theoretically investigate Floquet states in the system of exchange-coupled spins in a ferromagnet. Periodic perturbation of the magnetization of an iron-garnet film by circularly polarized femtosecond laser pulses is shown to establish the magnetization dynamics behaving like Floquet states. An external magnetic field allows tuning of the Floquet states, leading to pronounced increase in the precession amplitude by one order of magnitude at the center of the Brillouin zone, i.e., when the precession frequency is a multiple of the laser pulse repetition rate. Floquet states might potentially allow for parametric generation of magnetic oscillations. The observed phenomena expand the capabilities of coherent ultrafast optical control of magnetization and pave the way for their application in quantum computation or data processing.

All-optical nonequilibrium pathway to stabilising magnetic Weyl semimetals in pyrochlore iridates

Nonequilibrium many-body dynamics is becoming a central topic in condensed matter physics. Floquet topological states were suggested to emerge in photodressed bands under periodic laser driving. Here we propose a viable nonequilibrium route without requiring coherent Floquet states to reach the elusive magnetic Weyl semimetallic phase in pyrochlore iridates by ultrafast modification of the effective electron-electron interaction with short laser pulses. Combining ab initio calculations for a time-dependent self-consistent light-reduced Hubbard U and nonequilibrium magnetism simulations for quantum quenches, we find dynamically modified magnetic order giving rise to transiently emerging Weyl cones that can be probed by time- and angle-resolved photoemission spectroscopy. Our work offers a unique and realistic pathway for nonequilibrium materials engineering beyond Floquet physics to create and sustain Weyl semimetals. This may lead to ultrafast, tens-of-femtoseconds switching protocols for light-engineered Berry curvature in combination with ultrafast magnetism.

Ab Initio Simulation of Attosecond Transient Absorption Spectroscopy in Two-Dimensional Materials

We extend the first-principles analysis of attosecond transient absorption spectroscopy to two-dimensional materials. As an example of two-dimensional materials, we apply the analysis to monolayer hexagonal boron nitride (h-BN) and compute its transient optical properties under intense few-cycle infrared laser pulses. Nonadiabatic features are observed in the computed transient absorption spectra. To elucidate the microscopic origin of these features, we analyze the electronic structure of h-BN with density functional theory and investigate the dynamics of specific energy bands with a simple two-band model. Finally, we find that laser-induced intraband transitions play a significant role in the transient absorption even for the two-dimensional material and that the nonadiabatic features are induced by the dynamical Franz–Keldysh effect with an anomalous band dispersion.

Ultrafast Modification of Hubbard U in a Strongly Correlated Material: Ab initio High-Harmonic Generation in NiO

Engineering effective electronic parameters is a major focus in condensed matter physics. Their dynamical modulation opens the possibility of creating and controlling physical properties in systems driven out of equilibrium. In this Letter, we demonstrate that the Hubbard U, the widely used on-site Coulomb repulsion in strongly correlated materials, can be modified on femtosecond timescales by a strong nonresonant laser pulse excitation in the prototypical charge-transfer insulator NiO. Using our recently developed time-dependent density-functional theory plus self-consistent U method, we demonstrate the importance of a dynamically modulated U in the description of the high-harmonic generation of NiO. Our study opens the door to novel ways of modifying effective interactions in strongly correlated materials via laser driving, which may lead to new control paradigms for field-induced phase transitions and perhaps laser-induced Mott insulation in charge-transfer materials.

Many-Body Dynamics and Gap Opening in Interacting Periodically Driven Systems

We study transient dynamics in a two-dimensional system of interacting Dirac fermions subject to a quenched drive with circularly polarized light. In the absence of interactions, the drive opens a gap at the Dirac point in the quasienergy spectrum, inducing nontrivial band topology. We investigate the dynamics of this gap opening process, taking into account the essential role of electron-electron interactions. Crucially, scattering due to interactions (1) induces dephasing, which erases memory of the system's prequench state and yields the intrinsic timescale for gap emergence, and (2) provides a mechanism for the system to absorb energy of the drive, leading to heating which must be mitigated to ensure the success of Floquet band engineering. We characterize the gap opening process via the system's generalized spectral function and correlators probed by photoemission experiments, and we identify a parameter regime at moderate driving frequencies where a hierarchy of timescales allows a well-defined Floquet gap to be produced and studied before the deleterious effects of heating set in.

Photoinduced Nonequilibrium Topological States in Strained Black Phosphorus

Black phosphorus (BP), an elemental semiconductor, has attracted tremendous interest because it exhibits a wealth of interesting electronic and optoelectronic properties in equilibrium condition. The nonequilibrium electronic structures of bulk BP under a periodic field of laser remain unexplored, but can lead to intriguing topological optoelectronic properties. Here we show that, under the irradiation of circularly polarized light (CPL), BP exhibits a photon-dressed Floquet-Dirac semimetal state, which can be continuously tuned by changing the direction, intensity, and frequency of the incident laser. The topological phase transition from type-I to type-II Floquet-Dirac fermions manifests a new form of type-III phase, which exists in a wide range of intensities and frequencies of the incident laser. Furthermore, topological surface states exhibit nonequilibrium electron transport in a direction locked by the helicity of CPL. Our findings not only deepen our understanding of fundamental properties of BP in relation to topology but also extend optoelectronic device applications of BP to the nonequilibrium regime.

Phonon Driven Floquet Matter

The effect of electron-phonon coupling in materials can be interpreted as a dressing of the electronic structure by the lattice vibration, leading to vibrational replicas and hybridization of electronic states. In solids, a resonantly excited coherent phonon leads to a periodic oscillation of the atomic lattice in a crystal structure bringing the material into a nonequilibrium electronic configuration. Periodically oscillating quantum systems can be understood in terms of Floquet theory, which has a long tradition in the study of semiclassical light-matter interaction. Here, we show that the concepts of Floquet analysis can be applied to coherent lattice vibrations. This coupling leads to phonon-dressed quasi-particles imprinting specific signatures in the spectrum of the electronic structure. Such dressed electronic states can be detected by time- and angular-resolved photoelectron spectroscopy (ARPES) manifesting as sidebands to the equilibrium band structure. Taking graphene as a paradigmatic material with strong electron-phonon interaction and nontrivial topology, we show how the phonon-dressed states display an intricate sideband structure revealing the electron-phonon coupling at the Brillouin zone center and topological ordering of the Dirac bands. We demonstrate that if time-reversal symmetry is broken by the coherent lattice perturbations a topological phase transition can be induced. This work establishes that the recently demonstrated concept of light-induced nonequilibrium Floquet phases can also be applied when using coherent phonon modes for the dynamical control of material properties.

Femtosecond to picosecond transient effects in WSe 2 observed by pump-probe angle-resolved photoemission spectroscopy

Time-dependent responses of materials to an ultrashort optical pulse carry valuable information about the electronic and lattice dynamics; this research area has been widely studied on novel two-dimensional materials such as graphene, transition metal dichalcogenides (TMDs) and topological insulators (TIs). We report herein a time-resolved and angle-resolved photoemission spectroscopy (TRARPES) study of WSe2, a layered semiconductor of interest for valley electronics. The results for below-gap optical pumping reveal energy-gain and -loss Floquet replica valence bands that appear instantaneously in concert with the pump pulse. Energy shift, broadening, and complex intensity variation and oscillation at twice the phonon frequency for the valence bands are observed at time scales ranging from the femtosecond to the picosecond and beyond. The underlying physics is rich, including ponderomotive interaction, dressing of the electronic states, creation of coherent phonon pairs, and diffusion of charge carriers - effects operating at vastly different time domains.

Towards properties on demand in quantum materials

The past decade has witnessed an explosion in the field of quantum materials, headlined by the predictions and discoveries of novel Landau-symmetry-broken phases in correlated electron systems, topological phases in systems with strong spin-orbit coupling, and ultra-manipulable materials platforms based on two-dimensional van der Waals crystals. Discovering pathways to experimentally realize quantum phases of matter and exert control over their properties is a central goal of modern condensed-matter physics, which holds promise for a new generation of electronic/photonic devices with currently inaccessible and likely unimaginable functionalities. In this Review, we describe emerging strategies for selectively perturbing microscopic interaction parameters, which can be used to transform materials into a desired quantum state. Particular emphasis will be placed on recent successes to tailor electronic interaction parameters through the application of intense fields, impulsive electromagnetic stimulation, and nanostructuring or interface engineering. Together these approaches outline a potential roadmap to an era of quantum phenomena on demand.

Observation of Topological Bloch-State Defects and Their Merging Transition

Topological defects in Bloch bands, such as Dirac points in graphene, and their resulting Berry phases play an important role for the electronic dynamics in solid state crystals. Such defects can arise in systems with a two-atomic basis due to the momentum-dependent coupling of the two sublattice states, which gives rise to a pseudospin texture. The topological defects appear as vortices in the azimuthal phase of this pseudospin texture. Here, we demonstrate a complete measurement of the azimuthal phase in a hexagonal optical lattice employing a versatile method based on time-of-flight imaging after off-resonant lattice modulation. Furthermore, we map out the merging transition of the two Dirac points induced by beam imbalance. Our work paves the way to accessing geometric properties in optical lattices also with spin-orbit coupling and interactions.

Effects of light on quantum phases and topological properties of two-dimensional Metal-organic frameworks

Periodically driven nontrivial quantum states open another door to engineer topological phases in solid systems by light. Here we show, based on the Floquet-Bloch theory, that the on-resonant linearly and circularly polarized infrared light brings in the exotic Floquet quantum spin Hall state and half-metal in two-dimensional Metal-organic frameworks (2D MOFs) because of the unbroken and broken time-reversal symmetry, respectively. We also observe that the off-resonant light triggers topological quantum phase transitions and induces semimetals with pseudospin-1 Dirac-Weyl fermions via the photon-dressed topological band structures of 2D MOFs. This work paves a way to design light-controlled spintronics and optoelectronics based on 2D MOFs.

Coherent destruction of tunneling in graphene irradiated by elliptically polarized lasers

Photo-induced transition probabilities in graphene are studied theoretically from the viewpoint of Floquet theory. Conduction band populations are computed for a strongly, periodically driven graphene sheet under linear, circular, and elliptic polarization. Features of the momentum spectrum of excited quasi-particles can be directly related to the avoided crossing of the Floquet quasi-energy levels. In particular, the impact of the ellipticity and the strength of the laser excitation on the avoided crossing structure-and on the resulting transition probabilities-is studied. It is shown that the ellipticity provides an additional control parameter over the phenomenon of coherent destruction of tunneling in graphene, allowing one to selectively suppress multiphoton resonances.

Creating stable Floquet-Weyl semimetals by laser-driving of 3D Dirac materials

Tuning and stabilizing topological states, such as Weyl semimetals, Dirac semimetals or topological insulators, is emerging as one of the major topics in materials science. Periodic driving of many-body systems offers a platform to design Floquet states of matter with tunable electronic properties on ultrafast timescales. Here we show by first principles calculations how femtosecond laser pulses with circularly polarized light can be used to switch between Weyl semimetal, Dirac semimetal and topological insulator states in a prototypical three-dimensional (3D) Dirac material, Na3Bi. Our findings are general and apply to any 3D Dirac semimetal. We discuss the concept of time-dependent bands and steering of Floquet-Weyl points and demonstrate how light can enhance topological protection against lattice perturbations. This work has potential practical implications for the ultrafast switching of materials properties, such as optical band gaps or anomalous magnetoresistance.

Monitoring Electron-Photon Dressing in WSe2

Optical pumping of solids creates a nonequilibrium electronic structure where electrons and photons combine to form quasiparticles of dressed electronic states. The resulting shift of electronic levels is known as the optical Stark effect, visible as a red shift in the optical spectrum. Here we show that in a pump-probe setup we can uniquely define a nonequilibrium quasiparticle bandstructure that can be directly measurable with photoelectron spectroscopy. The dynamical photon-dressing (and undressing) of the many-body electronic states can be monitored by pump-probe time and angular-resolved photoelectron spectroscopy (tr-ARPES) as the photon-dressed bandstructure evolves in time depending on the pump-probe pulse overlap. The computed tr-ARPES spectrum agrees perfectly with the quasi-energy spectrum of Floquet theory at maximum overlap and goes to the equilibrium bandstructure as the pump-probe overlap goes to zero. Additionally, we show how this time-dependent nonequilibrium quasiparticle structure can be understood to be the bandstructure underlying the optical Stark effect. The extension to spin-resolved ARPES can be used to predict asymmetric dichroic response linked to the valley selective optical excitations in monolayer transition metal dichalcogenides (TMDs). These results establish the photon dressed nonequilibrium bandstructures as the underlying quasiparticle structure of light-driven steady-state quantum phases of matter.

Photo-electrons unveil topological transitions in graphene-like systems

The topological structure of the wavefunctions of particles in periodic potentials is characterized by the Berry curvature Ω_kn whose integral on the Brillouin zone is a topological invariant known as the Chern number. The bulk-boundary correspondence states that these numbers define the number of edge or surface topologically protected states. It is then of primary interest to find experimental techniques able to measure the Berry curvature. However, up to now, there are no spectroscopic experiments that proved to be capable to obtain information on Ω_kn to distinguish different topological structures of the bulk wavefunctions of semiconducting materials. Based on experimental results of the dipolar matrix elements for graphene, here we show that ARPES experiments with the appropriate x-ray energies and polarization can unambiguously detect changes of the Chern numbers in dynamically driven graphene and graphene-like materials opening new routes towards the experimental study of topological properties of condensed matter systems.

All-optical materials design of chiral edge modes in transition-metal dichalcogenides

Monolayer transition-metal dichalcogenides are novel materials which at low energies constitute a condensed-matter realization of massive relativistic fermions in two dimensions. Here, we show that this picture breaks for optical pumping—instead, the added complexity of a realistic materials description leads to a new mechanism to optically induce topologically protected chiral edge modes, facilitating optically switchable conduction channels that are insensitive to disorder. In contrast to graphene and previously discussed toy models, the underlying mechanism relies on the intrinsic three-band nature of transition-metal dichalcogenide monolayers near the band edges. Photo-induced band inversions scale linearly in applied pump field and exhibit transitions from one to two chiral edge modes on sweeping from red to blue detuning. We develop an ab initio strategy to understand non-equilibrium Floquet–Bloch bands and topological transitions, and illustrate for WS₂ that control of chiral edge modes can be dictated solely from symmetry principles and is not qualitatively sensitive to microscopic materials details.

Transition metal dichalcogenides offer a platform to study light-matter interaction in atomically thin semiconductors. Here, the authors perform ab initio calculations to illustrate the possibility of optical control of chiral edge modes, outlining a strategy to manipulate topological states.

Topological nature of nonlinear optical effects in solids

There are a variety of nonlinear optical effects including higher harmonic generations, photovoltaic effects, and nonlinear Kerr rotations. They are realized by strong light irradiation to materials that results in nonlinear polarizations in the electric field. These are of great importance in studying the physics of excited states of the system as well as for applications to optical devices and solar cells. Nonlinear properties of materials are usually described by nonlinear susceptibilities, which have complex expressions including many matrix elements and energy denominators. On the other hand, a nonequilibrium steady state under an electric field periodic in time has a concise description in terms of the Floquet bands of electrons dressed by photons. We show theoretically, using the Floquet formalism, that various nonlinear optical effects, such as the shift current in noncentrosymmetric materials, photovoltaic Hall response, and photo-induced change of order parameters under the continuous irradiation of monochromatic light, can be described in a unified fashion by topological quantities involving the Berry connection and Berry curvature. We found that vector fields defined with the Berry connections in the space of momentum and/or parameters govern the nonlinear responses. This topological view offers a route to designing nonlinear optical materials.