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

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.

Efficient exact exchange using Wannier functions and other related developments in planewave-pseudopotential implementation of RT-TDDFT

The plane-wave pseudopotential (PW-PP) formalism is widely used for the first-principles electronic structure calculation of extended periodic systems. The PW-PP approach has also been adapted for real-time time-dependent density functional theory (RT-TDDFT) to investigate time-dependent electronic dynamical phenomena. In this work, we detail recent advances in the PW-PP formalism for RT-TDDFT, particularly how maximally localized Wannier functions (MLWFs) are used to accelerate simulations using the exact exchange. We also discuss several related developments, including an anti-Hermitian correction for the time-dependent MLWFs (TD-MLWFs) when a time-dependent electric field is applied, the refinement procedure for TD-MLWFs, comparison of the velocity and length gauge approaches for applying an electric field, and elimination of long-range electrostatic interaction, as well as usage of a complex absorbing potential for modeling isolated systems when using the PW-PP formalism.

Defect-induced helicity dependent terahertz emission in Dirac semimetal PtTe2 thin films

Nonlinear transport enabled by symmetry breaking in quantum materials has aroused considerable interest in condensed matter physics and interdisciplinary electronics. However, achieving a nonlinear optical response in centrosymmetric Dirac semimetals via defect engineering has remained a challenge. Here, we observe the helicity dependent terahertz emission in Dirac semimetal PtTe2 thin films via the circular photogalvanic effect under normal incidence. This is activated by a controllable out-of-plane Te-vacancy defect gradient, which we unambiguously evidence with electron ptychography. The defect gradient lowers the symmetry, which not only induces the band spin splitting but also generates the giant Berry curvature dipole responsible for the circular photogalvanic effect. We demonstrate that the THz emission can be manipulated by the Te-vacancy defect concentration. Furthermore, the temperature evolution of the THz emission features a minimum in the THz amplitude due to carrier compensation. Our work provides a universal strategy for symmetry breaking in centrosymmetric Dirac materials for efficient nonlinear transport.

Tracking electron motion within and outside of Floquet bands from attosecond pulse trains in time-resolved ARPES

Floquet engineering has recently emerged as a technique for controlling material properties with light. Floquet phases can be probed with time- and angle-resolved photoelectron spectroscopy (Tr-ARPES), providing direct access to the laser-dressed electronic bands. Applications of Tr-ARPES to date focused on observing the Floquet-Bloch bands themselves, and their build-up and dephasing on sub-laser-cycle timescales. However, momentum and energy resolved sub-laser-cycle dynamics between Floquet bands have not been analyzed. Given that Floquet theory strictly applies in time-periodic conditions, the notion of resolving sub-laser-cycle dynamics between Floquet states seems contradictory-it requires probe pulse durations below a laser cycle that inherently cannot discern the time-periodic nature of the light-matter system. Here we propose to employ attosecond pulse train probes with the same temporal periodicity as the Floquet-dressing pump pulse, allowing both attosecond sub-laser-cycle resolution and a proper projection of Tr-ARPES spectra on the Floquet-Bloch bands. We formulate and employ this approach inab-initiocalculations in light-driven graphene. Our calculations predict significant sub-laser-cycle dynamics occurring within the Floquet phase with the majority of electrons moving within and in-between Floquet bands, and a small portion residing and moving outside of them in what we denote as 'non-Floquet' bands. We establish that non-Floquet bands arise from the pump laser envelope that induces non-adiabatic electronic excitations during the pulse turn-on and turn-off. By performing calculations in systems with poly-chromatic pumps we also show that Floquet states are not formed on a sub-laser-cycle level. This work indicates that the Floquet-Bloch states are generally not a complete basis set for sub-laser-cycle dynamics in steady-state phases of matter.

Real-Time Time-Dependent Density Functional Theory for Simulating Nonequilibrium Electron Dynamics

The explicit real-time propagation approach for time-dependent density functional theory (RT-TDDFT) has increasingly become a popular first-principles computational method for modeling various time-dependent electronic properties of complex chemical systems. In this Perspective, we provide a nontechnical discussion of how this first-principles simulation approach has been used to gain novel physical insights into nonequilibrium electron dynamics phenomena in recent years. Following a concise overview of the RT-TDDFT methodology from a practical standpoint, we discuss our recent studies on the electronic stopping of DNA in water and the Floquet topological phase as examples. Our discussion focuses on how RT-TDDFT simulations played a unique role in deriving new scientific understandings. We then discuss existing challenges and some new advances at the frontier of RT-TDDFT method development for studying increasingly complex dynamic phenomena and systems.

Chirality manipulation of ultrafast phase switches in a correlated CDW-Weyl semimetal

Light engineering of correlated states in topological materials provides a new avenue of achieving exotic topological phases inaccessible by conventional tuning methods. Here we demonstrate a light control of correlation gaps in a model charge-density-wave (CDW) and polaron insulator (TaSe4)2I recently predicted to be an axion insulator. Our ultrafast terahertz photocurrent spectroscopy reveals a two-step, non-thermal melting of polarons and electronic CDW gap via the fluence dependence of a longitudinal circular photogalvanic current. This helicity-dependent photocurrent reveals continuous ultrafast phase switches from the polaronic state to the CDW (axion) phase, and finally to a hidden Weyl phase as the pump fluence increases. Additional distinctive attributes aligning with the light-induced switches include: the mode-selective coupling of coherent phonons to the polaron and CDW modulation, and the emergence of a non-thermal chiral photocurrent above the pump threshold of CDW-related phonons. The demonstrated ultrafast chirality control of correlated topological states here holds large potentials for realizing axion electrodynamics and advancing quantum-computing applications.

Light-Induced Ideal Weyl Semimetal in HgTe via Nonlinear Phononics

Interactions between light and matter allow the realization of out-of-equilibrium states in quantum solids. In particular, nonlinear phononics is one of the most efficient approaches to realizing the stationary electronic state in nonequilibrium. Herein, by an extended ab initio molecular dynamics method, we identify that long-lived light-driven quasistationary geometry could stabilize the topological nature in the material family of HgTe compounds. We show that coherent excitation of the infrared-active phonon mode results in a distortion of the atomic geometry with a lifetime of several picoseconds. We show that four Weyl points are located exactly at the Fermi level in this nonequilibrium geometry, making it an ideal long-lived metastable Weyl semimetal. We propose that such a metastable topological phase can be identified by photoelectron spectroscopy of the Fermi arc surface states or ultrafast pump-probe transport measurements of the nonlinear Hall effect.

Microscopic nonlinear optical response: Analysis and calculations with the Floquet-Bloch formalism

We analyze microscopic nonlinear optical response of periodic structures within the Floquet-Bloch formalism. The analysis is focused on the real-space distributions of optically induced charge and electron current density within the unit cell of a crystal. We demonstrate that the time-reversal symmetry of a crystal determines the phases of the temporal oscillations of these distributions. We further analyze their spatial symmetries and connection to macroscopic optical response. We illustrate our study with ab initio calculations that combine density functional theory with the Floquet-Bloch formalism. The calculations provide time-dependent optically induced charge distributions and electron current densities within the unit cells of a crystal with inversion symmetry MgO and a crystal without inversion symmetry GaAs in response to a strong-field excitation. The real-space, microscopic view on nonlinear optical response provides insightful information about the strong field-matter interaction.

Ultrafast Spin Dynamics and Photoinduced Insulator-to-Metal Transition in α-RuCl3

Laser-induced ultrafast demagnetization is a phenomenon of utmost interest and attracts significant attention because it enables potential applications in ultrafast optoelectronics and spintronics. As a spin-orbit coupling assisted magnetic insulator, α-RuCl3 provides an attractive platform to explore the physics of electronic correlations and unconventional magnetism. Using time-dependent density functional theory, we explore the ultrafast laser-induced dynamics of the electronic and magnetic structures in α-RuCl3. Our study unveils that laser pulses can introduce ultrafast demagnetizations, accompanied by an out-of-equilibrium insulator-to-metal transition in a few tens of femtoseconds. The spin response significantly depends on the laser wavelength and polarization on account of the electron correlations, band renormalizations, and charge redistributions. These findings provide physical insights into the coupling between the electronic and magnetic degrees of freedom in α-RuCl3 and shed light on suppressing the long-range magnetic orders and reaching a proximate spin liquid phase for two-dimensional magnets on an ultrafast time scale.

Floquet Engineering of Black Phosphorus upon Below-Gap Pumping

Time-periodic light field can dress the electronic states and lead to light-induced emergent properties in quantum materials. While below-gap pumping is regarded favorable for Floquet engineering, so far direct experimental evidence of momentum-resolved band renormalization still remains missing. Here, we report experimental evidence of light-induced band renormalization in black phosphorus by pumping at photon energy of 160 meV, which is far below the band gap, and the distinction between below-gap pumping and near-resonance pumping is revealed. Our Letter demonstrates light-induced band engineering upon below-gap pumping, and provides insights for extending Floquet engineering to more quantum materials.

Disentangling the Competing Mechanisms of Light-Induced Anomalous Hall Conductivity in Three-Dimensional Dirac Semimetal

We experimentally elucidate the origin of the anomalous Hall conductivity in a three-dimensional Dirac semimetal, Cd_{3}As_{2}, driven by circularly polarized light. Using time-resolved terahertz Faraday rotation spectroscopy, we determine the transient Hall conductivity spectrum with special attention to its sign. Our results clearly show the dominance of direct photocurrent generation assisted by the terahertz electric field. The contribution from the Floquet-Weyl nodes is found to be minor when the driving light is in resonance with interband transitions. We develop a generally applicable classification of microscopic mechanisms of light-induced anomalous Hall conductivity.

Band Nonlinearity-Enabled Manipulation of Dirac Nodes, Weyl Cones, and Valleytronics with Intense Linearly Polarized Light

We study low-frequency linearly polarized laser-dressing in materials with valley (graphene and hexagonal-Boron-Nitride) and topological (Dirac- and Weyl-semimetals) properties. In Dirac-like linearly dispersing bands, the laser substantially moves the Dirac nodes away from their original position, and the movement direction can be fully controlled by rotating the laser polarization. We prove that this effect originates from band nonlinearities away from the Dirac nodes. We further demonstrate that this physical mechanism is widely applicable and can move the positions of the valley minima in hexagonal materials to tune valley selectivity, split and move Weyl cones in higher-order Weyl semimetals, and merge Dirac nodes in three-dimensional Dirac semimetals. The model results are validated with ab initio calculations. Our results directly affect efforts for exploring light-dressed electronic structure, suggesting that one can benefit from band nonlinearity for tailoring material properties, and highlight the importance of the full band structure in nonlinear optical phenomena in solids.

Narrowband, Angle-Tunable, Helicity-Dependent Terahertz Emission from Nanowires of the Topological Dirac Semimetal Cd3As2

All-optical control of terahertz pulses is essential for the development of optoelectronic devices for next-generation quantum technologies. Despite substantial research in THz generation methods, polarization control remains difficult. Here, we demonstrate that by exploiting band structure topology, both helicity-dependent and helicity-independent THz emission can be generated from nanowires of the topological Dirac semimetal Cd₃As₂. We show that narrowband THz pulses can be generated at oblique incidence by driving the system with optical (1.55 eV) pulses with circular polarization. Varying the incident angle also provides control of the peak emission frequency, with peak frequencies spanning 0.21-1.40 THz as the angle is tuned from 15 to 45°. We therefore present Cd₃As₂ nanowires as a promising novel material platform for controllable terahertz emission.

Dominant Two-Dimensional Electron-Phonon Interactions in the Bulk Dirac Semimetal Na3Bi

Bulk Dirac semimetals (DSMs) exhibit unconventional transport properties and phase transitions due to their peculiar low-energy band structure, yet the electronic interactions governing nonequilibrium phenomena in DSMs are not fully understood. Here we show that electron-phonon (e-ph) interactions in a prototypical bulk DSM, Na₃Bi, are predominantly two-dimensional (2D). Our first-principles calculations reveal a 2D optical phonon with strong e-ph interactions associated with in-plane vibrations of Na atoms. We show that this 2D mode governs e-ph scattering and charge transport in Na₃Bi and induces a dynamical phase transition to a Weyl semimetal. Our work advances the quantitative analysis of electron interactions in Na₃Bi and reveals a dominant low-dimensional interaction in a bulk Dirac semimetal.

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.

Pseudospin-selective Floquet band engineering in black phosphorus

Time-periodic light field has emerged as a control knob for manipulating quantum states in solid-state materials^1-3, cold atoms⁴ and photonic systems⁵ through hybridization with photon-dressed Floquet states⁶ in the strong-coupling limit, dubbed Floquet engineering. Such interaction leads to tailored properties of quantum materials^7-11, for example, modifications of the topological properties of Dirac materials^12,13 and modulation of the optical response^14-16. Despite extensive research interests over the past decade^3,8,17-20, there is no experimental evidence of momentum-resolved Floquet band engineering of semiconductors, which is a crucial step to extend Floquet engineering to a wide range of solid-state materials. Here, on the basis of time and angle-resolved photoemission spectroscopy measurements, we report experimental signatures of Floquet band engineering in a model semiconductor, black phosphorus. On near-resonance pumping at a photon energy of 340-440 meV, a strong band renormalization is observed near the band edges. In particular, light-induced dynamical gap opening is resolved at the resonance points, which emerges simultaneously with the Floquet sidebands. Moreover, the band renormalization shows a strong selection rule favouring pump polarization along the armchair direction, suggesting pseudospin selectivity for the Floquetband engineering as enforced by the lattice symmetry. Our work demonstrates pseudospin-selective Floquet band engineering in black phosphorus and provides important guiding principles for Floquet engineering of semiconductors.

Probing magnetic orbitals and Berry curvature with circular dichroism in resonant inelastic X-ray scattering

Resonant inelastic X-ray scattering (RIXS) can probe localized excitations at selected atoms in materials, including particle-hole transitions between the valence and conduction bands. These transitions are governed by fundamental properties of the corresponding Bloch wave functions, including orbital and magnetic degrees of freedom, and quantum geometric properties such as the Berry curvature. In particular, orbital angular momentum (OAM), which is closely linked to the Berry curvature, can exhibit a nontrivial momentum dependence. We demonstrate how information on such OAM textures can be extracted from the circular dichroism in RIXS. Based on accurate modeling with a first-principles treatment of the key ingredient-the light-matter interaction-we simulate dichroic RIXS spectra for the prototypical transition-metal dichalcogenide MoSe2 and the two-dimensional topological insulator 1T'-MoS2. Guided by an intuitive picture of the optical selection rules, we discuss how the momentum-dependent OAM manifests itself in the dichroic RIXS signal if one controls the momentum transfer. Our calculations are performed for typical experimental geometries and parameter regimes, and demonstrate the possibility of observing the predicted circular dichroism in forthcoming experiments. Thus, our work establishes a new avenue for observing Berry curvature and topological states in quantum materials.

Single-shot measurement of the near-field and focal spot profiles of a 351 nm laser beam for SGII-upgraded facility with multiple-focal-plane constraint coherent modulation imaging

Inertial confinement fusion (ICF) places an urgent demand for precise measurement of 351 nm (3ω) laser beam parameters when performing physical experiments on high-power laser facilities. The near-field and focal spot distributions are the utmost important parameters to characterize the quality of the laser beam. Coherent modulation imaging (CMI) is a promising technique for online laser beam measurement, however, it fails to reconstruct the near-field and focal spot profiles when it is used to measure the beam quality of a 351 nm laser beam for SGII-upgrade facility. To solve this problem, a novel CMI reconstruction algorithm is proposed in this work, and the performance of the algorithm in 3ω laser beam measurement can be obviously improved. By adopting multiple-virtual-focal-plane constraint in the proposed algorithm, the near-field and focal spot profiles of the 3ω laser beam can be successfully reconstructed. Experiments have been conducted on SGII-upgrade facility to verify the feasibility of the proposed method.

Stimulated Rayleigh Scattering Enhanced by a Longitudinal Plasma Mode in a Periodically Driven Dirac Semimetal Cd_{3}As_{2}

Using broadband (12-45 THz) multi-terahertz spectroscopy, we show that stimulated Rayleigh scattering dominates the transient optical conductivity of cadmium arsenide, a Dirac semimetal, under an optical driving field at 30 THz. The characteristic dispersive line shape with net optical gain is accounted for by optical transitions between light-induced Floquet subbands, strikingly enhanced by the longitudinal plasma mode. Stimulated Rayleigh scattering with an unprecedentedly large refractive index change may pave the way for slow light generation in conductive solids at room temperature.

Recent Development of Ultrafast Optical Characterizations for Quantum Materials

The advent of intense ultrashort optical pulses spanning a frequency range from terahertz to the visible has opened a new era in the experimental investigation and manipulation of quantum materials. The generation of strong optical field in an ultrashort time scale enables the steering of quantum materials nonadiabatically, inducing novel phenomenon or creating new phases which may not have an equilibrium counterpart. Ultrafast time-resolved optical techniques have provided rich information and played an important role in characterization of the nonequilibrium and nonlinear properties of solid systems. Here, some of the recent progress of ultrafast optical techniques and their applications to the detection and manipulation of physical properties in selected quantum materials are reviewed. Specifically, the new development in the detection of the Higgs mode and photoinduced nonequilibrium response in the study of superconductors by time-resolved terahertz spectroscopy are discussed.

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.

Tracking Ultrafast Change of Multiterahertz Broadband Response Functions in a Photoexcited Dirac Semimetal Cd3As2 Thin Film

The electromagnetic response of Dirac semimetals in the infrared and terahertz frequency ranges is attracting growing interest for potential applications in optoelectronics and nonlinear optics. The interplay between the free-carrier response and interband transitions in the gapless, linear dispersion relation plays a key role in enabling novel functionalities. Here we investigate ultrafast dynamics in thin films of a photoexcited Dirac semimetal Cd₃As₂ by probing the broadband response functions as complex quantities in the multiterahertz region (10-45 THz, 40-180 meV, or 7-30 μm), which covers the crossover between the inter- and intraband response. We resolve dynamics of the photoexcited nonthermal electrons, which merge with originally existing carriers to form a single thermalized electron gas and how it is facilitated by high-density excitation. We also demonstrate that a large reduction of the refractive index by 80% dominates the nonequilibrium infrared response, which can be utilized for designing ultrafast switches in active optoelectronics.

Bicircular Light Floquet Engineering of Magnetic Symmetry and Topology and Its Application to the Dirac Semimetal Cd_{3}As_{2}

We show that bicircular light (BCL) is a versatile way to control magnetic symmetries and topology in materials. The electric field of BCL, which is a superposition of two circularly polarized light waves with frequencies that are integer multiples of each other, traces out a rose pattern in the polarization plane that can be chosen to break selective symmetries, including spatial inversion. Using a realistic low-energy model, we theoretically demonstrate that the three-dimensional Dirac semimetal Cd_{3}As_{2} is a promising platform for BCL Floquet engineering. Without strain, BCL irradiation induces a transition to a noncentrosymmetric magnetic Weyl semimetal phase with tunable energy separation between the Weyl nodes. In the presence of strain, we predict the emergence of a magnetic topological crystalline insulator with exotic unpinned surface Dirac states that are protected by a combination of twofold rotation and time reversal (2^{'}) and can be controlled by light.

Population Inversion and Dirac Fermion Cooling in 3D Dirac Semimetal Cd3As2

Revealing the ultrafast dynamics of three-dimensional (3D) Dirac fermions is critical for both fundamental science and device applications. So far, how the cooling of 3D Dirac fermions differs from that of two-dimensional (2D) and whether there is population inversion are fundamental questions to be answered. Here we reveal the ultrafast dynamics of Dirac fermions in a model 3D Dirac semimetal Cd₃As₂ by time- and angle-resolved photoemission spectroscopy with a tunable probe photon energy. The energy- and momentum-resolved relaxation rate shows a linear dependence on the energy, suggesting Dirac fermion cooling through intraband relaxation. Moreover, a population inversion is reported based on the observation of accumulated photoexcited carriers in the conduction band with a lifetime of 3.0 ps. Our work provides direct experimental evidence for a long-lived population inversion in a 3D Dirac semimetal, which is in contrast to 2D graphene with a much shorter lifetime.

Detecting multiple chiral centers in chiral molecules with high harmonic generation

Characterizing chiral is highly important for applications in the pharmaceutical industry, as well as in the study of dynamical chemical and biological systems. However, this task has remained challenging, especially due to the ongoing increasing complexity and size of the molecular structure of drugs and active compounds. In particular, large molecules with many active chiral centers are today ubiquitous, but remain difficult to structurally analyze due to their high number of stereoisomers. Here we theoretically explore the sensitivity of high harmonic generation (HHG) to the chiral of molecules with a varying number of active chiral centers. We find that HHG driven by bi-chromatic non-collinear lasers is a sensitive probe for the stereo-configuration of a chiral molecule. We first show through calculations (from benchmark chiral molecules with up to three chiral centers) that the HHG spectrum is imprinted with information about the handedness of each chiral center in the driven molecule. Next, we show that using both classical- and deep-learning-based reconstruction algorithms, the composition of an unknown mixture of stereoisomers can be reconstructed with high fidelity by a single-shot HHG measurement. Our work illustrates how the combination of non-linear optics and machine learning might open routes for ultra-sensitive sensing in chiral systems.

Control of the Geometric Phase and Nonequivalence between Geometric-Phase Definitions in the Adiabatic Limit

If the time evolution of a quantum state leads back to the initial state, a geometric phase is accumulated that is known as the Berry phase for adiabatic evolution or as the Aharonov-Anandan (AA) phase for nonadiabatic evolution. We evaluate these geometric phases using Floquet theory for systems in time-dependent external fields with a focus on paths leading through a degeneracy of the eigenenergies. Contrary to expectations, the low-frequency limits of the two phases do not always coincide. This happens as the degeneracy leads to a slow convergence of the quantum states to adiabaticity, resulting in a nonzero finite or divergent contribution to the AA phase. Steering the system adiabatically through a degeneracy provides control over the geometric phase as it can cause a π shift of the Berry phase. On the other hand, we revisit an example of degeneracy crossing proposed by AA. We find that, at suitable driving frequencies, both geometric-phase definitions give the same result and the dynamical phase is zero due to the symmetry of time evolution about the point of degeneracy, providing an advantageous setup for manipulation of quantum states.

Ultrafast time- and angle-resolved photoemission spectroscopy with widely tunable probe photon energy of 5.3-7.0 eV for investigating dynamics of three-dimensional materials

Time- and angle-resolved photoemission spectroscopy (TrARPES) is a powerful technique for capturing the ultrafast dynamics of charge carriers and revealing photo-induced phase transitions in quantum materials. However, the lack of widely tunable probe photon energy, which is critical for accessing the dispersions at different out-of-plane momentum k_z in TrARPES measurements, has hindered the ultrafast dynamics investigation of 3D quantum materials, such as Dirac or Weyl semimetals. Here, we report the development of a TrARPES system with a highly tunable probe photon energy from 5.3 to 7.0 eV. The tunable probe photon energy is generated by the fourth harmonic generation of a tunable wavelength femtosecond laser source by combining a β-BaB₂O₄ crystal and a KBe₂BO₃F₂ crystal. A high energy resolution of 29-48 meV and time resolution of 280-320 fs are demonstrated on 3D topological materials ZrTe₅ and Sb₂Te₃. Our work opens up new opportunities for exploring ultrafast dynamics in 3D quantum materials.

Giant modulation of optical nonlinearity by Floquet engineering

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^1-6, emergent spin interactions^7-11 and even superconductivity¹². However, the prospects and methods of coherently engineering optical properties on demand are far less understood¹³. Here we demonstrate coherent control and giant modulation of optical nonlinearity in a van der Waals layered magnetic insulator, manganese phosphorus trisulfide (MnPS₃). By driving far off-resonance from the lowest on-site manganese d-d transition, we observe a coherent on-off switching of its optical second harmonic generation efficiency on the timescale of 100 femtoseconds with no measurable dissipation. At driving electric fields of the order of 10⁹ volts per metre, the on-off ratio exceeds 10, which is limited only by the sample damage threshold. Floquet theory calculations¹⁴ based on a single-ion model of MnPS₃ are able to reproduce the measured driving field amplitude and polarization dependence of the effect. Our approach can be applied to a broad range of insulating materials and could lead to dynamically designed nonlinear optical elements.

The generation of switchable polarized currents in nodal ring semimetals using high-frequency periodic driving

A nodal ring semimetal (NRSM) can be driven to a spin-polarized NRSM or a spin-polarized Weyl semimetal (WSM) by a high-frequency electromagnetic field. We investigate the conditions in realizing these phases and propose a switchable spin-polarized currents generator based on periodically driven NRSMs. Both bulk and surface polarized currents are investigated. The polarization of bulk current is sensitive to the amplitude of the driving field and robust against the direction and polarization of the driving, the opaqueness of the lead-device interface and the misalignment between the nodal ring and the interface, which provides sufficient flexibility in manipulating the devices. Similar switchable polarized surface currents are also expected, which is contributed by the Fermi arc surface state associated with the WSM phases. The generation of polarized currents and the polarization switching effect offer opportunities to design periodic driving controlled topological spintronics devices based on NRSMs.

Topological hybrid semimetal phases and anomalous Hall effects in a three dimensional magnetic topological insulator

In this work, we propose a ferromagnetic Bi₂Se₃as a candidate to hold the coexistence of Weyl- and nodal-line semimetal phases, which breaks the time reversal symmetry. We demonstrate that the type-I Weyl semimetal phase, type-I-, type-II- and their hybrid nodal-line semimetal phases can arise by tuning the Zeeman exchange field strength and the Fermi velocity. Their topological responses under U(1) gauge field are also discussed. Our results raise a new way for realizing Weyl and nodal-line semimetals and will be helpful in understanding the topological transport phenomena in three-dimensional material systems.

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.

Light-Driven Extremely Nonlinear Bulk Photogalvanic Currents

We predict the generation of bulk photocurrents in materials driven by bichromatic fields that are circularly polarized and corotating. The nonlinear photocurrents have a fully controllable directionality and amplitude without requiring carrier-envelope-phase stabilization or few-cycle pulses, and can be generated with photon energies much smaller than the band gap (reducing heating in the photoconversion process). We demonstrate with ab initio calculations that the photocurrent generation mechanism is universal and arises in gaped materials (Si, diamond, MgO, hBN), in semimetals (graphene), and in two- and three-dimensional systems. Photocurrents are shown to rely on sub-laser-cycle asymmetries in the nonlinear response that build-up coherently from cycle to cycle as the conduction band is populated. Importantly, the photocurrents are always transverse to the major axis of the co-circular lasers regardless of the material's structure and orientation (analogously to a Hall current), which we find originates from a generalized time-reversal symmetry in the driven system. At high laser powers (∼10^{13}  W/cm^{2}) this symmetry can be spontaneously broken by vast electronic excitations, which is accompanied by an onset of carrier-envelope-phase sensitivity and ultrafast many-body effects. Our results are directly applicable for efficient light-driven control of electronics, and for enhancing sub-band-gap bulk photogalvanic effects.

Simulating electronic excitation and dynamics with real-time propagation approach to TDDFT within plane-wave pseudopotential formulation

We give a perspective on simulating electronic excitation and dynamics using the real-time propagation approach to time-dependent density functional theory (RT-TDDFT) in the plane-wave pseudopotential formulation. RT-TDDFT is implemented in various numerical formalisms in recent years, and its practical application often dictates the most appropriate implementation of the theory. We discuss recent developments and challenges, emphasizing numerical aspects of studying real systems. Several applications of RT-TDDFT simulation are discussed to highlight how the approach is used to study interesting electronic excitation and dynamics phenomena in recent years.

Moving Dirac nodes by chemical substitution

Dirac fermions play a central role in the study of topological phases, for they can generate a variety of exotic states, such as Weyl semimetals and topological insulators. The control and manipulation of Dirac fermions constitute a fundamental step toward the realization of novel concepts of electronic devices and quantum computation. By means of Angle-Resolved Photo-Emission Spectroscopy (ARPES) experiments and ab initio simulations, here, we show that Dirac states can be effectively tuned by doping a transition metal sulfide, [Formula: see text], through Co/Ni substitution. The symmetry and chemical characteristics of this material, combined with the modification of the charge-transfer gap of [Formula: see text] across its phase diagram, lead to the formation of Dirac lines, whose position in k-space can be displaced along the [Formula: see text] symmetry direction and their form reshaped. Not only does the doping x tailor the location and shape of the Dirac bands, but it also controls the metal-insulator transition in the same compound, making [Formula: see text] a model system to functionalize Dirac materials by varying the strength of electron correlations.

First-Principles Demonstration of Nonadiabatic Thouless Pumping of Electrons in a Molecular System

We demonstrate nonadiabatic Thouless pumping of electrons in trans-polyacetylene in the framework of Floquet engineering using first-principles theory. We identify the regimes in which the quantized pump is operative with respect to the driving electric field for a time-dependent Hamiltonian. By employing the time-dependent maximally localized Wannier functions in real-time time-dependent density functional theory simulation, we connect the winding number, a topological invariant, to a molecular-level understanding of the quantized pumping. While the pumping dynamics constitutes the opposing movement of the Wannier functions that represent both double and single bonds, the resulting current is unidirectional due to the greater number of double-bond electrons. Using a gauge-invariant formulation called dynamical transition orbitals, an alternative viewpoint on the nonequilibrium dynamics is obtained in terms of the particle-hole excitation. A single time-dependent transition orbital is found to be largely responsible for the observed quantized pumping. In this representation, the pumping dynamics manifests itself in the dynamics of this single orbital as it undergoes changes from its π bonding orbital character at equilibrium to acquiring resonance and antibonding character in the driving cycle. The work demonstrates the Floquet engineering of the nonadiabatic topological state in an extended molecular system, paving the way for experimental realization of the new quantum material phase.

Manipulating Weyl quasiparticles by orbital-selective photoexcitation in WTe2

Optical control of structural and electronic properties of Weyl semimetals allows development of switchable and dissipationless topological devices at the ultrafast scale. An unexpected orbital-selective photoexcitation in type-II Weyl material WTe2 is reported under linearly polarized light (LPL), inducing striking transitions among several topologically-distinct phases mediated by effective electron-phonon couplings. The symmetry features of atomic orbitals comprising the Weyl bands result in asymmetric electronic transitions near the Weyl points, and in turn a switchable interlayer shear motion with respect to linear light polarization, when a near-infrared laser pulse is applied. Consequently, not only annihilation of Weyl quasiparticle pairs, but also increasing separation of Weyl points can be achieved, complementing existing experimental observations. In this work, we provide a new perspective on manipulating the Weyl node singularity and coherent control of electron and lattice quantum dynamics simultaneously.

A light-induced phononic symmetry switch and giant dissipationless topological photocurrent in ZrTe5

Dissipationless currents from topologically protected states are promising for disorder-tolerant electronics and quantum computation. Here, we photogenerate giant anisotropic terahertz nonlinear currents with vanishing scattering, driven by laser-induced coherent phonons of broken inversion symmetry in a centrosymmetric Dirac material ZrTe₅. Our work suggests that this phononic terahertz symmetry switching leads to formation of Weyl points, whose chirality manifests in a transverse, helicity-dependent current, orthogonal to the dynamical inversion symmetry breaking axis, via circular photogalvanic effect. The temperature-dependent topological photocurrent exhibits several distinct features: Berry curvature dominance, particle-hole reversal near conical points and chirality protection that is responsible for an exceptional ballistic transport length of ~10 μm. These results, together with first-principles modelling, indicate two pairs of Weyl points dynamically created by B_1u phonons of broken inversion symmetry. Such phononic terahertz control breaks ground for coherent manipulation of Weyl nodes and robust quantum transport without application of static electric or magnetic fields.

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.

Edge states of Floquet-Dirac semimetal in a laser-driven semiconductor quantum-well

Band crossings observed in a wide range of condensed matter systems are recognized as a key to understand low-energy fermionic excitations that behave as massless Dirac particles. Despite rapid progress in this field, the exploration of non-equilibrium topological states remains scarce and it has potential ability of providing a new platform to create unexpected massless Dirac states. Here we show that in a semiconductor quantum-well driven by a cw-laser with linear polarization, the optical Stark effect conducts bulk-band crossing, and the resulting Floquet-Dirac semimetallic phase supports an unconventional edge state in the projected one-dimensional Brillouin zone under a boundary condition that an electron is confined in the direction perpendicular to that of the laser polarization. Further, we reveal that this edge state mediates a transition between topological and non-topological edge states that is caused by tuning the laser intensity. We also show that the properties of the edge states are strikingly changed under a different boundary condition. It is found that such difference originates from that nearly fourfold-degenerate points exist in a certain intermediate region of the bulk Brillouin zone between high-symmetry points.

Higher-Order Weyl Semimetals

We investigate higher-order Weyl semimetals (HOWSMs) having bulk Weyl nodes attached to both surface and hinge Fermi arcs. We identify a new type of Weyl node, which we dub a 2nd-order Weyl node, that can be identified as a transition in momentum space in which both the Chern number and a higher order topological invariant change. As a proof of concept we use a model of stacked higher order quadrupole insulators (QI) to identify three types of WSM phases: 1st order, 2nd order, and hybrid order. The model can also realize type-II and hybrid-tilt WSMs with various surface and hinge arcs. After a comprehensive analysis of the topological properties of various HOWSMs, we turn to their physical implications that show the very distinct behavior of 2nd-order Weyl nodes when they are gapped out. We obtain three remarkable results: (i) the coupling of a 2nd-order Weyl phase with a conventional 1st-order one can lead to a hybrid-order topological insulator having coexisting surface cones and flat hinge arcs that are independent and not attached to each other. (ii) A nested 2nd-order inversion-symmetric WSM by a charge-density wave (CDW) order generates an insulating phase having coexisting flatband surface and hinge states all over the Brillouin zone. (iii) A CDW order in a time-reversal symmetric higher-order WSM gaps out a 2nd-order node with a 1st-order node and generates an insulating phase having coexisting surface Dirac cone and hinge arcs. Moreover, we show that a measurement of charge density in the presence of magnetic flux can help to identify some classes of 2nd-order WSMs. Finally, we show that periodic driving can be utilized as a way for generating HOWSMs. Our results are relevant to metamaterials as well as various phases of Cd_{3}As_{2}, KMgBi, and rutile-structure PtO_{2} that have been predicted to realize higher order Dirac semimetals.

Magneto-Optical Tools to Study Effects in Dirac and Weyl Semimetals

Research regarding topological Dirac and Weyl semimetals contributes to our understanding not only of the field of solid-state physics, but also the field of high-energy physics as the physics of Dirac and Weyl semimetals resembles the physics of Dirac and Weyl massless fermions. In condensed matter physics, the Weyl nodes are detached in momentum space and may be realized as emergent quasiparticles with a distinct chirality, left-handed or right-handed. These states lead to phenomena like the chiral anomaly and the anomalous Hall effect (AHE). Furthermore, the combination of quantum effects and magnetic effects in magnetic Weyl semimetals is very intriguing. Magneto-optical tools, which are usually used to study magnetic phenomena, also contribute to magnetic Weyl semimetals. Moreover, with the magneto-optical technique, it is possible to follow the dynamics of the processes and to study the lifetime of the Weyl states. In this work, we review and discuss the effects of using magneto-optical tools for studying quantum effects like the chiral anomaly or magnetic effects in magnetic Weyl and Dirac systems using the magneto-optical Kerr effect (MOKE) or Faraday systems including a single detection and imaging. Examples of using magneto-optical systems in the research of ultrafast magnetic dynamics of thin polycrystalline nickel and permaloy are reviewed as are the magnetic spatial dynamics by employing magneto-optical Kerr or Faraday microscopy tools with ferromagnetic thin films. Interestingly, the excitation of a circularly polarized femtosecond laser pulse could lead to the breakage of time-reversal symmetry and to the transformation of the Dirac state to the Floquet–Weyl semimetal state. The development of a suitable ultrafast magneto-optical system for Weyl systems is discussed, and the practical difficulties for the realization of such a system are considered.

A Large Effective Phonon Magnetic Moment in a Dirac Semimetal

We investigated the magnetoterahertz response of the Dirac semimetal Cd₃As₂ and observed a particularly low frequency optical phonon as well as a very prominent and field-sensitive cyclotron resonance. As the cyclotron frequency is tuned with the field to pass through the phonon, the phonon becomes circularly polarized, as shown by a notable splitting in its response to right- and left-hand polarized light. This splitting can be expressed as an effective phonon magnetic moment that is approximately 2.7 times the Bohr magneton, which is almost 4 orders of magnitude larger than ab initio calculations predict for phonon magnetic moments in nonmagnetic insulators. This exceedingly large value is due to the coupling of the phonons to the cyclotron motion and is controlled directly by the electron-phonon coupling constant. This field-tunable circular-polarization-selective coupling provides new functionality for nonlinear optics to create light-induced topological phases in Dirac semimetals.

Folding Graphene into a Chern Insulator with Light Irradiation

Recently, the precise folding of flexible graphene is reported experimentally [ Science, 2019, 365, 1036-1040], demonstrating an efficient approach to manipulate its electronic and optoelectronic properties. Here, we propose a light-induced high-Chern-number Chern insulator (CI) in the folded graphene. Along both armchair and zigzag folding directions, we demonstrate that there are two-handedness-dependent chiral interface states localized at the curved region. Physically, they can be attributed to the light-induced mass-term inversion across the folded graphene. Most remarkably, by rationally designing the folding processes, 2D and 3D CIs are also realizable in a single-wall carbon nanotube and periodic folded graphene, respectively, illustrating a high tunability of the folding degree of freedom. We envision that this intriguing form of "foldtronics" will provide a new platform for investigating the topological state in 2D materials to draw immediate experimental attention.

Robust Majorana edge modes with low frequency multiple time periodic driving

Floquet Majorana edge modes capture the topological features of periodically driven p-wave superconductors. We present a Kitaev chain with multiple time periodic driving terms. Our results demonstrate how multiple driving will affect Floquet bands in frequency space, leading to more robust Floquet Majorana edge modes against driving frequencyωin comparison with the single driving scenario. Meanwhile, we have proposed how to predict Majorana edge modes via the Zak phase of Floquet bands. Besides, in contrast to the cases with single driving term, where the constant phase can be gauged out by properly choosing the initial time, we have shown the relative phase between multiple driving can not be gauged out and will play a dominant role in deciding topological phase transitions. For the sake of completeness, we also investigate the high frequency limit. Analytical results on effective Hamiltonian can be obtained via Magnus expansion and relative phase induced topological transitions can be shown explicitly.

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).

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.