Transient electronic structure and melting of a charge density wave in TbTe3

Charge density waves tuned by biaxial tensile stress

The precise arrangement and nature of atoms drive electronic phase transitions in condensed matter. To explore this tenuous link, we developed a true biaxial mechanical deformation device working at cryogenic temperatures, compatible with x-ray diffraction and transport measurements, well adapted to layered samples. Here we show that a slight deformation of TbTe3 can have a dramatic influence on its Charge Density Wave (CDW), with an orientational transition from c to a driven by the a/c parameter, a tiny coexistence region near a = c, and without space group change. The CDW transition temperature Tc displays a linear dependence witha / c - 1 while the gap saturates out of the coexistence region. This behaviour is well accounted for within a tight-binding model. Our results question the relationship between gap and Tc in RTe3 systems. This method opens a new route towards the study of coexisting or competing electronic orders in condensed matter.

Three-dimensional ultrafast charge-density-wave dynamics in CuTe

Charge density waves (CDWs) involved with electronic and phononic subsystems simultaneously are a common quantum state in solid-state physics, especially in low-dimensional materials. However, CDW phase dynamics in various dimensions are yet to be studied, and their phase transition mechanism is currently moot. Here we show that using the distinct temperature evolution of orientation-dependent ultrafast electron and phonon dynamics, different dimensional CDW phases are verified in CuTe. When the temperature decreases, the shrinking of c-axis length accompanied with the appearance of interchain and interlayer interactions causes the quantum fluctuations (QF) of the CDW phase until 220 K. At T < 220 K, the CDWs on the different ab-planes are finally locked with each other in anti-phase to form a CDW phase along the c-axis. This study shows the dimension evolution of CDW phases in one CDW system and their stabilized mechanisms in different temperature regimes.

High-resolution MHz time- and angle-resolved photoemission spectroscopy based on a tunable vacuum ultraviolet source

The time- and angle-resolved photoemission spectroscopy (trARPES) allows for direct mapping of the electronic band structure and its dynamic response on femtosecond timescales. Here, we present a new ARPES system, powered by a new fiber-based femtosecond light source in the vacuum ultraviolet range, accessing the complete first Brillouin zone for most materials. We present trARPES data on Au(111), polycrystalline Au, Bi2Se3, and TaTe2, demonstrating an energy resolution of 21 meV with a time resolution of <360 fs, at a high repetition rate of 1 MHz. The system is integrated with an extreme ultraviolet high harmonic generation beamline, enabling an excellent tunability of the time-bandwidth resolution.

Real-time observation of non-equilibrium phonon-electron energy and angular momentum flow in laser-heated nickel

Identifying the microscopic nature of non-equilibrium energy transfer mechanisms among electronic, spin, and lattice degrees of freedom is central to understanding ultrafast phenomena such as manipulating magnetism on the femtosecond timescale. Here, we use time- and angle-resolved photoemission spectroscopy to go beyond the often-used ensemble-averaged view of non-equilibrium dynamics in terms of quasiparticle temperature evolutions. We show for ferromagnetic Ni that the non-equilibrium electron and spin dynamics display pronounced variations with electron momentum, whereas the magnetic exchange interaction remains isotropic. This highlights the influence of lattice-mediated scattering processes and opens a pathway toward unraveling the still elusive microscopic mechanism of spin-lattice angular momentum transfer.

Time-resolved ARPES with probe energy of 6.0/7.2 eV and switchable resolution configuration

We present a detailed exposition of the design for time- and angle-resolved photoemission spectroscopy using a UV probe laser source that combines the nonlinear effects of β-BaB2O4 and KBe2BO3F2 optical crystals. The photon energy of the probe laser can be switched between 6.0 and 7.2 eV, with the flexibility to operate each photon energy setting under two distinct resolution configurations. Under the fully optimized energy resolution configuration, we achieve an energy resolution of 8.5 meV at 6.0 eV and 10 meV at 7.2 eV. Alternatively, switching to the other configuration enhances the temporal resolution, yielding a temporal resolution of 72 fs for 6.0 eV and 185 fs for 7.2 eV. We validated the performance and reliability of our system by applying it to measuring two typical materials: the topological insulator MnBi2Te4 and the excitonic insulator candidate Ta2NiSe5.

Melting of Unidirectional Charge Density Waves across Twin Domain Boundaries in GdTe3

Solids undergoing a transition from order to disorder experience a proliferation of topological defects. The melting process generates transient quantum states. However, their dynamic nature with a femtosecond lifetime hinders exploration with atomic precision. Here, we suggest an alternative approach to the dynamic melting process by focusing on the interface created by competing degenerate quantum states. We use a scanning tunneling microscope (STM) to visualize the unidirectional charge density wave (CDW) and its spatial progression ("static melting") across a twin domain boundary (TDB) in the layered material GdTe3. Combining the STM with a spatial lock-in technique, we reveal that the order parameter amplitude attenuates with the formation of dislocations and thus two different unidirectional CDWs coexist near the TDB, reducing the CDW anisotropy. Notably, we discovered a correlation between this anisotropy and the CDW gap. Our study provides valuable insight into the behavior of topological defects and transient quantum states.

Angle-resolved photoelectron spectroscopy in a low-energy electron microscope

Spectroscopic photoemission microscopy is a well-established method to investigate the electronic structure of surfaces. In modern photoemission microscopes, the electron optics allow imaging of the image plane, momentum plane, or dispersive plane, depending on the lens setting. Furthermore, apertures allow filtering of energy-, real-, and momentum space. Here, we describe how a standard spectroscopic and low-energy electron microscope can be equipped with an additional slit at the entrance of the already present hemispherical analyzer to enable an angle- and energy-resolved photoemission mode with micrometer spatial selectivity. We apply a photogrammetric calibration to correct for image distortions of the projective system behind the analyzer and present spectra recorded on Au(111) as a benchmark. Our approach makes data acquisition in energy-momentum space more efficient, which is a necessity for laser-based pump-probe photoemission microscopy with femtosecond time resolution.

Observation of momentum-dependent charge density wave gap in a layered antiferromagnet [Formula: see text]

Charge density wave (CDW) ordering has been an important topic of study for a long time owing to its connection with other exotic phases such as superconductivity and magnetism. The [Formula: see text] (R = rare-earth elements) family of materials provides a fertile ground to study the dynamics of CDW in van der Waals layered materials, and the presence of magnetism in these materials allows to explore the interplay among CDW and long range magnetic ordering. Here, we have carried out a high-resolution angle-resolved photoemission spectroscopy (ARPES) study of a CDW material [Formula: see text], which is antiferromagnetic below [Formula: see text], along with thermodynamic, electrical transport, magnetic, and Raman measurements. Our ARPES data show a two-fold symmetric Fermi surface with both gapped and ungapped regions indicative of the partial nesting. The gap is momentum dependent, maximum along [Formula: see text] and gradually decreases going towards [Formula: see text]. Our study provides a platform to study the dynamics of CDW and its interaction with other physical orders in two- and three-dimensions.

Direct observation of the collective modes of the charge density wave in the kagome metal CsV3Sb5

A recently discovered group of kagome metals AV[Formula: see text]Sb[Formula: see text] (A = K, Rb, Cs) exhibit a variety of intertwined unconventional electronic phases, which emerge from a puzzling charge density wave phase. Understanding of this charge-ordered parent phase is crucial for deciphering the entire phase diagram. However, the mechanism of the charge density wave is still controversial, and its primary source of fluctuations-the collective modes-has not been experimentally observed. Here, we use ultrashort laser pulses to melt the charge order in CsV[Formula: see text]Sb[Formula: see text] and record the resulting dynamics using femtosecond angle-resolved photoemission. We resolve the melting time of the charge order and directly observe its amplitude mode, imposing a fundamental limit for the fastest possible lattice rearrangement time. These observations together with ab initio calculations provide clear evidence for a structural rather than electronic mechanism of the charge density wave. Our findings pave the way for a better understanding of the unconventional phases hosted on the kagome lattice.

The spontaneous symmetry breaking in Ta2NiSe5 is structural in nature

The excitonic insulator is an electronically driven phase of matter that emerges upon the spontaneous formation and Bose condensation of excitons. Detecting this exotic order in candidate materials is a subject of paramount importance, as the size of the excitonic gap in the band structure establishes the potential of this collective state for superfluid energy transport. However, the identification of this phase in real solids is hindered by the coexistence of a structural order parameter with the same symmetry as the excitonic order. Only a few materials are currently believed to host a dominant excitonic phase, Ta2NiSe5 being the most promising. Here, we test this scenario by using an ultrashort laser pulse to quench the broken-symmetry phase of this transition metal chalcogenide. Tracking the dynamics of the material's electronic and crystal structure after light excitation reveals spectroscopic fingerprints that are compatible only with a primary order parameter of phononic nature. We rationalize our findings through state-of-the-art calculations, confirming that the structural order accounts for most of the gap opening. Our results suggest that the spontaneous symmetry breaking in Ta2NiSe5 is mostly of structural character, hampering the possibility to realize quasi-dissipationless energy transport.

Photo-induced phase-transitions in complex solids

Photo-induced phase-transitions (PIPTs) driven by highly cooperative interactions are of fundamental interest as they offer a way to tune and control material properties on ultrafast timescales. Due to strong correlations and interactions, complex quantum materials host several fascinating PIPTs such as light-induced charge density waves and ferroelectricity and have become a desirable setting for studying these PIPTs. A central issue in this field is the proper understanding of the underlying mechanisms driving the PIPTs. As these PIPTs are highly nonlinear processes and often involve multiple time and length scales, different theoretical approaches are often needed to understand the underlying mechanisms. In this review, we present a brief overview of PIPTs realized in complex materials, followed by a discussion of the available theoretical methods with selected examples of recent progress in understanding of the nonequilibrium pathways of PIPTs.

A newly designed femtosecond KBe2BO3F2 device with pulse duration down to 55 fs for time- and angle-resolved photoemission spectroscopy

Developing a widely tunable vacuum ultraviolet (VUV) source with a sub-100 fs pulse duration is critical for ultrafast pump-probe techniques such as time- and angle-resolved photoemission spectroscopy (TrARPES). While a tunable probe source with a photon energy of 5.3-7.0 eV has been recently implemented for TrARPES by using a KBe₂BO₃F₂ (KBBF) device, the time resolution of 280-320 fs is still not ideal, which is mainly limited by the duration of the VUV probe pulse generated by the KBBF device. Here, by designing a new KBBF device, which is specially optimized for fs applications, an optimum pulse duration of 55 fs is obtained after systematic diagnostics and optimization. More importantly, a high time resolution of 81-95 fs is achieved for TrARPES measurements covering the probe photon energy range of 5.3-7.0 eV, making it particularly useful for investigating the ultrafast dynamics of quantum materials. Our work extends the application of the KBBF device to ultrafast pump-probe techniques with the advantages of both a widely tunable VUV source and ultimate time resolution.

Charge filling induced quasi-two dimensional charge/spin density wave channel in a ballistic transport device

Charge filling controlled mean field metal-insulator phase transition is examined in the context of two dimensional Fermi surface nesting and van Hove singularity induced charge density wave (CDW), spin density wave (SDW) condensates. In the framework of a coherent ballistic transport model utilizing the Non-Equilibrium Green Function approach (NEGF), a three terminal device with metallic gate, source, drain and CDW/SDW channel is simulated and studied. Within the validity of mean field approximation, we exposit the commensurability and boundary effects. The efficacy of the Hubbard model for (quasi) two dimensional Charge and Spin Density Wave materials is discussed. A two orbital generalization of the effective Hamiltonian is proposed for transport calculations in rare earth TelluridesRTe₃.

Revealing the order parameter dynamics of 1T-TiSe[Formula: see text] following optical excitation

The formation of a charge density wave state is characterized by an order parameter. The way it is established provides unique information on both the role that correlation plays in driving the charge density wave formation and the mechanism behind its formation. Here we use time and angle resolved photoelectron spectroscopy to optically perturb the charge-density phase in 1T-TiSe[Formula: see text] and follow the recovery of its order parameter as a function of energy, momentum and excitation density. Our results reveal that two distinct orders contribute to the gap formation, a CDW order and pseudogap-like order, manifested by an overall robustness to optical excitation. A detailed analysis of the magnitude of the the gap as a function of excitation density and delay time reveals the excitonic long-range nature of the CDW gap and the short-range Jahn-Teller character of the pseudogap order. In contrast to the gap, the intensity of the folded Se[Formula: see text]* band can only give access to the excitonic order. These results provide new information into the the long standing debate on the origin of the gap in TiSe[Formula: see text] and place it in the same context of other quantum materials where a pseudogap phase appears to be a precursor of long-range order.

Multispectral time-resolved energy-momentum microscopy using high-harmonic extreme ultraviolet radiation

A 790-nm-driven high-harmonic generation source with a repetition rate of 6 kHz is combined with a toroidal-grating monochromator and a high-detection-efficiency photoelectron time-of-flight momentum microscope to enable time- and momentum-resolved photoemission spectroscopy over a spectral range of 23.6-45.5 eV with sub-100 fs time resolution. Three-dimensional (3D) Fermi surface mapping is demonstrated on graphene-covered Ir(111) with energy and momentum resolutions of ≲100 meV and ≲0.1 Å^-1, respectively. The tabletop experiment sets the stage for measuring the k_z-dependent ultrafast dynamics of 3D electronic structure, including band structure, Fermi surface, and carrier dynamics in 3D materials as well as 3D orbital dynamics in molecular layers.

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.

Far-from-Equilibrium Electron-Phonon Interactions in Optically Excited Graphene

Comprehending far-from-equilibrium many-body interactions is one of the major goals of current ultrafast condensed matter physics research. Here, a particularly interesting but barely understood situation occurs during a strong optical excitation, where the electron and phonon systems can be significantly perturbed and the quasiparticle distributions cannot be described with equilibrium functions. In this work, we use time- and angle-resolved photoelectron spectroscopy to study such far-from-equilibrium many-body interactions for the prototypical material graphene. In accordance with theoretical simulations, we find remarkable transient renormalizations of the quasiparticle self-energy caused by the photoinduced nonequilibrium conditions. These observations can be understood by ultrafast scatterings between nonequilibrium electrons and strongly coupled optical phonons, which signify the crucial role of ultrafast nonequilibrium dynamics on many-body interactions. Our results advance the understanding of many-body physics in extreme conditions, which is important for any endeavor to optically manipulate or create non-equilibrium states of matter.

Observation of anomalous amplitude modes in the kagome metal CsV3Sb5

The kagome lattice provides a fertile platform to explore novel symmetry-breaking states. Charge-density wave (CDW) instabilities have been recently discovered in a new kagome metal family, commonly considered to arise from Fermi-surface instabilities. Here we report the observation of Raman-active CDW amplitude modes in CsV₃Sb₅, which are collective excitations typically thought to emerge out of frozen soft phonons, although phonon softening is elusive experimentally. The amplitude modes strongly hybridize with other superlattice modes, imparting them with clear temperature-dependent frequency shift and broadening, rarely seen in other known CDW materials. Both the mode mixing and the large amplitude mode frequencies suggest that the CDW exhibits the character of strong electron-phonon coupling, a regime in which phonon softening can cease to exist. Our work highlights the importance of the lattice degree of freedom in the CDW formation and points to the complex nature of the mechanism.

The mechanism of the charge density wave in kagome metals is not fully understood. Here, the authors report the observation of unusual large-frequency collective lattice excitations, or amplitude modes, in CsV₃Sb₅ in the absence of phonon mode softening, evidencing the strong electron-phonon coupling regime.

Development of a versatile micro-focused angle-resolved photoemission spectroscopy system with Kirkpatrick-Baez mirror optics

Angle-resolved photoemission spectroscopy using a micro-focused beam spot [micro-angle-resolved photoemission spectroscopy (ARPES)] is becoming a powerful tool to elucidate key electronic states of exotic quantum materials. We have developed a versatile micro-ARPES system based on the synchrotron radiation beam focused with a Kirkpatrick-Baez mirror optics. The mirrors are monolithically installed on a stage, which is driven with five-axis motion, and are vibrationally separated from the ARPES measurement system. Spatial mapping of the Au photolithography pattern on Si signifies the beam spot size of 10 µm (horizontal) × 12 µm (vertical) at the sample position, which is well suited to resolve the fine structure in local electronic states. Utilization of the micro-beam and the high precision sample motion system enables the accurate spatially resolved band-structure mapping, as demonstrated by the observation of a small band anomaly associated with tiny sample bending near the edge of a cleaved topological insulator single crystal.

Real-time evolution of static electron-phonon models in time-dependent electric fields

We present an exact Monte Carlo method to simulate the nonequilibrium dynamics of electron-phonon models in the adiabatic limit of zero phonon frequency. The classical nature of the phonons allows us to sample the equilibrium phonon distribution and efficiently evolve the electronic subsystem in a time-dependent electromagnetic field for each phonon configuration. We demonstrate that our approach is particularly useful for charge-density-wave systems experiencing pulsed electric fields, as they appear in pump-probe experiments. For the half-filled Holstein model in one and two dimensions, we calculate the out-of-equilibrium response of the current and the energy after a pulse is applied as well as the photoemission spectrum before and after the pump. Finite-size effects are under control for chains of 162 sites (in one dimension) or 16×16 square lattices (in two dimensions).

Square-Net Topological Semimetals: How Spectroscopy Furthers Understanding and Control

Square-net materials are well positioned to lead optical spectroscopic explorations into the electronic structure, photoinduced dynamics, and phase transitions in topological semimetals. Hundreds of square-net topological semimetals can be prepared that have remarkably different electronic and optical properties despite having similar structures. Here we present what has been gleaned recently from these materials with the whole gamut of optical spectroscopies, ranging from steady-state reflectance and Raman investigations into topological band structures, electronic correlations, and equilibrium phase transitions to time-resolved techniques used to decipher ultrafast relaxation dynamics and nonequilibrium photoinduced phase transitions. We end with a discussion of some major remaining questions and possible future research directions.

Coherent Modulation of Quasiparticle Scattering Rates in a Photoexcited Charge-Density-Wave System

We present a complementary experimental and theoretical investigation of relaxation dynamics in the charge-density-wave (CDW) system TbTe_{3} after ultrafast optical excitation. Using time- and angle-resolved photoemission spectroscopy, we observe an unusual transient modulation of the relaxation rates of excited photocarriers. A detailed analysis of the electron self-energy based on a nonequilibrium Green's function formalism reveals that the phase space of electron-electron scattering is critically modulated by the photoinduced collective CDW excitation, providing an intuitive microscopic understanding of the observed dynamics and revealing the impact of the electronic band structure on the self-energy.

Time-resolved structural dynamics of the out-of-equilibrium charge density wave phase transition in GdTe3

We use ultrafast electron diffraction to study the out-of-equilibrium dynamics of the charge density wave (CDW) phase transition in GdTe3, a quasi-two-dimensional compound displaying a unidirectional CDW state. Experiments were conducted at different incident fluences and different initial sample temperatures below Tc. We find that following photo-excitation, the system undergoes a non-thermal ultrafast phase transition that occurs in out-of-equilibrium conditions. The intrinsic crystal temperature was estimated at each time delay from the atomic thermal motion, which affects each Bragg peak intensity via the Debye Waller factor. We find that the crystal temperature stabilizes with a 6 ps timescale in a quasi-equilibrium state at temperature T q . e . . We then relate the recovery time of the CDW and its correlation lengths as a function of T q . e . . The charge density wave is suppressed in less than a picosecond while its recovery time increases linearly with incident fluence and initial temperature. Our results highlight that the dynamics is strongly determined by the initial sample temperature. In addition, the transient CDW phase recently observed along the transverse direction in LaTe3 and CeTe3 is not observed in GdTe3.

Spiers Memorial Lecture: Prospects for photoelectron spectroscopy

An overview is presented of recent advances in photoelectron spectroscopy, focussing on advances in in situ and time-resolved measurements, and in extending the sampling depth of the technique. The future...

Light-Tunable Charge Density Wave Orders in MoTe_{2} and WTe_{2} Single Layers

By using constrained density functional theory modeling, we demonstrate that ultrafast optical pumping unveils hidden charge orders in group VI monolayer transition metal ditellurides. We show that irradiation of the insulating 2H phases stabilizes multiple transient charge density wave orders with light-tunable distortion, periodicity, electronic structure, and band gap. Moreover, optical pumping of the semimetallic 1T^{'} phases generates a transient charge ordered metallic phase composed of 2D diamond clusters. For each transient phase we identify the critical fluence at which it is observed and the specific optical and Raman fingerprints to directly compare with future ultrafast pump-probe experiments. Our work demonstrates that it is possible to stabilize charge density waves even in insulating 2D transition metal dichalcogenides by ultrafast irradiation.

Expanding the momentum field of view in angle-resolved photoemission systems with hemispherical analyzers

In photoelectron spectroscopy, the measured electron momentum range is intrinsically related to the excitation photon energy. Low photon energies <10 eV are commonly encountered in laser-based photoemission and lead to a momentum range that is smaller than the Brillouin zones of most materials. This can become a limiting factor when studying condensed matter with laser-based photoemission. An additional restriction is introduced by widely used hemispherical analyzers that record only electrons photoemitted in a solid angle set by the aperture size at the analyzer entrance. Here, we present an upgrade to increase the effective solid angle that is measured with a hemispherical analyzer. We achieve this by accelerating the photoelectrons toward the analyzer with an electric field that is generated by a bias voltage on the sample. Our experimental geometry is comparable to a parallel plate capacitor, and therefore, we approximate the electric field to be uniform along the photoelectron trajectory. With this assumption, we developed an analytic, parameter-free model that relates the measured angles to the electron momenta in the solid and verify its validity by comparing with experimental results on the charge density wave material TbTe₃. By providing a larger field of view in momentum space, our approach using a bias potential considerably expands the flexibility of laser-based photoemission setups.

An integrated quantum material testbed with multi-resolution photoemission spectroscopy

We present the development of a multi-resolution photoemission spectroscopy (MRPES) setup, which probes quantum materials in energy, momentum, space, and time. This versatile setup integrates three light sources in one photoemission setup and can conveniently switch between traditional angle-resolved photoemission spectroscopy (ARPES), time-resolved ARPES (trARPES), and micrometer-scale spatially resolved ARPES. It provides a first-time all-in-one solution to achieve an energy resolution of <4 meV, a time resolution of <35 fs, and a spatial resolution of ∼10 μm in photoemission spectroscopy. Remarkably, we obtain the shortest time resolution among the trARPES setups using solid-state nonlinear crystals for frequency upconversion. Furthermore, this MRPES setup is integrated with a shadow-mask assisted molecular beam epitaxy system, which transforms the traditional photoemission spectroscopy into a quantum device characterization instrument. We demonstrate the functionalities of this novel quantum material testbed using FeSe/SrTiO₃ thin films and MnBi₄Te₇ magnetic topological insulators.

A versatile sample fabrication method for ultrafast electron diffraction

Integral to the exploration of nonequilibrium phenomena in solid-state systems is the study of lattice motion after photoexcitation by a femtosecond laser pulse. For the past two decades, ultrafast electron diffraction (UED) has played a critical role in this regard. Despite remarkable progress in instrumental development, this technique is still bottlenecked by a demanding sample preparation process, where ultrathin single crystals of large lateral size are typically required. In this work, we describe an efficient, versatile method that yields high-quality, laterally extended (≥ 100 µm), and thin (≤ 50 nm) single crystals on amorphous films of Si₃N₄ windows. It applies to most exfoliable materials, including those reactive in ambient conditions, and promises clean, flat surfaces. Besides the natural extension to fabricating van der Waals heterostructures, our method can also be applied to future-generation UED that enables additional control of sample parameters, such as electrostatic gating and excitation by a locally enhanced terahertz field. Our work significantly expands the type of samples for UED studies and also finds application in other time-resolved techniques such as attosecond extreme-ultraviolet absorption spectroscopy. This method hence provides further opportunities to explore photoinduced transitions and to discover novel states of matter out of equilibrium.

Revealing momentum-dependent electron-phonon and phonon-phonon coupling in complex materials with ultrafast electron diffuse scattering

ABSTRACT

Despite their fundamental role in determining many important properties of materials, detailed momentum-dependent information on the strength of electron-phonon and phonon-phonon coupling across the entire Brillouin zone has remained elusive. Ultrafast electron diffuse scattering (UEDS) is a recently developed technique that is making a significant contribution to these questions. Here, we describe both the UEDS methodology and the information content of ultrafast, photoinduced changes in phonon-diffuse scattering from single-crystal materials. We present results obtained from Ni, WSe₂, and TiSe₂, materials that are characterized by a complex interplay between electronic (charge, spin) and lattice degrees of freedom. We demonstrate the power of this technique by unraveling carrier-phonon and phonon-phonon interactions in both momentum and time and following nonequilibrium phonon dynamics in detail on ultrafast time scales. By combining ab initio calculations with ultrafast diffuse electron scattering, insights into electronic and magnetic dynamics that impact UEDS indirectly can also be obtained.

New insights into correlated materials in the time domain-combining far-infrared excitation with x-ray probes at cryogenic temperatures

Modern techniques for the investigation of correlated materials in the time domain combine selective excitation in the THz frequency range with selective probing of coupled structural, electronic and magnetic degrees of freedom using x-ray scattering techniques. Cryogenic sample temperatures are commonly required to prevent thermal occupation of the low energy modes and to access relevant material ground states. Here, we present a chamber optimized for high-field THz excitation and (resonant) x-ray diffraction at sample temperatures between 5 and 500 K. Directly connected to the beamline vacuum and featuring both a Beryllium window and an in-vacuum detector, the chamber covers the full (2-12.7) keV energy range of the femtosecond x-ray pulses available at the Bernina endstation of the SwissFEL free electron laser. Successful commissioning experiments made use of the energy tunability to selectively track the dynamics of the structural, magnetic and orbital order of Ca₂RuO₄and Tb₂Ti₂O₇at the Ru (2.96 keV) and Tb (7.55 keV)L-edges, respectively. THz field amplitudes up to 1.12 MV cm^-1peak field were demonstrated and used to excite the samples at temperatures as low as 5 K.

The 2021 ultrafast spectroscopic probes of condensed matter roadmap

In the 60 years since the invention of the laser, the scientific community has developed numerous fields of research based on these bright, coherent light sources, including the areas of imaging, spectroscopy, materials processing and communications. Ultrafast spectroscopy and imaging techniques are at the forefront of research into the light-matter interaction at the shortest times accessible to experiments, ranging from a few attoseconds to nanoseconds. Light pulses provide a crucial probe of the dynamical motion of charges, spins, and atoms on picosecond, femtosecond, and down to attosecond timescales, none of which are accessible even with the fastest electronic devices. Furthermore, strong light pulses can drive materials into unusual phases, with exotic properties. In this roadmap we describe the current state-of-the-art in experimental and theoretical studies of condensed matter using ultrafast probes. In each contribution, the authors also use their extensive knowledge to highlight challenges and predict future trends.

Nonequilibrium charge-density-wave order beyond the thermal limit

The interaction of many-body systems with intense light pulses may lead to novel emergent phenomena far from equilibrium. Recent discoveries, such as the optical enhancement of the critical temperature in certain superconductors and the photo-stabilization of hidden phases, have turned this field into an important research frontier. Here, we demonstrate nonthermal charge-density-wave (CDW) order at electronic temperatures far greater than the thermodynamic transition temperature. Using time- and angle-resolved photoemission spectroscopy and time-resolved X-ray diffraction, we investigate the electronic and structural order parameters of an ultrafast photoinduced CDW-to-metal transition. Tracking the dynamical CDW recovery as a function of electronic temperature reveals a behaviour markedly different from equilibrium, which we attribute to the suppression of lattice fluctuations in the transient nonthermal phonon distribution. A complete description of the system's coherent and incoherent order-parameter dynamics is given by a time-dependent Ginzburg-Landau framework, providing access to the transient potential energy surfaces.

Suppression of the vacuum space-charge effect in fs-photoemission by a retarding electrostatic front lens

The performance of time-resolved photoemission experiments at fs-pulsed photon sources is ultimately limited by the e-e Coulomb interaction, downgrading energy and momentum resolution. Here, we present an approach to effectively suppress space-charge artifacts in momentum microscopes and photoemission microscopes. A retarding electrostatic field generated by a special objective lens repels slow electrons, retaining the k-image of the fast photoelectrons. The suppression of space-charge effects scales with the ratio of the photoelectron velocities of fast and slow electrons. Fields in the range from -20 to -1100 V/mm for E_kin = 100 eV to 4 keV direct secondaries and pump-induced slow electrons back to the sample surface. Ray tracing simulations reveal that this happens within the first 40 to 3 μm above the sample surface for E_kin = 100 eV to 4 keV. An optimized front-lens design allows switching between the conventional accelerating and the new retarding mode. Time-resolved experiments at E_kin = 107 eV using fs extreme ultraviolet probe pulses from the free-electron laser FLASH reveal that the width of the Fermi edge increases by just 30 meV at an incident pump fluence of 22 mJ/cm² (retarding field -21 V/mm). For an accelerating field of +2 kV/mm and a pump fluence of only 5 mJ/cm², it increases by 0.5 eV (pump wavelength 1030 nm). At the given conditions, the suppression mode permits increasing the slow-electron yield by three to four orders of magnitude. The feasibility of the method at high energies is demonstrated without a pump beam at E_kin = 3830 eV using hard x rays from the storage ring PETRA III. The approach opens up a previously inaccessible regime of pump fluences for photoemission experiments.

Antiphase Oscillations in the Time-Resolved Spin Structure Factor of a Photoexcited Mott Insulator

Motivated by the recent development of time-resolved resonant-inelastic x-ray scattering (TRRIXS) in photoexcited antiferromagnetic Mott insulators, we numerically investigate momentum-dependent transient spin dynamics in a half-filled Hubbard model on a square lattice. After turning off a pumping photon pulse, the intensity of a dynamical spin structure factor temporally oscillates with frequencies determined by the energy of two magnons in the antiferromagnetic Mott insulator. We find an antiphase behavior in the oscillations between two orthogonal momentum directions, parallel and perpendicular to the electric field of a pump pulse. The phase difference comes from the B_{1g} channel of the two-magnon excitation. Observing the antiphase oscillations will be a big challenge for TRRIXS experiments when their time resolution will be improved by more than an order of magnitude.

Nonequilibrium Lattice Dynamics in Monolayer MoS2

The coupled nonequilibrium dynamics of electrons and phonons in monolayer MoS₂ is investigated by combining first-principles calculations of the electron-phonon and phonon-phonon interactions with the time-dependent Boltzmann equation. Strict phase-space constraints in the electron-phonon scattering are found to influence profoundly the decay path of excited electrons and holes, restricting the emission of phonons to crystal momenta close to a few high-symmetry points in the Brillouin zone. As a result of momentum selectivity in the phonon emission, the nonequilibrium lattice dynamics is characterized by the emergence of a highly anisotropic population of phonons in reciprocal space, which persists for up to 10 ps until thermal equilibrium is restored by phonon-phonon scattering. Achieving control of the nonequilibrium dynamics of the lattice may provide unexplored opportunities to selectively enhance the phonon population of two-dimensional crystals and, thereby, transiently tailor electron-phonon interactions over subpicosecond time scales.

Nonequilibrium dynamics of spontaneous symmetry breaking into a hidden state of charge-density wave

Nonequilibrium phase transitions play a pivotal role in broad physical contexts, from condensed matter to cosmology. Tracking the formation of nonequilibrium phases in condensed matter requires a resolution of the long-range cooperativity on ultra-short timescales. Here, we study the spontaneous transformation of a charge-density wave in CeTe₃ from a stripe order into a bi-directional state inaccessible thermodynamically but is induced by intense laser pulses. With ≈100 fs resolution coherent electron diffraction, we capture the entire course of this transformation and show self-organization that defines a nonthermal critical point, unveiling the nonequilibrium energy landscape. We discuss the generation of instabilities by a swift interaction quench that changes the system symmetry preference, and the phase ordering dynamics orchestrated over a nonadiabatic timescale to allow new order parameter fluctuations to gain long-range correlations. Remarkably, the subsequent thermalization locks the remnants of the transient order into longer-lived topological defects for more than 2 ns.

Bypassing the Structural Bottleneck in the Ultrafast Melting of Electronic Order

Impulsive optical excitation generally results in a complex nonequilibrium electron and lattice dynamics that involves multiple processes on distinct timescales, and a common conception is that for times shorter than about 100 fs the gap in the electronic spectrum is not seriously affected by lattice vibrations. Here, however, by directly monitoring the photoinduced collapse of the spectral gap in a canonical charge-density-wave material, the blue bronze Rb_{0.3}MoO_{3}, we find that ultrafast (∼60  fs) vibrational disordering due to efficient hot-electron energy dissipation quenches the gap significantly faster than the typical structural bottleneck time corresponding to one half-cycle oscillation (∼315  fs) of the coherent charge-density-wave amplitude mode. This result not only demonstrates the importance of incoherent lattice motion in the photoinduced quenching of electronic order, but also resolves the perennial debate about the nature of the spectral gap in a coupled electron-lattice system.

A quantitative comparison of time-of-flight momentum microscopes and hemispherical analyzers for time- and angle-resolved photoemission spectroscopy experiments

Time-of-flight-based momentum microscopy has a growing presence in photoemission studies, as it enables parallel energy- and momentum-resolved acquisition of the full photoelectron distribution. Here, we report table-top extreme ultraviolet time- and angle-resolved photoemission spectroscopy (trARPES) featuring both a hemispherical analyzer and a momentum microscope within the same setup. We present a systematic comparison of the two detection schemes and quantify experimentally relevant parameters, including pump- and probe-induced space-charge effects, detection efficiency, photoelectron count rates, and depth of focus. We highlight the advantages and limitations of both instruments based on exemplary trARPES measurements of bulk WSe₂. Our analysis demonstrates the complementary nature of the two spectrometers for time-resolved ARPES experiments. Their combination in a single experimental apparatus allows us to address a broad range of scientific questions with trARPES.

Fermionic order by disorder in a van der Waals antiferromagnet

CeTe₃ is a unique platform to investigate the itinerant magnetism in a van der Waals (vdW) coupled metal. Despite chemical pressure being a promising route to boost quantum fluctuation in this system, a systematic study on the chemical pressure effect on Ce³⁺(4f¹) states is absent. Here, we report on the successful growth of a series of Se doped single crystals of CeTe₃. We found a fluctuation driven exotic magnetic rotation from the usual easy-axis ordering to an unusual hard-axis ordering. Unlike in localized magnetic systems, near-critical magnetism can increase itinerancy hand-in-hand with enhancing fluctuation of magnetism. Thus, seemingly unstable hard-axis ordering emerges through kinetic energy gain, with the self-consistent observation of enhanced magnetic fluctuation (disorder). As far as we recognize, this order-by-disorder process in fermionic system is observed for the first time within vdW materials. Our finding opens a unique experimental platform for direct visualization of the rich quasiparticle Fermi surface deformation associated with the Fermionic order-by-disorder process. Also, the search for emergent exotic phases by further tuning of quantum fluctuation is suggested as a promising future challenge.

Mode-resolved reciprocal space mapping of electron-phonon interaction in the Weyl semimetal candidate Td-WTe2

The excitation of coherent phonons provides unique capabilities to control fundamental properties of quantum materials on ultrafast time scales. Recently, it was predicted that a topologically protected Weyl semimetal phase in the transition metal dichalcogenide Td-WTe₂ can be controlled and, ultimately, be destroyed upon the coherent excitation of an interlayer shear mode. By monitoring electronic structure changes with femtosecond resolution, we provide here direct experimental evidence that the shear mode acts on the electronic states near the phase-defining Weyl points. Furthermore, we observe a periodic reduction in the spin splitting of bands, a distinct electronic signature of the Weyl phase-stabilizing non-centrosymmetric Td ground state of WTe₂. The comparison with higher-frequency coherent phonon modes finally proves the shear mode-selectivity of the observed changes in the electronic structure. Our real-time observations reveal direct experimental insights into electronic processes that are of vital importance for a coherent phonon-induced topological phase transition in Td-WTe₂.

It is predicted that topological phase transitions in quantum materials can be triggered by selective excitation of coherent phonons. Upon excitation of a shear mode, Hein et al. observe distinct perturbations of electronic Weyl semimetal fingerprints in Td-WTe₂.

High resolution time- and angle-resolved photoemission spectroscopy with 11 eV laser pulses

Performing time- and angle-resolved photoemission (tr-ARPES) spectroscopy at high momenta necessitates extreme ultraviolet laser pulses, which are typically produced via high harmonic generation (HHG). Despite recent advances, HHG-based setups still require large pulse energies (from hundreds of μJ to mJ) and their energy resolution is limited to tens of meV. Here, we present a novel 11 eV tr-ARPES setup that generates a flux of 5 × 10¹⁰ photons/s and achieves an unprecedented energy resolution of 16 meV. It can be operated at high repetition rates (up to 250 kHz) while using input pulse energies down to 3 µJ. We demonstrate these unique capabilities by simultaneously capturing the energy and momentum resolved dynamics in two well-separated momentum space regions of a charge density wave material ErTe₃. This novel setup offers the opportunity to study the non-equilibrium band structure of solids with exceptional energy and time resolutions at high repetition rates.

Ab Initio Linear and Pump-Probe Spectroscopy of Excitons in Molecular Crystals

Linear and nonlinear spectroscopies are powerful tools used to investigate the energetics and dynamics of electronic excited states of both molecules and crystals. While highly accurate ab initio calculations of molecular spectra can be performed relatively routinely, extending these calculations to periodic systems is challenging. Here, we present calculations of the linear absorption spectrum and pump-probe two-photon photoemission spectra of the naphthalene crystal using equation-of-motion coupled-cluster theory with single and double excitations (EOM-CCSD). Molecular acene crystals are of interest due to the low-energy multiexciton singlet states they exhibit, which have been studied extensively as intermediates involved in singlet fission. Our linear absorption spectrum is in good agreement with experiment, predicting a first exciton absorption peak at 4.4 eV, and our two-photon photoemission spectra capture the qualitative behavior of multiexciton states, whose double-excitation character cannot be captured by current methods. The simulated pump-probe spectra provide support for existing interpretations of two-photon photoemission experiments in closely related acene crystals such as tetracene and pentacene.

NpSe2 : a Binary Chalcogenide Containing Modulated Selenide Chains and Ambiguous-Valent Metal

A new binary compound, NpSe_2, possesses metal-chalcogen and chalcogen-chalcogen interactions different from those reported for other metal dichalcogenides. Its structure is incommensurately modulated and features linear Se chains and valence-ambiguous Np cations.

Magnetic Liquid Metal (Fe-EGaIn) Based Multifunctional Electronics for Remote Self-Healing Materials, Degradable Electronics, and Thermal Transfer Printing

Flexible materials with the ability to be bent, strained, or twisted play a critical role in soft robots and stretchable electronics. Although tremendous efforts are focused on developing new stretchable materials with excellent stability, inevitable mechanical damage due to long term deformation is still an urgent problem to be tackled. Here, a magnetic healing method based on Fe-doped liquid metal (Fe-GaIn) conductive ink via a noncontact way is proposed. Further, multifunctional flexible electronics are designed with combined performances of superior remote self-healing under magnetic field, water-degradable, and thermal transfer printing, which attribute to three parts of the materials including Fe-GaIn conductive ink, degradable PVA substrate, and adhesive fructose. The as-made light emitting diodes (LED) circuit is demonstrated with both structural and functional repairing after single or multipoint damage. The self-healing time from multipoint damage is pretty fast within 10 s. Due to the water-soluble PVA film, the recycling process is simple via immersing into water. Through heating, the electric circuit on fructose can be transferred to other flexible substrate with high efficiency, which broadens the practical applications of the present system. The novel and multifunctional electronics hold great promise for self-healing electronics, transient electronics, and soft robots.

Quantum jamming transition to a correlated electron glass in 1T-TaS2

Distinct many-body states may be created under non-equilibrium conditions through different ordering paths, even when their constituents are subjected to the same fundamental interactions. The phase-transition mechanism to such states remains poorly understood. Here, we show that controlled optical or electromagnetic perturbations can lead to an amorphous metastable state of strongly correlated electrons in a quasi-two-dimensional dichalcogenide. Scanning tunnelling microscopy reveals a hyperuniform pattern of localized charges, whereas multitip surface nanoscale conductivity measurements and tunnelling spectroscopy show an electronically gapless conducting state that is different from conventional Coulomb glasses and many-body localized systems. The state is stable up to room temperature and shows no signs of either local charge order or phase separation. The mechanism for its formation is attributed to a dynamical localization of electrons through mutual interactions. Theoretical calculations confirm the correlations between localized charges to be crucial for the state's unusual stability.

Photoexcitation Induced Quantum Dynamics of Charge Density Wave and Emergence of a Collective Mode in 1T-TaS2

Photoexcitation is a powerful means in distinguishing different interactions and manipulating the states of matter, especially in charge density wave (CDW) materials. The CDW state of 1T-TaS₂ has been widely studied experimentally mainly because of its intriguing laser-induced ultrafast responses of electronic and lattice subsystems. However, the microscopic atomic dynamics and underlying electronic mechanism upon photoexcitation remain unclear. Here, we demonstrate photoexcitation induced ultrafast dynamics of CDW in 1T-TaS₂ using time-dependent density functional theory molecular dynamics. We discover a novel collective oscillation mode between the CDW state and a transient state induced by photodoping, which is significantly different from thermally induced phonon mode and attributed to the modification of the potential energy surface from laser excitation. In addition, our finding validates nonthermal melting of CDW induced at low light intensities, supporting that conventional hot electron model is inadequate to explain photoinduced dynamics. Our results provide a deep insight into the coherent electron and lattice quantum dynamics during the formation and excitation of CDW in 1T-TaS₂.

Dynamical Slowing-Down in an Ultrafast Photoinduced Phase Transition

Complex systems, which consist of a large number of interacting constituents, often exhibit universal behavior near a phase transition. A slowdown of certain dynamical observables is one such recurring feature found in a vast array of contexts. This phenomenon, known as critical slowing-down, is well studied mostly in thermodynamic phase transitions. However, it is less understood in highly nonequilibrium settings, where the time it takes to traverse the phase boundary becomes comparable to the timescale of dynamical fluctuations. Using transient optical spectroscopy and femtosecond electron diffraction, we studied a photoinduced transition of a model charge-density-wave (CDW) compound LaTe_{3}. We observed that it takes the longest time to suppress the order parameter at the threshold photoexcitation density, where the CDW transiently vanishes. This finding can be captured by generalizing the time-dependent Landau theory to a system far from equilibrium. The experimental observation and theoretical understanding of dynamical slowing-down may offer insight into other general principles behind nonequilibrium phase transitions in many-body systems.