Ultrafast Doublon Dynamics in Photoexcited 1T-TaS_{2}

Charge density waves in two-dimensional transition metal dichalcogenides

Charge density wave (CDW is one of the most ubiquitous electronic orders in quantum materials. While the essential ingredients of CDW order have been extensively studied, a comprehensive microscopic understanding is yet to be reached. Recent research efforts on the CDW phenomena in two-dimensional (2D) materials provide a new pathway toward a deeper understanding of its complexity. This review provides an overview of the CDW orders in 2D with atomically thin transition metal dichalcogenides (TMDCs) as the materials platform. We mainly focus on the electronic structure investigations on the epitaxially grown TMDC samples with angle-resolved photoemission spectroscopy and scanning tunneling microscopy/spectroscopy as complementary experimental tools. We discuss the possible origins of the 2D CDW, novel quantum states coexisting with them, and exotic types of charge orders that can only be realized in the 2D limit.

Coherent light control of a metastable hidden state

Metastable phases present a promising route to expand the functionality of complex materials. Of particular interest are light-induced metastable phases that are inaccessible under equilibrium conditions, as they often host new, emergent properties switchable on ultrafast timescales. However, the processes governing the trajectories to such hidden phases remain largely unexplored. Here, using time- and angle-resolved photoemission spectroscopy, we investigate the ultrafast dynamics of the formation of a hidden quantum state in the layered dichalcogenide 1T-TaS2 upon photoexcitation. Our results reveal the nonthermal character of the transition governed by a collective charge-density-wave excitation. Using a double-pulse excitation of the structural mode, we show vibrational coherent control of the phase-transition efficiency. Our demonstration of exceptional control, switching speed, and stability of the hidden state are key for device applications at the nexus of electronics and photonics.

Charge density wave surface reconstruction in a van der Waals layered material

Surface reconstruction plays a vital role in determining the surface electronic structure and chemistry of semiconductors and metal oxides. However, it has been commonly believed that surface reconstruction does not occur in van der Waals layered materials, as they do not undergo significant bond breaking during surface formation. In this study, we present evidence that charge density wave (CDW) order in these materials can, in fact, cause CDW surface reconstruction through interlayer coupling. Using density functional theory calculations on the 1T-TaS2 surface, we reveal that CDW reconstruction, involving concerted small atomic displacements in the subsurface layer, results in a significant modification of the surface electronic structure, transforming it from a Mott insulator to a band insulator. This new form of surface reconstruction explains several previously unexplained observations on the 1T-TaS2 surface and has important implications for interpreting surface phenomena in CDW-ordered layered materials.

Exploring the Charge Density Wave Phase of 1T-TaSe_{2}: Mott or Charge-Transfer Gap?

1T-TaSe_{2} is widely believed to host a Mott metal-insulator transition in the charge density wave (CDW) phase according to the spectroscopic observation of a band gap that extends across all momentum space. Previous investigations inferred that the occurrence of the Mott phase is limited to the surface only of bulk specimens, but recent analysis on thin samples revealed that the Mott-like behavior, observed in the monolayer, is rapidly suppressed with increasing thickness. Here, we report combined time- and angle-resolved photoemission spectroscopy and theoretical investigations of the electronic structure of 1T-TaSe_{2}. Our experimental results confirm the existence of a state above E_{F}, previously ascribed to the upper Hubbard band, and an overall band gap of ∼0.7  eV at Γ[over ¯]. However, supported by density functional theory calculations, we demonstrate that the origin of this state and the gap rests on band structure modifications induced by the CDW phase alone, without the need for Mott correlation effects.

Mobile Kink Solitons in a Van der Waals Charge-Density-Wave Layer

Kinks, point-like geometrical defects along dislocations, domain walls, and DNA, are stable and mobile, as solutions of a sine-Gordon wave equation. While they are widely investigated for crystal deformations and domain wall motions, electronic properties of individual kinks have received little attention. In this work, electronically and topologically distinct kinks are discovered along electronic domain walls in a correlated van der Waals insulator of 1T-TaS₂ . Mobile kinks and antikinks are identified as trapped by pinning defects and imaged in scanning tunneling microscopy. Their atomic structures and in-gap electronic states are unveiled, which are mapped approximately into Su-Schrieffer-Heeger solitons. The twelvefold degeneracy of the domain walls in the present system guarantees an extraordinarily large number of distinct kinks and antikinks to emerge. Such large degeneracy together with the robust geometrical nature may be useful for handling multilevel information in van der Waals materials architectures.

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.

Mott versus Hybridization Gap in the Low-Temperature Phase of 1T-TaS_{2}

We address the long-standing problem of the ground state of 1T-TaS_{2} by computing the correlated electronic structure of stacked bilayers using the GW+EDMFT method. Depending on the surface termination, the semi-infinite uncorrelated system is either band insulating or exhibits a metallic surface state. For realistic values of the on-site and inter-site interactions, a Mott gap opens in the surface state, but it is smaller than the gap originating from the bilayer structure. Our results are consistent with recent scanning tunneling spectroscopy measurements for different terminating layers, and with our own photoemission measurements, which indicate the coexistence of spatial regions with different gaps in the electronic spectrum. By comparison to exact diagonalization data, we clarify the interplay between Mott insulating and band insulating behavior in this archetypal layered system.

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).

Inq, a Modern GPU-Accelerated Computational Framework for (Time-Dependent) Density Functional Theory

We present inq, a new implementation of density functional theory (DFT) and time-dependent DFT (TDDFT) written from scratch to work on graphic processing units (GPUs). Besides GPU support, inq makes use of modern code design features and takes advantage of newly available hardware. By designing the code around algorithms, rather than against specific implementations and numerical libraries, we aim to provide a concise and modular code. The result is a fairly complete DFT/TDDFT implementation in roughly 12 000 lines of open-source C++ code representing a modular platform for community-driven application development on emerging high-performance computing architectures.

Distinguishing a Mott Insulator from a Trivial Insulator with Atomic Adsorbates

In an electronic system with various interactions intertwined, revealing the origin of its many-body ground state is challenging and a direct experimental way to verify the correlated nature of an insulator has been lacking. Here we demonstrate a way to unambiguously distinguish a paradigmatic correlated insulator, a Mott insulator, from a trivial band insulator based on their distinct chemical behavior for a surface adsorbate using 1T-TaS_{2}, which has been debated between a spin-frustrated Mott insulator or a spin-singlet trivial insulator. We start from the observation of different sizes of spectral gaps on different surface terminations and show that potassium adatoms on these two surface layers behave in totally different ways. This can be straightforwardly understood from distinct properties of Mott and band insulators due to the fundamental difference of the half- and full-filled orbitals involved, respectively. This work not only solves an outstanding problem in this particularly interesting material but also provides a simple touchstone to identify the correlated ground state of electrons experimentally.

A time-domain phase diagram of metastable states in a charge ordered quantum material

Metastable self-organized electronic states in quantum materials are of fundamental importance, displaying emergent dynamical properties that may be used in new generations of sensors and memory devices. Such states are typically formed through phase transitions under non-equilibrium conditions and the final state is reached through processes that span a large range of timescales. Conventionally, phase diagrams of materials are thought of as static, without temporal evolution. However, many functional properties of materials arise as a result of complex temporal changes in the material occurring on different timescales. Hitherto, such properties were not considered within the context of a temporally-evolving phase diagram, even though, under non-equilibrium conditions, different phases typically evolve on different timescales. Here, by using time-resolved optical techniques and femtosecond-pulse-excited scanning tunneling microscopy (STM), we track the evolution of the metastable states in a material that has been of wide recent interest, the quasi-two-dimensional dichalcogenide 1T-TaS₂. We map out its temporal phase diagram using the photon density and temperature as control parameters on timescales ranging from 10⁻¹² to 10³ s. The introduction of a time-domain axis in the phase diagram enables us to follow the evolution of metastable emergent states created by different phase transition mechanisms on different timescales, thus enabling comparison with theoretical predictions of the phase diagram, and opening the way to understanding of the complex ordering processes in metastable materials.

Tracking the evolution of non-equilibrium phases requires measurements over a wide range of timescales. Here, using a combination of femtosecond spectroscopy and scanning tunneling microscopy, the authors map out a temporal phase diagram of metastable states in a charge-ordered material 1T-TaS₂.

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.

Band insulator to Mott insulator transition in 1T-TaS2

1T-TaS₂ undergoes successive phase transitions upon cooling and eventually enters an insulating state of mysterious origin. Some consider this state to be a band insulator with interlayer stacking order, yet others attribute it to Mott physics that support a quantum spin liquid state. Here, we determine the electronic and structural properties of 1T-TaS₂ using angle-resolved photoemission spectroscopy and X-Ray diffraction. At low temperatures, the 2π/2c-periodic band dispersion, along with half-integer-indexed diffraction peaks along the c axis, unambiguously indicates that the ground state of 1T-TaS₂ is a band insulator with interlayer dimerization. Upon heating, however, the system undergoes a transition into a Mott insulating state, which only exists in a narrow temperature window. Our results refute the idea of searching for quantum magnetism in 1T-TaS₂ only at low temperatures, and highlight the competition between on-site Coulomb repulsion and interlayer hopping as a crucial aspect for understanding the material’s electronic properties.

1T-TaS2 possesses complex electronic phase behaviors in transition-metal di-chalcogenides, undergoing several charge-ordered phases before finally into an insulating state of unknown origin. Here, the authors determine its electronic and structural properties experimentally, revealing its origin.

Mottness versus unit-cell doubling as the driver of the insulating state in 1T-TaS2

If a material with an odd number of electrons per unit-cell is insulating, Mott localisation may be invoked as an explanation. This is widely accepted for the layered compound 1T-TaS₂, which has a low-temperature insulating phase comprising charge order clusters with 13 unpaired orbitals each. But if the stacking of layers doubles the unit-cell to include an even number of orbitals, the nature of the insulating state is ambiguous. Here, scanning tunnelling microscopy reveals two distinct terminations of the charge order in 1T-TaS₂, the sign of such a double-layer stacking pattern. However, spectroscopy at both terminations allows us to disentangle unit-cell doubling effects and determine that Mott localisation alone can drive gap formation. We also observe the collapse of Mottness at an extrinsically re-stacked termination, demonstrating that the microscopic mechanism of insulator-metal transitions lies in degrees of freedom of inter-layer stacking.

In many strongly correlated systems the coupling of electronic and lattice degrees of freedom leads to ambiguity over the mechanism driving electronic phase transitions. Here the authors show that inter-layer effects play an important role in the charge ordering transition of 1T-TaS₂.

Structural dynamics of incommensurate charge-density waves tracked by ultrafast low-energy electron diffraction

We study the non-equilibrium structural dynamics of the incommensurate and nearly commensurate charge-density wave (CDW) phases in 1T-TaS 2 . Employing ultrafast low-energy electron diffraction with 1 ps temporal resolution, we investigate the ultrafast quench and recovery of the CDW-coupled periodic lattice distortion (PLD). Sequential structural relaxation processes are observed by tracking the intensities of main lattice as well as satellite diffraction peaks and the diffuse scattering background. Comparing distinct groups of diffraction peaks, we disentangle the ultrafast quench of the PLD amplitude from phonon-related reductions of the diffraction intensity. Fluence-dependent relaxation cycles reveal a long-lived partial suppression of the order parameter for up to 60 ps, far outlasting the initial amplitude recovery and electron-phonon scattering times. This delayed return to a quasi-thermal level is controlled by lattice thermalization and coincides with the population of zone-center acoustic modes, as evidenced by a structured diffuse background. The long-lived non-equilibrium order parameter suppression suggests hot populations of CDW-coupled lattice modes. Finally, a broadening of the superlattice peaks is observed at high fluences, pointing to a non-linear generation of phase fluctuations.

Collapse of layer dimerization in the photo-induced hidden state of 1T-TaS2

Photo-induced switching between collective quantum states of matter is a fascinating rising field with exciting opportunities for novel technologies. Presently, very intensively studied examples in this regard are nanometer-thick single crystals of the layered material 1T-TaS₂, where picosecond laser pulses can trigger a fully reversible insulator-to-metal transition (IMT). This IMT is believed to be connected to the switching between metastable collective quantum states, but the microscopic nature of this so-called hidden quantum state remained largely elusive up to now. Here, we characterize the hidden quantum state of 1T-TaS₂ by means of state-of-the-art x-ray diffraction and show that the laser-driven IMT involves a marked rearrangement of the charge and orbital order in the direction perpendicular to the TaS₂-layers. More specifically, we identify the collapse of interlayer molecular orbital dimers as a key mechanism for this non-thermal collective transition between two truly long-range ordered electronic crystals.

The microscopic understanding of photo-induced insulator-to-metal transition (IMT) in 1T-TaS₂ remains elusive. Here, Stahl et al. identify the collapse of interlayer molecular orbital dimers during a collective electronic phase transition as a key mechanism for the IMT in 1T-TaS₂.

Quantum Simulation Meets Nonequilibrium Dynamical Mean-Field Theory: Exploring the Periodically Driven, Strongly Correlated Fermi-Hubbard Model

We perform an ab initio comparison between nonequilibrium dynamical mean-field theory and optical lattice experiments by studying the time evolution of double occupations in the periodically driven Fermi-Hubbard model. For off-resonant driving, the range of validity of a description in terms of an effective static Hamiltonian is determined and its breakdown due to energy absorption close to resonance is demonstrated. For near-resonant driving, we investigate the response to a change in driving amplitude and discover an asymmetric excitation spectrum with respect to the detuning. In general, we find good agreement between experiment and theory, which cross validates the experimental and numerical approaches in a strongly correlated nonequilibrium system.

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.

Ultrafast X-Ray Absorption Spectroscopy of Strongly Correlated Systems: Core Hole Effect

In recent years, ultrafast pump-probe spectroscopy has provided insightful information about the nonequilibrium dynamics of excitations in materials. In a typical experiment of time-resolved x-ray absorption spectroscopy, the systems are excited by a femtosecond laser pulse (pump pulse) followed by an x-ray probe pulse after a time delay to measure the absorption spectra of the photoexcited systems. We present a theory for nonequilibrium x-ray absorption spectroscopy in one-dimensional strongly correlated systems. The core hole created by the x ray is modeled as an additional effective potential of the core hole site, which changes the spectrum qualitatively. In equilibrium, the spectrum reveals the charge gap at half-filling and the metal-insulator transition in the presence of the core hole effect. Furthermore, a pump-probe scheme is introduced to drive the system out of equilibrium before the x-ray probe. The effects of the pump pulse with varying frequencies, shapes, and fluences are discussed for the dynamics of strongly correlated systems in and out of resonance. The spectrum indicates that the driven insulating state has a metallic droplet around the core hole. The rich structures of the nonequilibrium x-ray absorption spectrum give more insight into the dynamics of electronic structures.

Origin of the Insulating Phase and First-Order Metal-Insulator Transition in 1T-TaS_{2}

Using density functional theory calculations, we investigate the origin of the insulating phase and metal-insulator transition (MIT) in octahedral tantalum disulfide (1T-TaS_{2}), a layered van der Waals material with a prominent two-dimensional (2D) charge density wave (CDW) order. We show that the MIT is driven not by the 2D order itself, but by the vertical ordering of the 2D CDWs or the 3D CDW order. We identify two exceptionally stable 3D CDW configurations; one is insulating and the other is metallic. The competition and mixing of the two CDW configurations account for many mysterious features of the MIT in 1T-TaS_{2}, including the pressure- and doping-induced transitions and the hysteresis behavior. The present results emphasize that interlayer electronic ordering can play an important role in electronic phase transitions in layered materials.

Mottness collapse without metallization in the domain wall of the triangular-lattice Mott insulator 1T-TaS_{2}

1T-TaS_{2} is a charge-density-wave (CDW) compound with a Mott-insulating ground state. The metallic state obtained by doping, substitution, or pulsed charge injection is characterized by an emergent CDW domain-wall network, while single domain walls can be found in the pristine Mott state. Here we study whether and how the single walls become metallic. Tunneling spectroscopy reveals partial suppression of the Mott gap and the presence of in-gap states strongly localized at the domain-wall sites. Using the real-space dynamical mean field theory description of the strongly correlated quantum-paramagnet ground state, we show that the local gap suppression follows from the increased hopping along the connected zigzag chain of lattice sites forming the domain wall. Furthermore, we show that full metallization is preempted by the splitting of the quasiparticle band into bonding and antibonding subbands due to the structural dimerization of the wall, explaining the presence of the in-gap states and the low density of states at the Fermi level.

Doublon Formation by Ions Impacting a Strongly Correlated Finite Lattice System

Strongly correlated systems of fermions have a number of exciting collective properties. Among them, the creation of a lattice that is occupied by doublons, i.e., two quantum particles with opposite spins, offers interesting electronic properties. In the past a variety of methods have been proposed to control doublon formation, both, spatially and temporally. Here, a novel mechanism is proposed and verified by exact diagonalization and nonequilibrium Green functions simulations-fermionic doublon creation by the impact of energetic ions. We report the formation of a nonequilibrium steady state with homogeneous doublon distribution. The effect should be particularly important for strongly correlated finite systems, such as graphene nanoribbons, and directly observable with fermionic atoms in optical lattices.

Excitation and Relaxation Dynamics of the Photo-Perturbed Correlated Electron System 1T-TaS2

We investigate the perturbation and subsequent recovery of the correlated electronic ground state of the Mott insulator 1T-TaS 2 by means of femtosecond time-resolved photoemission spectroscopy in normal emission geometry. Upon an increase of near-infrared excitation strength, a considerable collapse of the occupied Hubbard band is observed, which reflects a quench of short-range correlations. It is furthermore found that these excitations are directly linked to the lifting of the periodic lattice distortion which provides the localization centers for the formation of the insulating Mott state. We discuss the observed dynamics in a localized real-space picture.