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

Nanometer-Scale 1D Negative Differential Resistance Channels in Van Der Waals Layers

Negative differential resistance (NDR) is the key feature of resonant tunneling diodes exploited for high-frequency and low-power devices and recent studies have focused on NDR in van der Waals heterostructures and nanoscale materials. Here, strong NDR confined along a 1-nm-wide 1D channel within a van der Waals layer 1T-TaS2 is reported. Using scanning tunneling microscopy, a double 1D NDR channel formed along the sides of a charge-density-wave domain wall of 1T-TaS2 is found. The density functional theory calculation elucidates that the strong local band-bending at the domain wall and the interlayer orbital overlap cooperate to bring about 1D NDR channels. Furthermore, the NDR is well controlled by changing the tunneling junction distance. This result would be important for nanoscale device applications based on strong nonlinear resistance within van der Waals material architectures.

Janus Monolayer of 1T-TaSSe: A Computational Study

Materials exhibiting charge density waves are attracting increasing attention owing to their complex physics and potential for applications. In this paper, we present a computational, first principles-based study of the Janus monolayer of 1T-TaSSe transition metal dichalcogenide. We extensively compare the results with those obtained for parent compounds, TaS2 and TaSe2 monolayers, with confirmed presence of 13×13 charge density waves. The structural and electronic properties of the normal (undistorted) phase and distorted phase with 13×13 periodic lattice distortion are discussed. In particular, for a normal phase, the emergence of dipolar moment due to symmetry breaking is demonstrated, and its sensitivity to an external electric field perpendicular to the monolayer is investigated. Moreover, the appearance of imaginary energy phonon modes suggesting structural instability is shown. For the distorted phase, we predict the presence of a flat, weakly dispersive band related to the appearance of charge density waves, similar to the one observed in parent compounds. The results suggest a novel platform for studying charge density waves in two-dimensional transition metal dichalcogenides.

Origin of Distinct Insulating Domains in the Layered Charge Density Wave Material 1T-TaS2

Vertical charge order shapes the electronic properties in layered charge density wave (CDW) materials. Various stacking orders inevitably create nanoscale domains with distinct electronic structures inaccessible to bulk probes. Here, the stacking characteristics of bulk 1T-TaS2 are analyzed using scanning tunneling spectroscopy (STS) and density functional theory (DFT) calculations. It is observed that Mott-insulating domains undergo a transition to band-insulating domains restoring vertical dimerization of the CDWs. Furthermore, STS measurements covering a wide terrace reveal two distinct band insulating domains differentiated by band edge broadening. These DFT calculations reveal that the Mott insulating layers preferably reside on the subsurface, forming broader band edges in the neighboring band insulating layers. Ultimately, buried Mott insulating layers believed to harbor the quantum spin liquid phase are identified. These results resolve persistent issues regarding vertical charge order in 1T-TaS2, providing a new perspective for investigating emergent quantum phenomena in layered CDW materials.

Coexistence of Interacting Charge Density Waves in a Layered Semiconductor

Coexisting orders are key features of strongly correlated materials and underlie many intriguing phenomena from unconventional superconductivity to topological orders. Here, we report the coexistence of two interacting charge-density-wave (CDW) orders in EuTe_{4}, a layered crystal that has drawn considerable attention owing to its anomalous thermal hysteresis and a semiconducting CDW state despite the absence of perfect Fermi surface nesting. By accessing unoccupied conduction bands with time- and angle-resolved photoemission measurements, we find that monolayers and bilayers of Te in the unit cell host different CDWs that are associated with distinct energy gaps. The two gaps display dichotomous evolutions following photoexcitation, where the larger bilayer CDW gap exhibits less renormalization and faster recovery. Surprisingly, the CDW in the Te monolayer displays an additional momentum-dependent gap renormalization that cannot be captured by density-functional theory calculations. This phenomenon is attributed to interlayer interactions between the two CDW orders, which account for the semiconducting nature of the equilibrium state. Our findings not only offer microscopic insights into the correlated ground state of EuTe_{4} but also provide a general nonequilibrium approach to understand coexisting, layer-dependent orders in a complex system.

Dualistic insulator states in 1T-TaS2 crystals

While the monolayer sheet is well-established as a Mott-insulator with a finite energy gap, the insulating nature of bulk 1T-TaS2 crystals remains ambiguous due to their varying dimensionalities and alterable interlayer coupling. In this study, we present a unique approach to unlock the intertwined two-dimensional Mott-insulator and three-dimensional band-insulator states in bulk 1T-TaS2 crystals by structuring a laddering stack along the out-of-plane direction. Through modulating the interlayer coupling, the insulating nature can be switched between band-insulator and Mott-insulator mechanisms. Our findings demonstrate the duality of insulating nature in 1T-TaS2 crystals. By manipulating the translational degree of freedom in layered crystals, our discovery presents a promising strategy for exploring fascinating physics, independent of their dimensionality, thereby offering a "three-dimensional" control for the era of slidetronics.

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.

Quantum spin liquid signatures in monolayer 1T-NbSe2

Quantum spin liquids (QSLs) are in a quantum disordered state that is highly entangled and has fractional excitations. As a highly sought-after state of matter, QSLs were predicted to host spinon excitations and to arise in frustrated spin systems with large quantum fluctuations. Here we report on the experimental observation and theoretical modeling of QSL signatures in monolayer 1T-NbSe2, which is a newly emerging two-dimensional material that exhibits both charge-density-wave (CDW) and correlated insulating behaviors. By using scanning tunneling microscopy and spectroscopy (STM/STS), we confirm the presence of spin fluctuations in monolayer 1T-NbSe2 by observing the Kondo resonance as monolayer 1T-NbSe2 interacts with metallic monolayer 1H-NbSe2. Subsequent STM/STS imaging of monolayer 1T-NbSe2 at the Hubbard band energy further reveals a long-wavelength charge modulation, in agreement with the spinon modulation expected for QSLs. By depositing manganese-phthalocyanine (MnPc) molecules with spin S = 3/2 onto monolayer 1T-NbSe2, new STS resonance peaks emerge at the Hubbard band edges of monolayer 1T-NbSe2. This observation is consistent with the spinon Kondo effect induced by a S = 3/2 magnetic impurity embedded in a QSL. Taken together, these experimental observations indicate that monolayer 1T-NbSe2 is a new promising QSL material.

Possible quantum-spin-liquid state in van der Waals cluster magnet Nb3Cl8

The cluster magnet Nb3Cl8consists of Nb3trimmers that form an emergentS= 1/2 two-dimensional triangular layers, which are bonded by weak van der Waals interactions. Recent studies show that its room-temperature electronic state can be well described as a single-band Mott insulator. However, the magnetic ground state is non-magnetic due to a structural transition below about 100 K. Here we show that there exists a thickness threshold below which the structural transition will not happen. For a bulk crystal, a small fraction of the sample maintains the high-temperature structure at low temperatures and such remnant gives rise to linear-temperature dependence of the specific heat at very low temperatures. This is further confirmed by the measurements on ground powder sample orc-axis pressed single crystals, which prohibits the formation of the non-magnetic state. Moreover, the intrinsic magnetic susceptibility also tends to be constant with decreasing temperature. Our results suggest that Nb3Cl8with the high-temperature structure may host a quantum-spin-liquid ground state with spinon Fermi surfaces, which can be achieved by making the thickness of a sample smaller than a certain threshold.

Kinkless Electronic Junction along 1D Electronic Channel Embedded in a Van Der Waals Layer

Here, the formation of type-I and type-II electronic junctions with or without any structural discontinuity along a well-defined 1 nm-wide 1D electronic channel within a van der Waals layer is reported. Scanning tunneling microscopy and spectroscopy techniques are employed to investigate the atomic and electronic structure along peculiar domain walls formed on the charge-density-wave phase of 1T-TaS2 . Distinct kinds of abrupt electronic junctions with discontinuities of the band gap along the domain walls are found, some of which even do not have any structural kinks and defects. Density-functional calculations reveal a novel mechanism of the electronic junction formation; they are formed by a kinked domain wall in the layer underneath through substantial electronic interlayer coupling. This work demonstrates that the interlayer electronic coupling can be an effective control knob over nanometer-scale electronic property of 2D atomic monolayers.

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.

Crystallization of polarons through charge and spin ordering transitions in 1T-TaS2

The interaction of electrons with the lattice in metals can lead to reduction of their kinetic energy to the point where they may form heavy, dressed quasiparticles-polarons. Unfortunately, polaronic lattice distortions are difficult to distinguish from more conventional charge- and spin-ordering phenomena at low temperatures. Here we present a study of local symmetry breaking of the lattice structure on the picosecond timescale in the prototype layered dichalcogenide Mott insulator 1T-TaS2 using X-ray pair-distribution function measurements. We clearly identify symmetry-breaking polaronic lattice distortions at temperatures well above the ordered phases, and record the evolution of broken symmetry states from 915 K to 15 K. The data imply that charge ordering is driven by polaron crystallization into a Wigner crystal-like state, rather than Fermi surface nesting or conventional electron-phonon coupling. At intermediate temperatures the local lattice distortions are found to be consistent with a quantum spin liquid state.

First-order quantum phase transition in the hybrid metal-Mott insulator transition metal dichalcogenide 4Hb-TaS2

Coupling together distinct correlated and topologically nontrivial electronic phases of matter can potentially induce novel electronic orders and phase transitions among them. Transition metal dichalcogenide compounds serve as a bedrock for exploration of such hybrid systems. They host a variety of exotic electronic phases, and their Van der Waals nature enables to admix them, either by exfoliation and stacking or by stoichiometric growth, and thereby induce novel correlated complexes. Here, we investigate the compound 4Hb-TaS2 that interleaves the Mott-insulating state of 1T-TaS2 and the putative spin liquid it hosts together with the metallic state of 2H-TaS2 and the low-temperature superconducting phase it harbors using scanning tunneling spectroscopy. We reveal a thermodynamic phase diagram that hosts a first-order quantum phase transition between a correlated Kondo-like cluster state and a depleted flat band state. We demonstrate that this intrinsic transition can be induced by an electric field and temperature as well as by manipulation of the interlayer coupling with the probe tip, hence allowing to reversibly toggle between the Kondo-like cluster and the depleted flat band states. The phase transition is manifested by a discontinuous change of the complete electronic spectrum accompanied by hysteresis and low-frequency noise. We find that the shape of the transition line in the phase diagram is determined by the local compressibility and the entropy of the two electronic states. Our findings set such heterogeneous structures as an exciting platform for systematic investigation and manipulation of Mott-metal transitions and strongly correlated phases and quantum phase transitions therein.

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.

Control over a Wide Phase Diagram of 2D Correlated Electrons by Surface Doping; K/1T-TaS2

We demonstrate the systematic tuning of a trivial insulator into a Mott insulator and a Mott insulator into a correlated metallic and a pseudogap state, which emerge in a quasi-two-dimensional electronic system of 1T-TaS2 through strong electron correlation. The band structure evolution is investigated upon surface doping by alkali adsorbates for two distinct phases occurring at around 220 and 10 K by angle-resolved photoelectron spectroscopy. We find contrasting behaviors upon doping that corroborate the fundamental difference of two electronic states: while the antibonding state of the spin-singlet insulator at 10 K is partially occupied to produce an emerging Mott insulating state, the presumed Mott insulating state at 220 K evolves into a correlated metallic state and then a pseudogap state. The work indicates that surface doping onto correlated 2D materials can be a powerful tool to systematically engineer a wide range of correlated electronic phases.

π-Stacking among the Anthracenyl Groups of a Copper Complex Resulted in Doubling of Unit Cell Volume To Provide New Polymorphs

Two polymorphs of the 9-N-(3-imidazolylpropylamino)methylanthracene (Hanthraimmida) containing hydrated copper(II)-2,6-pyridinedicarboxylate complex are reported. The two polymorphs have either lamellar or Herringbone arrangements of π-stacks among the anthracenyl groups of organocation. The difference between the two polymorphs originated from having face-to-face stacking arrangements between the two anthracenyl groups of the symmetry independent cations within the unit cell in one of the polymorphs. The π-stacked anthracenyl groups in consecutive layers of the polymorphs are oriented in one direction in the polymorph designated as P1, whereas the polymorph designated as P2 has such orientations in opposite directions. The unit cell volume of the polymorph P2 (Z = 4) has approximately twice the volume of the polymorph P1 (Z = 2); it happend due to coalescence of two unit cells of P1 in the ab-crystallographic plane. A mixed methanol/water solvate of the copper complex is also reported. It has a channel-like arrangement of the cations; has the anions and the solvents within the cation embraced channel-like enclosures. This complex is unstable, once taken out from the methanol solvent, it transforms in real time to P2 by replacements of the methanol molecules by water molecules.

Selective Electron-Phonon Coupling in Dimerized 1T-TaS2 Revealed by Resonance Raman Spectroscopy

The layered transition-metal dichalcogenide material 1T-TaS2 possesses successive phase transitions upon cooling, resulting in strong electron-electron correlation effects and the formation of charge density waves (CDWs). Recently, a dimerized double-layer stacking configuration was shown to form a Peierls-like instability in the electronic structure. To date, no direct evidence for this double-layer stacking configuration using optical techniques has been reported, in particular through Raman spectroscopy. Here, we employ a multiple excitation and polarized Raman spectroscopy to resolve the behavior of phonons and electron-phonon interactions in the commensurate CDW lattice phase of dimerized 1T-TaS2. We observe a distinct behavior from what is predicted for a single layer and probe a richer number of phonon modes that are compatible with the formation of double-layer units (layer dimerization). The multiple-excitation results show a selective coupling of each Raman-active phonon with specific electronic transitions hidden in the optical spectra of 1T-TaS2, suggesting that selectivity in the electron-phonon coupling must also play a role in the CDW order of 1T-TaS2.

Electrical switching of ferro-rotational order in nanometre-thick 1T-TaS2 crystals

Hysteretic switching of domain states is a salient characteristic of all ferroic materials and the foundation for their multifunctional applications. Ferro-rotational order is emerging as a type of ferroic order that features structural rotations, but control over state switching remains elusive due to its invariance under both time reversal and spatial inversion. Here we demonstrate electrical switching of ferro-rotational domain states in the charge-density-wave phases of nanometre-thick 1T-TaS2 crystals. Cooling from the high-symmetry phase to the ferro-rotational phase under an external electric field induces domain state switching and domain wall formation, which is realized in a simple two-terminal configuration using a volt-scale bias. Although the electric field does not couple with the order due to symmetry mismatch, it drives domain wall propagation to give rise to reversible, durable and non-volatile isothermal state switching at room temperature. These results offer a route to the manipulation of ferro-rotational order and its nanoelectronic applications.

Abnormal Metal-Semiconductor-Like Transition and Exceptional Enhanced Superconducting State in Pressurized Restacked TaS2

Interlayer coupling and stacking order play essential roles in shaping the exotic electronic properties of two-dimensional materials. Here, we employ restacked TaS₂─a novel transition metal dichalcogenide (TMD) with weak vdW bonding and twisted angles─to investigate the strain effects of interlayer modulation on the electronic properties. Under pressure, an unexpected transition from metallic to semiconducting-like states occurs. Superconductivity coexists with the semiconducting-like state over a wide pressure range, which has never before been observed in TMDs. Upon further compression, a new superconducting SC-II state emerges without structural evolution and gradually replaces the initial SC-I state. The emerging SC-II state exhibits robust zero-resistance superconductivity and an ultrahigh upper critical field. The abundant electronic state changes in RS-TaS₂ are strongly related to band-structure engineering resulting from pressure-induced interlayer stacking angle modulation. Our results reveal the remarkable effect of interlayer rearrangement on electronic properties and provide a special way to explore the unique properties of 2D materials.

First principles investigation of screened Coulomb interaction and electronic structure of low-temperature phase TaS2

By means of ab initio computation schemes, we examine the electronic screening, Coulomb interaction strength, and the electronic structure of a quantum spin liquid candidate monolayer TaS2 in its low-temperature commensurate charge-density-wave phase. Not only local (U ) but non-local (V ) correlations are estimated within random phase approximation based on two different screening models. Using GW + EDMFT (GW plus extended dynamical mean-field theory) method, we investigate the detailed electronic structure by increasing the level of non-local approximation from DMFT (V = 0 ) to EDMFT and GW + EDMFT.

Spectroscopic visualization and phase manipulation of chiral charge density waves in 1T-TaS2

The chiral charge density wave is a many-body collective phenomenon in condensed matter that may play a role in unconventional superconductivity and topological physics. Two-dimensional chiral charge density waves provide the building blocks for the fabrication of various stacking structures and chiral homostructures, in which physical properties such as chiral currents and the anomalous Hall effect may emerge. Here, we demonstrate the phase manipulation of two-dimensional chiral charge density waves and the design of in-plane chiral homostructures in 1T-TaS₂. We use chiral Raman spectroscopy to directly monitor the chirality switching of the charge density wave-revealing a temperature-mediated reversible chirality switching. We find that interlayer stacking favours homochirality configurations, which is confirmed by first-principles calculations. By exploiting the interlayer chirality-locking effect, we realise in-plane chiral homostructures in 1T-TaS₂. Our results provide a versatile way to manipulate chiral collective phases by interlayer coupling in layered van der Waals semiconductors.

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.

Order-disorder phase transition driven by interlayer sliding in lead iodides

A variety of phase transitions have been found in two-dimensional layered materials, but some of their atomic-scale mechanisms are hard to clearly understand. Here, we report the discovery of a phase transition whose mechanism is identified as interlayer sliding in lead iodides, a layered material widely used to synthesize lead halide perovskites. The low-temperature crystal structure of lead iodides is found not 2H polytype as known before, but non-centrosymmetric 4H polytype. This undergoes the order-disorder phase transition characterized by the abrupt spectral broadening of valence bands, taken by angle-resolved photoemission, at the critical temperature of 120 K. It is accompanied by drastic changes in simultaneously taken photocurrent and photoluminescence. The transmission electron microscopy is used to reveal that lead iodide layers stacked in the form of 4H polytype at low temperatures irregularly slide over each other above 120 K, which can be explained by the low energy barrier of only 10.6 meV/atom estimated by first principles calculations. Our findings suggest that interlayer sliding is a key mechanism of the phase transitions in layered materials, which can significantly affect optoelectronic and optical characteristics.

Unveiling Electronic Behaviors in Heterochiral Charge-Density-Wave Twisted Stacking Materials with 1.25 nm Unit Dependence

Layered charge-density-wave (CDW) materials have gained increasing interest due to their CDW stacking-dependent electronic properties for practical applications. Among the large family of CDW materials, those with star of David (SOD) patterns are very important due to the potentials for quantum spin liquid and related device applications. However, the spatial extension and the spin coupling information down to the nanoscale remain elusive. Here, we report the study of heterochiral CDW stackings in bilayer (BL) NbSe₂ with high spatial resolution. We reveal that there exist well-defined heterochiral stackings, which have inhomogeneous electronic states among neighboring CDW units (star of David, SOD), significantly different from the homogeneous electronic states in the homochiral stackings. Intriguingly, the different electronic behaviors are spatially localized within each SOD with a unit size of 1.25 nm, and the gap sizes are determined by the different types of SOD stackings. Density functional theory (DFT) calculations match the experimental measurements well and reveal the SOD-stacking-dependent correlated electronic states and antiferromagnetic/ferromagnetic couplings. Our findings give a deep understanding of the spatial distribution of interlayer stacking and the delicate modulation of the spintronic states, which is very helpful for CDW-based nanoelectronic devices.

Impenetrable Barrier at the Metal-Mott Insulator Junction in Polymorphic 1H and 1T NbSe2 Lateral Heterostructure

When a metal makes contact with a band insulator, charge transfer occurs across the interface leading to band bending and a Schottky barrier with rectifying behavior. The nature of metal-Mott insulator junctions, however, is still debated due to challenges in experimental probes of such vertical heterojunctions with buried interfaces. Here, we grow lateral polymorphic heterostructures of single-layer metallic 1H and Mott insulating 1T NbSe₂ by molecular beam epitaxy. We find a one-dimensional metallic channel along the interface due to the appearance of quasiparticle states with an intensity decay following 1/x², indicating an impenetrable barrier. Near the interface, the Mott gap exhibits a strong spatial dependence arising from the difference in lattice constants between the two phases, consistent with our density functional theory calculations. These results provide clear experimental evidence for an impenetrable barrier at the metal-Mott insulator junction and the high tunability of a Mott insulator by strain.

Tunable Mott Dirac and Kagome Bands Engineered on 1T-TaS2

Strongly interacting electrons in hexagonal and kagome lattices exhibit rich phase diagrams of exotic quantum states, including superconductivity and correlated topological orders. However, material realizations of these electronic states have been scarce in nature or by design. Here, we theoretically propose an approach to realize artificial lattices by metal adsorption on a 2D Mott insulator 1T-TaS₂. Alkali, alkaline-earth, and group 13 metal atoms are deposited in (√3 × √3)R30° and 2 × 2 TaS₂ superstructures of honeycomb- and kagome-lattice symmetries exhibiting Dirac and kagome bands, respectively. The strong electron correlation of 1T-TaS₂ drives the honeycomb and kagome systems into correlated topological phases described by Kane-Mele-Hubbard and kagome-Hubbard models. We further show that the 2/3 or 3/4 band filling of Mott Dirac and flat bands can be achieved with a proper concentration of Mg adsorbates. Our proposal may be readily implemented in experiments, offering an attractive condensed-matter platform to exploit the interplay of correlated topological order and superconductivity.

Atomic-scale thermopower in charge density wave states

The microscopic origins of thermopower have been investigated to design efficient thermoelectric devices, but strongly correlated quantum states such as charge density waves and Mott insulating phase remain to be explored for atomic-scale thermopower engineering. Here, we report on thermopower and phonon puddles in the charge density wave states in 1T-TaS₂, probed by scanning thermoelectric microscopy. The Star-of-David clusters of atoms in 1T-TaS₂ exhibit counterintuitive variations in thermopower with broken three-fold symmetry at the atomic scale, originating from the localized nature of valence electrons and their interlayer coupling in the Mott insulating charge density waves phase of 1T-TaS₂. Additionally, phonon puddles are observed with a spatial range shorter than the conventional mean free path of phonons, revealing the phonon propagation and scattering in the subsurface structures of 1T-TaS₂.

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.

Fractionalization on the Surface: Is Type-II Terminated 1T-TaS_{2} Surface an Anomalously Realized Spin Liquid?

The type-II terminated 1T-TaS_{2} surface of a three-dimensional 1T-TaS_{2} bulk material realizes the effective spin-1/2 degree of freedom on each David star cluster with T^{2}=-1 such that the time-reversal symmetry is realized anomalously, despite the fact that bulk three-dimensional 1T-TaS_{2} material has an even number of electrons per unit cell with T^{2}=+1. This surface is effectively viewed as a spin-1/2 triangular lattice magnet, except with a fully gapped topological bulk. We further propose this surface termination realizes a spinon Fermi surface spin liquid with the surface fractionalization but with a nonexotic three-dimensional bulk. We analyze possible experimental consequences, especially the surface spectroscopic measurements, of the type-II terminated surface spin liquid.

Atomic structure and Mott nature of the insulating charge density wave phase of 1T-TaS2

Using x-ray pair distribution function (PDF) analysis and computer modeling, we explore structure models for the complex charge density wave (CDW) phases of layered 1T-TaS₂that both well capture their atomic-level features and are amenable to electronic structure calculations. The models give the most probable position of constituent atoms in terms of 3D repetitive unit cells comprising a minimum number of Ta-S layers. Structure modeling results confirm the emergence of star-of-David (SD) like clusters of Ta atoms in the high-temperature incommensurate (IC) CDW phase and show that, contrary to the suggestions of recent studies, the low-temperature commensurate (C) CDW phase expands upon cooling thus reducing lattice strain. The C-CDW phase is also found to preserve the stacking sequence of Ta-S layers found in the room temperature, nearly commensurate (NC) CDW phase to a large extent. DFT based on the PDF refined model shows that bulk C-CDW 1T-TaS₂also preserves the insulating state of individual layers of SD clusters, favoring the Mott physics description of the metal-to-insulator (NC-CDW to C-CDW) phase transition in 1T-TaS₂. Our work highlights the importance of using precise crystal structure models in determining the nature of electronic phases in complex materials.

Inducing and tuning Kondo screening in a narrow-electronic-band system

Although the single-impurity Kondo physics has already been well understood, the understanding of the Kondo lattice where a dense array of local moments couples to the conduction electrons is still far from complete. The ability of creating and tuning the Kondo lattice in non-f-electron systems will be great helpful for further understanding the Kondo lattice behavior. Here we show that the Pb intercalation in the charge-density-wave-driven narrow-electronic-band system 1T-TaS₂ induces a transition from the insulating gap to a sharp Kondo resonance in the scanning tunneling microscopy measurements. It results from the Kondo screening of the localized moments in the 13-site Star-of-David clusters of 1T-TaS₂. As increasing the Pb concentration, the narrow electronic band derived from the localized electrons shifts away from the Fermi level and the Kondo resonance peak is gradually suppressed. Our results pave the way for creating and tuning many-body electronic states in layered narrow-electronic-band materials.

Observation and Manipulation of a Phase Separated State in a Charge Density Wave Material

The 1T polytype of TaS₂ has been studied extensively as a strongly correlated system. As 1T-TaS₂ is thinned toward the 2D limit, its phase diagram shows significant deviations from that of the bulk material. Optoelectronic maps of ultrathin 1T-TaS₂ have indicated the presence of nonequilibrium charge density wave phases within the hysteresis region of the nearly commensurate (NC) to commensurate (C) transition. We perform scanning tunneling microscopy on exfoliated ultrathin flakes of 1T-TaS₂ within the NC-C hysteresis window, finding evidence that the observed nonequilibrium phases consist of intertwined, irregularly shaped NC-like and C-like domains. After applying lateral electrical signals to the sample, we image changes in the geometric arrangement of the different regions. We use a phase separation model to explore the relationship between electronic inhomogeneity present in ultrathin 1T-TaS₂ and its bulk resistivity. These results demonstrate the role of phase competition morphologies in determining the properties of 2D materials.

Erratum: Identification of the Mott Insulating Charge Density Wave State in 1T-TaS_{2} [Phys. Rev. Lett. 126, 196406 (2021)]

This corrects the article DOI: 10.1103/PhysRevLett.126.196406.

Engineering Domain Wall Electronic States in Strongly Correlated van der Waals Material of 1T-TaS2

Although a few physical methods were demonstrated for domain wall engineering in various electronic or ferroic materials with broken discrete symmetries, the direct control over the electronic properties of individual domain walls has been extremely limited. Here, we introduce a chemical method to tune the electronic property of domain walls in 1T tantalum disulfide. By using scanning tunneling microscopy and spectroscopy techniques, we find that indium adatoms on 1T-TaS₂ have distinct behaviors on the domains with different bulk terminations. Moreover, the adatoms form their own chains along the edges of neighboring domains. The density functional theory calculations reveal a 1D Mott insulating state on a modified domain wall, resulting from the degenerated spin-polarized bands with electron doping from adsorbates and charge transfer from neighboring domains. This work suggests that chemical decoration by adsorbates can be widely used to tune local electronic states of domain walls and various 2D materials.

Robust charge-density wave strengthened by electron correlations in monolayer 1T-TaSe2 and 1T-NbSe2

Combination of low-dimensionality and electron correlation is vital for exotic quantum phenomena such as the Mott-insulating phase and high-temperature superconductivity. Transition-metal dichalcogenide (TMD) 1T-TaS2 has evoked great interest owing to its unique nonmagnetic Mott-insulator nature coupled with a charge-density-wave (CDW). To functionalize such a complex phase, it is essential to enhance the CDW-Mott transition temperature TCDW-Mott, whereas this was difficult for bulk TMDs with TCDW-Mott < 200 K. Here we report a strong-coupling 2D CDW-Mott phase with a transition temperature onset of ~530 K in monolayer 1T-TaSe2. Furthermore, the electron correlation derived lower Hubbard band survives under external perturbations such as carrier doping and photoexcitation, in contrast to the bulk counterpart. The enhanced Mott-Hubbard and CDW gaps for monolayer TaSe2 compared to NbSe2, originating in the lattice distortion assisted by strengthened correlations and disappearance of interlayer hopping, suggest stabilization of a likely nonmagnetic CDW-Mott insulator phase well above the room temperature. The present result lays the foundation for realizing monolayer CDW-Mott insulator based devices operating at room temperature.

Topical review: recent progress of charge density waves in 2D transition metal dichalcogenide-based heterojunctions and their applications

Charge density wave (CDW) is an intriguing physical phenomenon especially found in two-dimensional (2D) layered systems such as transition-metal dichalcogenides (TMDs). The study of CDW is vital for understanding lattice modification, strongly correlated electronic behaviors, and other related physical properties. This paper gives a review of the recent studies on CDW emerging in 2D TMDs. First, a brief introduction and the main mechanisms of CDW are given. Second, the interplay between CDW patterns and the related unique electronic phenomena (superconductivity, spin, and Mottness) is elucidated. Then various manipulation methods such as doping, applying strain, local voltage pulse to induce the CDW change are discussed. Finally, examples of the potential application of devices based on CDW materials are given. We also discuss the current challenge and opportunities at the frontier in this research field.

Charge Transfer Gap Tuning via Structural Distortion in Monolayer 1T-NbSe2

The Mott state in 1T-TaS₂ is predicted to host quantum spin liquids (QSLs). However, its insulating mechanism is controversial due to complications from interlayer coupling. Here, we study the charge transfer state in monolayer 1T-NbSe₂, an electronic analogue to TaS₂ exempt from interlayer coupling, using spectroscopic imaging scanning tunneling microscopy and first-principles calculations. Monolayer NbSe₂ surprisingly displays two types of star of David (SD) motifs with different charge transfer gap sizes, which are interconvertible via temperature variation. In addition, bilayer 1T-NbSe₂ shows a Mott collapse by interlayer coupling. Our calculation unveils that the two types of SDs possess distinct structural distortions, altering the effective Coulomb energies of the central Nb orbital. Our calculation suggests that the charge transfer gap, the same parameter for determining the QSL regime, is tunable with strain. This finding offers a general strategy for manipulating the charge transfer state in related systems, which may be tuned into the potential QSL regime.

Roles of the Narrow Electronic Band near the Fermi Level in 1T-TaS_{2}-Related Layered Materials

Here we use low-temperature scanning tunneling microscopy and spectroscopy to reveal the roles of the narrow electronic band in two 1T-TaS_{2}-related materials (bulk 1T-TaS_{2} and 4H_{b}-TaS_{2}). 4H_{b}-TaS_{2} is a superconducting compound with alternating 1T-TaS_{2} and 1H-TaS_{2} layers, where the 1H-TaS_{2} layer has a weak charge density wave (CDW) pattern and reduces the CDW coupling between the adjacent 1T-TaS_{2} layers. In the 1T-TaS_{2} layer of 4H_{b}-TaS_{2}, we observe a narrow electronic band located near the Fermi level, and its spatial distribution is consistent with the tight-binding calculations for two-dimensional 1T-TaS_{2} layers. The weak electronic hybridization between the 1T-TaS_{2} and 1H-TaS_{2} layers in 4H_{b}-TaS_{2} shifts the narrow electronic band to be slightly above the Fermi level, which suppresses the electronic correlation-induced band splitting. In contrast, in bulk 1T-TaS_{2}, there is an interlayer CDW coupling-induced insulating gap. In comparison with the spatial distributions of the electronic states in bulk 1T-TaS_{2} and 4H_{b}-TaS_{2}, the insulating gap in bulk 1T-TaS_{2} results from the formation of a bonding band and an antibonding band due to the overlap of the narrow electronic bands in the dimerized 1T-TaS_{2} layers.

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.

Identification of the Mott Insulating Charge Density Wave State in 1T-TaS_{2}

We investigate the low-temperature charge density wave (CDW) state of bulk TaS_{2} with a fully self-consistent density-functional theory with the Hubbard U potential, over which the controversy has remained unresolved regarding the out-of-plane metallic band. By examining the innate structure of the Hubbard U potential, we reveal that the conventional use of atomic-orbital basis could seriously misevaluate the electron correlation in the CDW state. By adopting a generalized basis, covering the whole David star, we successfully reproduce the Mott insulating nature with the layer-by-layer antiferromagnetic order. Similar consideration should be applied for description of the electron correlation in molecular solid.

Direct identification of Mott Hubbard band pattern beyond charge density wave superlattice in monolayer 1T-NbSe2

Understanding Mott insulators and charge density waves (CDW) is critical for both fundamental physics and future device applications. However, the relationship between these two phenomena remains unclear, particularly in systems close to two-dimensional (2D) limit. In this study, we utilize scanning tunneling microscopy/spectroscopy to investigate monolayer 1T-NbSe2 to elucidate the energy of the Mott upper Hubbard band (UHB), and reveal that the spin-polarized UHB is spatially distributed away from the dz2 orbital at the center of the CDW unit. Moreover, the UHB shows a √3 × √3 R30° periodicity in addition to the typically observed CDW pattern. Furthermore, a pattern similar to the CDW order is visible deep in the Mott gap, exhibiting CDW without contribution of the Mott Hubbard band. Based on these findings in monolayer 1T-NbSe2, we provide novel insights into the relation between the correlated and collective electronic structures in monolayer 2D systems.

Single-water-dipole-layer-driven Reversible Charge Order Transition in 1T-TaS2

Water-solid interactions are crucial for many fundamental phenomena and technological processes. Here, we report a scanning tunneling microscopy study about the charge density wave (CDW) transition in 1T-TaS₂ driven by a single water dipole layer. At low temperature, pristine 1T-TaS₂ is a prototypical CDW compound with 13 × 13 charge order. After growing a highly ordered water adlayer, a new charge order with 3 × 3 periodicity emerges on water-covered 1T-TaS₂. After water desorption, the entire 1T-TaS₂ surface appears as localized 13 × 13 CDW domains that are separated by residual-water-cluster-pinned CDW domain walls. First-principles calculations show that the electric dipole moments in the water adlayer attract electrons to the top layer of 1T-TaS₂, which shifts the phonon softening mode and induces the 13 × 13 to 3 × 3 charge order transition. Our results pave the way for creating new collective quantum states of matter with a molecular dipole layer.

Honeycomb-Lattice Mott Insulator on Tantalum Disulphide

Effects of electron many-body interactions amplify in an electronic system with a narrow bandwidth opening a way to exotic physics. A narrow band in a two-dimensional (2D) honeycomb lattice is particularly intriguing as combined with Dirac bands and topological properties but the material realization of a strongly interacting honeycomb lattice described by the Kane-Mele-Hubbard model has not been identified. Here we report a novel approach to realize a 2D honeycomb-lattice narrow-band system with strongly interacting 5d electrons. We engineer a well-known triangular lattice 2D Mott insulator 1T-TaS_{2} into a honeycomb lattice utilizing an adsorbate superstructure. Potassium (K) adatoms at an optimum coverage deplete one-third of the unpaired d electrons and the remaining electrons form a honeycomb lattice with a very small hopping. Ab initio calculations show extremely narrow Z_{2} topological bands mimicking the Kane-Mele model. Electron spectroscopy detects an order of magnitude bigger charge gap confirming the substantial electron correlation as confirmed by dynamical mean field theory. It could be the first artificial Mott insulator with a finite spin Chern number.

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.