1T-TaS2 as a quantum spin liquid

Charge-neutral electronic excitations in quantum insulators

Experiments on quantum materials have uncovered many interesting quantum phases ranging from superconductivity to a variety of topological quantum matter including the recently observed fractional quantum anomalous Hall insulators. The findings have come in parallel with the development of approaches to probe the rich excitations inherent in such systems. In contrast to observing electrically charged excitations, the detection of charge-neutral electronic excitations in condensed matter remains difficult, although they are essential to understanding a large class of strongly correlated phases. Low-energy neutral excitations are especially important in characterizing unconventional phases featuring electron fractionalization, such as quantum spin liquids, spin ices and insulators with neutral Fermi surfaces. In this Perspective, we discuss searches for neutral fermionic, bosonic or anyonic excitations in unconventional insulators, highlighting theoretical and experimental progress in probing excitonic insulators, new quantum spin liquid candidates and emergent correlated insulators based on two-dimensional layered crystals and moiré materials. We outline the promises and challenges in probing and using quantum insulators, and discuss exciting new opportunities for future advancements offered by ideas rooted in next-generation quantum materials, devices and experimental schemes.

Unusual Geometric and Electronic Structures at Domain Boundaries in a Heterochiral Charge Density Wave Superlattice

Domain boundaries (DBs) in charge density wave (CDW) systems not only are important for understanding the mechanism of how CDW interplays with other quantum phases but also have potential for future CDW-based nanodevices. However, current research on DBs in CDW materials has been mainly limited to those between homochiral CDW domains, whereas DBs between heterochiral CDW domains, especially in the atomic layers, remain largely unexplored. Here, we have studied the geometric and electronic states of heterochiral DBs in single-layer and bilayer 1T-NbSe2 using scanning tunneling microscopy/spectroscopy. We observe the existence of diverse CDW configurations in a single heterochiral CDW DB with atomic resolution and reveal the corresponding electronic states. In addition, interlayer stacking further enriches the electronic properties of the DB. Our results offer deep insights into the relationship between the detailed CDW nanostructures and electronic behaviors, which has significant implications for DB engineering in strongly correlated CDW systems and related nanodevices.

Intercalating Architecture for the Design of Charge Density Wave in Metallic MA2Z4 Materials

We present a novel approach to induce charge density waves (CDWs) in metallic MA2Z4 materials, resembling the behavior observed in transition metal dichalcogenides (TMDCs). This method leverages the intercalating architecture to maintain the same crystal field and Fermi surface topologies. Our investigation reveals that CDW instability in these materials arises from electron-phonon coupling (EPC) between the d band and longitudinal acoustic (LA) phonons, mirroring TMDC's behavior. By combining α-MA2Z4 with 1H-MX2 materials in a predictive CDW phase diagram using critical EPC constants, we demonstrate the feasibility of extending CDW across material families with comparable crystal fields and reveal the crucial role in CDW instability of the competition between ionic charge transfer and electron correlation. We further uncover a strain-induced Mott transition in β2-NbGe2N4 monolayer featuring star-of-David patterns. This work highlights the potential of intercalating architecture to engineer CDW materials, expanding our understanding of CDW instability and correlation physics.

Unveiling the Interlayer Interaction in a 1H/1T TaS2 van der Waals Heterostructure

This study delves into the intriguing properties of the 1H/1T-TaS2 van der Waals heterostructure, focusing on the transparency of the 1H layer to the charge density wave of the underlying 1T layer. Despite the sizable interlayer separation and metallic nature of the 1H layer, positive bias voltages result in a pronounced superposition of the 1T charge density wave structure on the 1H layer. The conventional explanation relying on tunneling effects proves insufficient. Through a comprehensive investigation combining low-temperature scanning tunneling microscopy, scanning tunneling spectroscopy, non-contact atomic force microscopy, and first-principles calculations, we propose an alternative interpretation. The transparency effect arises from a weak yet substantial electronic coupling between the 1H and 1T layers, challenging prior understanding of the system. Our results highlight the critical role played by interlayer electronic interactions in van der Waals heterostructures to determine the final ground states of the systems.

Nematic Ising superconductivity with hidden magnetism in few-layer 6R-TaS2

In van der Waals heterostructures (vdWHs), the manipulation of interlayer stacking/coupling allows for the construction of customizable quantum systems exhibiting exotic physics. An illustrative example is the diverse range of states of matter achieved through varying the proximity coupling between two-dimensional (2D) quantum spin liquid (QSL) and superconductors within the TaS2 family. This study presents a demonstration of the intertwined physics of spontaneous rotational symmetry breaking, hidden magnetism, and Ising superconductivity (SC) in the three-fold rotationally symmetric, non-magnetic natural vdWHs 6R-TaS2. A distinctive phase emerges in 6R-TaS2 below a characteristic temperature (T*) of approximately 30 K, which is characterized by a remarkable set of features, including a giant extrinsic anomalous Hall effect (AHE), Kondo screening, magnetic field-tunable thermal hysteresis, and nematic magneto-resistance. At lower temperatures, a coexistence of nematicity and Kondo screening with Ising superconductivity is observed, providing compelling evidence of hidden magnetism within a superconductor. This research not only sheds light on unexpected emergent physics resulting from the coupling of itinerant electrons and localized/correlated electrons in natural vdWHs but also emphasizes the potential for tailoring exotic quantum states through the manipulation of interlayer interactions.

Spin-Mechanical Coupling in 2D Antiferromagnet CrSBr

Spin-mechanical coupling is vital in diverse fields including spintronics, sensing, and quantum transduction. Two-dimensional (2D) magnetic materials provide a unique platform for investigating spin-mechanical coupling, attributed to their mechanical flexibility and novel spin orderings. However, studying their spin-mechanical coupling presents challenges in probing mechanical deformation and thermodynamic property changes at the nanoscale. Here we use nano-optoelectromechanical interferometry to mechanically detect the phase transition and magnetostriction effect in multilayer CrSBr, an air-stable antiferromagnet with large magnon-exciton coupling. The transitions among antiferromagnetism, spin-canted ferromagnetism, and paramagnetism are visualized. Nontrivial magnetostriction coefficient 2.3 × 10-5 and magnetoelastic coupling strength on the order of 106 J/m3 have been found. Moreover, we demonstrate the substantial tunability of the magnetoelastic constant by nearly 50% via gate-induced strain. Our findings demonstrate the strong spin-mechanical coupling in CrSBr and pave the way for developing sensitive magnetic sensing and efficient quantum transduction at the atomically thin limit.

Pressure Induced Nonmonotonic Evolution of Superconductivity in 6R-TaS_{2} with a Natural Bulk Van der Waals Heterostructure

The natural bulk Van der Waals heterostructure compound 6R-TaS_{2} consists of alternate stacking 1T- and 1H-TaS_{2} monolayers, creating a unique system that incorporates charge-density-wave (CDW) order and superconductivity (SC) in distinct monolayers. Here, after confirming that the 2D nature of the lattice is preserved up to 8 GPa in 6R-TaS_{2}, we documented an unusual evolution of CDW and SC by conducting high-pressure electronic transport measurements. Upon compression, we observe a gradual suppression of CDW within the 1T layers, while the SC exhibits a dome-shaped behavior that terminates at a critical pressure P_{c} around 2.9 GPa. By taking account of the fact that the substantial suppression of SC is concomitant with the complete collapse of CDW order at P_{c}, we argue that the 6R-TaS_{2} behaves like a stack of Josephson junctions and thus the suppressed superconductivity can be attributed to the weakening of Josephson coupling associated with the presence of CDW fluctuations in the 1T layers. Furthermore, the SC reversely enhances above P_{c}, implying the development of emergent superconductivity in the 1T layers after the melting of T-layer CDW orders. These results show that the 6R-TaS_{2} not only provides a promising platform to explore emergent phenomena but also serves as a model system to study the complex interactions between competing electronic states.

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.

Self-doped flat band and spin-triplet superconductivity in monolayer 1T-TaSe2-xTex

Two-dimensional van der Waals materials have become an established platform to engineer flat bands which can lead to strongly-correlated emergent phenomena. In particular, the family of Ta dichalcogenides in the 1T phase presents a star-of-David charge density wave that creates a flat band at the Fermi level. For TaS2and TaSe2this flat band is at half filling leading to a magnetic insulating phase. In this work, we theoretically demonstrate that ligand substitution in the TaSe2-xTexsystem produces a transition from the magnetic insulator to a non-magnetic metal in which the flat band gets doped away from half-filling. Forx∈[0.846,1.231]the spin-polarized flat band is self-doped and the system becomes a magnetic metal. In this regime, we show that attractive interactions promote three different spin-triplet superconducting phases as a function ofx, corresponding to a nodal f-wave and two topologically-different chiral p-wave superconducting phases. Our results establish monolayer TaSe2-xTexas a promising platform for correlated flat band physics leading to unconventional superconducting states.

Engineering the Kitaev Spin Liquid in a Quantum Dot System

The Kitaev model on a honeycomb lattice may provide a robust topological quantum memory platform, but finding a material that realizes the unique spin-liquid phase remains a considerable challenge. We demonstrate that an effective Kitaev Hamiltonian can arise from a half-filled Fermi-Hubbard Hamiltonian where each site can experience a magnetic field in a different direction. As such, we provide a method for realizing the Kitaev spin liquid on a single hexagonal plaquette made up of 12 quantum dots. Despite the small system size, there are clear signatures of the Kitaev spin-liquid ground state, and there is a range of parameters where these signatures are predicted, allowing a potential platform where Kitaev spin-liquid physics can be explored experimentally in quantum dot plaquettes.

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.

Predicted multiple charge density wave phases in monolayer 1T-NbO2

Layered transition-metal dichalcogenides, such as NbSe2, have been extensively studied for almost half a century due to their intriguing properties, such as charge density wave (CDW) and superconductivity. Can the layered transition-metal dioxide, such as NbO2, be stable and exhibit CDW, given that it has the same crystal structure and electronic configuration as NbSe2? Here, we use first-principles calculations to predict that 1T-NbO2is possibly stable at high temperatures, but it would undergo two CDW transitions with12×12and13×13periodicities at low temperatures. Both CDW transitions are accompanied by a metal-semiconductor transition. Notably, the13×13CDW phase of NbO2possesses localized magnetic moments and hosts a Mott insulating state. This work offers a fresh outlook on studying CDW and Mott transition in low-dimensional oxide materials.

Probing the Phase Transition to a Coherent 2D Kondo Lattice

Kondo lattices are systems with unusual electronic properties that stem from strong electron correlation, typically studied in intermetallic 3D compounds containing lanthanides or actinides. Lowering the dimensionality of the system enhances the role of electron correlations providing a new tuning knob for the search of novel properties in strongly correlated quantum matter. The realization of a 2D Kondo lattice by stacking a single-layer Mott insulator on a metallic surface is reported. The temperature of the system is steadily lowered and by using high-resolution scanning tunneling spectroscopy, the phase transition leading to the Kondo lattice is followed. Above 27 K the interaction between the Mott insulator and the metal is negligible and both keep their original electronic properties intact. Below 27 K the Kondo screening of the localized electrons in the Mott insulator begins and below 11 K the formation of a coherent quantum electronic state extended to the entire sample, i.e., the Kondo lattice, takes place. By means of density functional theory, the electronic properties of the system and its evolution with temperature are explained. The findings contribute to the exploration of unconventional states in 2D correlated materials.

Two-component nematic superconductivity in 4Hb-TaS2

Most superconductors have an isotropic, single component order parameter and are well described by the standard (BCS) theory for superconductivity. Unconventional, multiple-component superconductors are exceptionally rare and are much less understood. Here, we combine scanning tunneling microscopy and angle-resolved macroscopic transport for studying the candidate chiral superconductor, 4Hb-TaS2. We reveal quasi-periodic one-dimensional modulations in the tunneling conductance accompanied by two-fold symmetric superconducting critical field. The strong modulation of the in-plane critical field, Hc2, points to a nematic, unconventional order parameter. However, the imaged vortex core is isotropic at low temperatures. We suggest a model that reconciles this apparent discrepancy and takes into account previously observed spontaneous time-reversal symmetry breaking at low temperatures. The model describes a competition between a dominating chiral superconducting order parameter and a nematic one. The latter emerges close to the normal phase. Our results strongly support the existence of two-component superconductivity in 4Hb-TaS2 and can provide valuable insights into other systems with coexistent charge order and superconductivity.

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.

Atomically Unraveling Highly Crystalline Self-Intercalated Tantalum Sulfide with Correlated Stacking Registry-Dependent Magnetism

In self-intercalated two-dimensional (ic-2D) materials, understanding the local chemical environment and the topology of the filling site remains elusive, and the subsequent correlation with the macroscopically manifested physical properties has rarely been investigated. Herein, highly crystalline gram-scale ic-2D Ta1.33S2 crystals were successfully grown by the high-pressure high-temperature method. Employing combined atomic-resolution scanning transmission electron microscopy annular dark field imaging and density functional theory calculations, we systematically unveiled the atomic structures of an atlas of stacking registries in a well-defined √3(a) × √3(a) Ta1.33S2 superlattice. Ferromagnetic order was observed in the AC' stacking registry, and it evolves into an antiferromagnetic state in AA/AB/AB' stacking registries; the AA' stacking registry shows ferrimagnetic ordering. Therefore, we present a novel approach for fabricating large-scale highly crystalline ic-2D crystals and shed light on a powerful means of modulating the magnetic order of ic-2D systems via stacking engineering, i.e., stackingtronics.

Selective Control of Phases and Electronic Structures of Monolayer TaTe2

Transition metal dichalcogenide (TMDC) films exhibit rich phases and superstructures, which can be controlled by the growth conditions as well as post-growth annealing treatment. Here, the selective growth of monolayer TaTe2 films with different phases as well as superstructures using molecular beam epitaxy (MBE) is reported. Monolayer 1H-TaTe2 and 1T-TaTe2 films can be selectively controlled by varying the growth temperature, and their different electronic structures are revealed through the combination of angle-resolved photoemission spectroscopy measurements (ARPES) and first-principles calculations. Moreover, post-growth annealing of the 1H-TaTe2 film further leads to a transition from a19 × 19 $\sqrt {19}{\times }\sqrt {19}$ superstructure to a new 2 × 2 superstructure, where two gaps are observed in the electronic structure and persist up to room temperature. First-principles calculations reveal the role of the phonon instability in the formation of superstructures and the effect of local atomic distortions on the modified electronic structures. This work demonstrates the manipulation of the rich phases and superstructures of monolayer TaTe2 films by controlling the growth kinetics and post-growth annealing.

Surface properties of 1T-TaS2 and contrasting its electron-phonon coupling with TlBiTe2 from helium atom scattering

We present a detailed helium atom scattering study of the charge-density wave (CDW) system and transition metal dichalcogenide 1T-TaS2. In terms of energy dissipation, we determine the electron-phonon (e-ph) coupling, a quantity that is at the heart of conventional superconductivity and may even "drive" phase transitions such as CDWs. The e-ph coupling of TaS2 in the commensurate CDW phase (λ = 0.59 ± 0.12) is compared with measurements of the topo-logical insulator TlBiTe2 (λ = 0.09 ± 0.01). Furthermore, by means of elastic He diffraction and resonance/interference effects in He scattering, the thermal expansion of the surface lattice, the surface step height, and the three-dimensional atom-surface interaction potential are determined including the electronic corrugation of 1T-TaS2. The linear thermal expansion coefficient is similar to that of other transition-metal dichalcogenides. The He-TaS2 interaction is best described by a corrugated Morse potential with a relatively large well depth and supports a large number of bound states, comparable to the surface of Bi2Se3, and the surface electronic corrugation of 1T-TaS2 is similar to the ones found for semimetal surfaces.

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.

A platform for far-infrared spectroscopy of quantum materials at millikelvin temperatures

Optical spectroscopy of quantum materials at ultralow temperatures is rarely explored, yet it may provide critical characterizations of quantum phases not possible using other approaches. We describe the development of a novel experimental platform that enables optical spectroscopic studies, together with standard electronic transport, of materials at millikelvin temperatures inside a dilution refrigerator. The instrument is capable of measuring both bulk crystals and micrometer-sized two-dimensional van der Waals materials and devices. We demonstrate its performance by implementing photocurrent-based Fourier transform infrared spectroscopy on a monolayer WTe2 device and a multilayer 1T-TaS2 crystal, with a spectral range available from the near-infrared to the terahertz regime and in magnetic fields up to 5 T. In the far-infrared regime, we achieve spectroscopic measurements at a base temperature as low as ∼43 mK and a sample electron temperature of ∼450 mK. Possible experiments and potential future upgrades of this versatile instrumental platform are envisioned.

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.

Alternative Structure Model of Correlated Charge Density Wave in Monolayer 1T-Nb(Ta)Se2

The putative Mott charge density wave (CDW) phases of monolayer 1T-NbSe2 and 1T-TaSe2 have attracted a lot of recent interest due to the unexpected orbital texture of their Mott-Hubbard states and the superstructure related to an exotic possibility of a quantum spin liquid with a spinon Fermi surface. The origins of the orbital texture and the superstructure have been, however, elusive. We find by using density functional theory calculations that these CDW phases can have an alternative metastable structure, an anion (Se) centered cluster, in contrast to the prevailing model of a cation (Nb or Ta) centered David star cluster. This structure can be stabilized by the charge transfer from the bilayer graphene/SiC substrate used commonly in the experiments. The anion-centered structure has a similar electronic band structure of a charge transfer insulator to that of DS clusters but naturally explains the orbital texture of the upper Hubbard band from simply its atomic structure. Moreover, this band structure exhibits a Fermi surface nesting to possibly break the symmetry spontaneously into a 3 × 3 -R30° superstructure observed experimentally. The resulting ground state of the superstructure is shown to be a trivial band insulator, in contrast to exotic proposals. This result emphasizes the huge structural flexibility of these heteroexpitaxial monolayers, for which careful studies on atomic structures and interactions with substrates are highly requested.

Observation of Electronic Strong Correlation in VTe_{2}-2sqrt[3]×2sqrt[3] Monolayer

Strong electron correlation under two-dimensional limit is intensely studied in the transition metal dichalcogenides monolayers, mostly within their charge density wave (CDW) states that host a star of David period. Here, by using scanning tunneling microscopy and spectroscopy and density functional theory calculations with on-site Hubbard corrections, we study the VTe_{2} monolayer with a different 2sqrt[3]×2sqrt[3] CDW period. We find that the dimerization of neighboring Te-Te and V-V atoms occurs during the CDW transition, and that the strong correlation effect opens a Mott-like full gap at Fermi energy (E_{F}). We further demonstrate that such a Mott phenomenon is ascribed to the combination of the CDW transition and on-site Coulomb interactions. Our work provides a new platform for exploring Mott physics in 2D materials.

Quantum simulator to emulate lower-dimensional molecular structure

Bottom-up quantum simulators have been developed to quantify the role of various interactions, dimensionality, and structure in creating electronic states of matter. Here, we demonstrated a solid-state quantum simulator emulating molecular orbitals, based solely on positioning individual cesium atoms on an indium antimonide surface. Using scanning tunneling microscopy and spectroscopy, combined with ab initio calculations, we showed that artificial atoms could be made from localized states created from patterned cesium rings. These artificial atoms served as building blocks to realize artificial molecular structures with different orbital symmetries. These corresponding molecular orbitals allowed us to simulate two-dimensional structures reminiscent of well-known organic molecules. This platform could further be used to monitor the interplay between atomic structures and the resulting molecular orbital landscape with submolecular precision.

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.

Multiple Electronic Phases Coexisting under Inhomogeneous Strains in the Correlated Insulator

Monolayer transition metal dichalcogenides (TMDs) can host exotic phenomena such as correlated insulating and charge-density-wave (CDW) phases. Such properties are strongly dependent on the precise atomic arrangements. Strain, as an effective tuning parameter in atomic arrangements, has been widely used for tailoring material's structures and related properties, yet to date, a convincing demonstration of strain-induced dedicate phase transition at nanometer scale in monolayer TMDs has been lacking. Here, a strain engineering technique is developed to controllably introduce out-of-plane atomic deformations in monolayer CDW material 1T-NbSe₂ . The scanning tunneling microscopy and spectroscopy (STM and STS) measurements, accompanied by first-principles calculations, demonstrate that the CDW phase of 1T-NbSe₂ can survive under both tensile and compressive strains even up to 5%. Moreover, significant strain-induced phase transitions are observed, i.e., tensile (compressive) strains can drive 1T-NbSe₂ from an intrinsic-correlated insulator into a band insulator (metal). Furthermore, experimental evidence of the multiple electronic phase coexistence at the nanoscale is provided. The results shed new lights on the strain engineering of correlated insulator and useful for design and development of strain-related nanodevices.

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.

Spin-Liquid Insulators Can Be Landau's Fermi Liquids

The long search for insulating materials that possess low-energy quasiparticles carrying electron's quantum numbers except charge-inspired by the neutral spin-1/2 excitations, the so-called spinons, exhibited by Anderson's resonating-valence-bond state-seems to have reached a turning point after the discovery of several Mott insulators displaying the same thermal and magnetic properties as metals, including quantum oscillations in a magnetic field. Here, we show that such anomalous behavior is not inconsistent with Landau's Fermi liquid theory of quasiparticles at a Luttinger surface. That is the manifold of zeros within the Brillouin zone of the single-particle Green's function at zero frequency, and which thus defines the spinon Fermi surface conjectured by Anderson.

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.

Simulating Chiral Spin Liquids with Projected Entangled-Pair States

Doubts have been raised on the representation of chiral spin liquids exhibiting topological order in terms of projected entangled pair states (PEPSs). Here, starting from a simple spin-1/2 chiral frustrated Heisenberg model, we show that a faithful representation of the chiral spin liquid phase is in fact possible in terms of a generic PEPS upon variational optimization. We find a perfectly chiral gapless edge mode and a rapid decay of correlation functions at short distances consistent with a bulk gap, concomitant with a gossamer long-range tail originating from a PEPS bulk-edge correspondence. For increasing bond dimension, (i) the rapid decrease of spurious features-SU(2) symmetry breaking and long-range tails in correlations-together with (ii) a faster convergence of the ground state energy as compared to state-of-the-art cylinder matrix-product state simulations involving far more variational parameters, prove the fundamental relevance of the PEPS ansatz for simulating systems with chiral topological order.

Controlling magnetic frustration in 1T-TaS2via Coulomb engineered long-range interactions

Magnetic frustrations in two-dimensional materials provide a rich playground to engineer unconventional phenomena. However, despite intense efforts, a realization of tunable frustrated magnetic order in two-dimensional materials remains an open challenge. Here we propose Coulomb engineering as a versatile strategy to tailor magnetic ground states in layered materials. Using the frustrated van der Waals monolayer 1T-TaS₂as an example, we show how long-range Coulomb interactions renormalize the low energy nearly flat band structure, leading to a Heisenberg model which depends on the Coulomb interactions. Based on this, we show that superexchange couplings in the material can be precisely tailored by means of environmental dielectric screening, ultimately allowing to externally drive the material towards a tunable frustrated regime. Our results put forward Coulomb engineering as a powerful tool to manipulate magnetic properties of van der Waals materials.

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.

Visualization of Chiral Electronic Structure and Anomalous Optical Response in a Material with Chiral Charge Density Waves

Chiral materials have attracted significant research interests as they exhibit intriguing physical properties, such as chiral optical response, spin-momentum locking, and chiral induced spin selectivity. Recently, layered transition metal dichalcogenide 1T-TaS_{2} has been found to host a chiral charge density wave (CDW) order. Nevertheless, the physical consequences of the chiral order, for example, in electronic structures and the optical properties, are yet to be explored. Here, we report the spectroscopic visualization of an emergent chiral electronic band structure in the CDW phase, characterized by windmill-shaped Fermi surfaces. We uncover a remarkable chirality-dependent circularly polarized Raman response due to the salient in-plane chiral symmetry of CDW, although the ordinary circular dichroism vanishes. Chiral Fermi surfaces and anomalous Raman responses coincide with the CDW transition, proving their lattice origin. Our Letter paves a path to manipulate the chiral electronic and optical properties in two-dimensional materials and explore applications in polarization optics and spintronics.

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.

Magnetic memory and spontaneous vortices in a van der Waals superconductor

Doped Mott insulators exhibit some of the most intriguing quantum phases of matter, including quantum spin liquids, unconventional superconductors and non-Fermi liquid metals^1-3. Such phases often arise when itinerant electrons are close to a Mott insulating state, and thus experience strong spatial correlations. Proximity between different layers of van der Waals heterostructures naturally realizes a platform for experimentally studying the relationship between localized, correlated electrons and itinerant electrons. Here we explore this relationship by studying the magnetic landscape of tantalum disulfide 4Hb-TaS₂, which realizes an alternating stacking of a candidate spin liquid and a superconductor⁴. We report on a spontaneous vortex phase whose vortex density can be trained in the normal state. We show that time-reversal symmetry is broken in the normal state, indicating the presence of a magnetic phase independent of the superconductor. Notably, this phase does not generate ferromagnetic signals that are detectable using conventional techniques. We use scanning superconducting quantum interference device microscopy to show that it is incompatible with ferromagnetic ordering. The discovery of this unusual magnetic phase illustrates how combining superconductivity with a strongly correlated system can lead to unexpected physics.

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.

Long-lifetime spin excitations near domain walls in 1T-TaS2

SignificanceThere is an intense ongoing search for two-level quantum systems with long lifetimes for applications in quantum communication and computation. Much research has been focused on studying isolated spins in semiconductors or band insulators. Mott insulators provide an interesting alternative platform but have been far less explored. In this work we use a technique capable of resolving individual spins at atomic length scales, to measure the two-level switching of spin states in 1T-TaS₂. We find quasi-1D chains of spin-1/2 electrons embedded in 1T-TaS₂ which have exceptionally long lifetimes. The discovery of long-lived spin states in a tractable van der Waal material opens doors to using Mott systems in future quantum information applications.

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.

Two-dimensional charge order stabilized in clean polytype heterostructures

Compelling evidence suggests distinct correlated electron behavior may exist only in clean 2D materials such as 1T-TaS2. Unfortunately, experiment and theory suggest that extrinsic disorder in free standing 2D layers disrupts correlation-driven quantum behavior. Here we demonstrate a route to realizing fragile 2D quantum states through endotaxial polytype engineering of van der Waals materials. The true isolation of 2D charge density waves (CDWs) between metallic layers stabilizes commensurate long-range order and lifts the coupling between neighboring CDW layers to restore mirror symmetries via interlayer CDW twinning. The twinned-commensurate charge density wave (tC-CDW) reported herein has a single metal-insulator phase transition at ~350 K as measured structurally and electronically. Fast in-situ transmission electron microscopy and scanned nanobeam diffraction map the formation of tC-CDWs. This work introduces endotaxial polytype engineering of van der Waals materials to access latent 2D ground states distinct from conventional 2D fabrication.

Between Harmonic Crystal and Glass: Solids with Dimpled Potential-Energy Surfaces Having Multiple Local Energy Minima

Solids with dimpled potential-energy surfaces are ubiquitous in nature and, typically, exhibit structural (elastic or phonon) instabilities. Dimpled potentials are not harmonic; thus, the conventional quasiharmonic approximation at finite temperatures fails to describe anharmonic vibrations in such solids. At sufficiently high temperatures, their crystal structure is stabilized by entropy; in this phase, a diffraction pattern of a periodic crystal is combined with vibrational properties of a phonon glass. As temperature is lowered, the solid undergoes a symmetry-breaking transition and transforms into a lower-symmetry phase with lower lattice entropy. Here, we identify specific features in the potential-energy surface that lead to such polymorphic behavior; we establish reliable estimates for the relative energies and temperatures associated with the anharmonic vibrations and the solid–solid symmetry-breaking phase transitions. We show that computational phonon methods can be applied to address anharmonic vibrations in a polymorphic solid at fixed temperature. To illustrate the ubiquity of this class of materials, we present a range of examples (elemental metals, a shape-memory alloy, and a layered charge-density-wave system); we show that our theoretical predictions compare well with known experimental data.

Reversible structural transition of two-dimensional copper selenide on Cu(111)

Structural engineering opens a door to manipulating the structures and thus tuning the properties of two-dimensional materials. Here, we report a reversible structural transition in honeycomb CuSe monolayer on Cu(111) through scanning tunneling microscopy and Auger electron spectroscopy (AES). Direct selenization of Cu(111) gives rise to the formation of honeycomb CuSe monolayers with one-dimensional moiré structures (stripe-CuSe), due to the asymmetric lattice distortions in CuSe induced by the lattice mismatch. Additional deposition of Se combined with post annealing results in the formation of honeycomb CuSe with quasi-ordered arrays of triangular holes (hole-CuSe), namely, the structural transition from stripe-CuSe to hole-CuSe. Further, annealing the hole-CuSe at higher temperature leads to the reverse structural transition, namely from hole-CuSe to stripe-CuSe. AES measurement unravels the Se content change in the reversible structural transition. Therefore, both the Se coverage and annealing temperature play significant roles in the reversible structural transition in CuSe on Cu(111). Our work provides insights in understanding of the structural transitions in two-dimensional materials.

Monolayer 1T-NbSe2 as a 2D-correlated magnetic insulator

Monolayer group V transition metal dichalcogenides in their 1T phase have recently emerged as a platform to investigate rich phases of matter, such as spin liquid and ferromagnetism, resulting from strong electron correlations. Newly emerging 1T-NbSe₂ has inspired theoretical investigations predicting collective phenomena such as charge transfer gap and ferromagnetism in two dimensions; however, the experimental evidence is still lacking. Here, by controlling the molecular beam epitaxy growth parameters, we demonstrate the successful growth of high-quality single-phase 1T-NbSe₂. By combining scanning tunneling microscopy/spectroscopy and ab initio calculations, we show that this system is a charge transfer insulator with the upper Hubbard band located above the valence band maximum. To demonstrate the electron correlation resulted magnetic property, we create a vertical 1T/2H NbSe₂ heterostructure, and we find unambiguous evidence of exchange interactions between the localized magnetic moments in 1T phase and the metallic/superconducting phase exemplified by Kondo resonances and Yu-Shiba-Rusinov–like bound states.

Artificial heavy fermions in a van der Waals heterostructure

Heavy-fermion systems represent one of the paradigmatic strongly correlated states of matter^1-5. They have been used as a platform for investigating exotic behaviour ranging from quantum criticality and non-Fermi liquid behaviour to unconventional topological superconductivity^4-12. The heavy-fermion phenomenon arises from the exchange interaction between localized magnetic moments and conduction electrons leading to Kondo lattice physics, and represents one of the long-standing open problems in quantum materials³. In a Kondo lattice, the exchange interaction gives rise to a band with heavy effective mass. This intriguing phenomenology has so far been realized only in compounds containing rare-earth elements with 4f or 5f electrons^1,4,13,14. Here we realize a designer van der Waals heterostructure where artificial heavy fermions emerge from the Kondo coupling between a lattice of localized magnetic moments and itinerant electrons in a 1T/1H-TaS₂ heterostructure. We study the heterostructure using scanning tunnelling microscopy and spectroscopy and show that depending on the stacking order of the monolayers, we can reveal either the localized magnetic moments and the associated Kondo effect, or the conduction electrons with a heavy-fermion hybridization gap. Our experiments realize an ultimately tunable platform for future experiments probing enhanced many-body correlations, dimensional tuning of quantum criticality and unconventional superconductivity in two-dimensional artificial heavy-fermion systems^15-17.

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.

Unconventional van der Waals heterostructures beyond stacking

Two-dimensional crystals provide exceptional opportunities for integrating dissimilar materials and forming interfaces where distinct properties and phenomena emerge. To date, research has focused on two basic heterostructure types: vertical van der Waals stacks and laterally joined monolayer crystals with in-plane line interfaces. Much more diverse architectures and interface configurations can be realized in the few-layer and multilayer regime, and if mechanical stacking and single-layer growth are replaced by processes taking advantage of self-organization, conversions between polymorphs, phase separation, strain effects, and shaping into the third dimension. Here, we highlight such opportunities for engineering heterostructures, focusing on group IV chalcogenides, a class of layered semiconductors that lend themselves exceptionally well for exploring novel van der Waals architectures, as well as advanced methods including in situ microscopy during growth and nanometer-scale probes of light-matter interactions. The chosen examples point to fruitful future directions and inspire innovative developments to create unconventional van der Waals heterostructures beyond stacking.

Emergent Moments and Random Singlet Physics in a Majorana Spin Liquid

We exhibit an exactly solvable example of a SU(2) symmetric Majorana spin liquid phase, in which quenched disorder leads to random-singlet phenomenology of emergent magnetic moments. More precisely, we argue that a strong-disorder fixed point controls the low temperature susceptibility χ(T) of an exactly solvable S=1/2 model on the decorated honeycomb lattice with vacancy and/or bond disorder, leading to χ(T)=C/T+DT^{α(T)-1}, where α(T)→0 slowly as the temperature T→0. The first term is a Curie tail that represents the emergent response of vacancy-induced spin textures spread over many unit cells: it is an intrinsic feature of the site-diluted system, rather than an extraneous effect arising from isolated free spins. The second term, common to both vacancy and bond disorder [with different α(T) in the two cases] is the response of a random singlet phase, familiar from random antiferromagnetic spin chains and the analogous regime in phosphorus-doped silicon (Si:P).