Emergence of coherence in the charge-density wave state of 2H-NbSe2

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.

Direct visualization of stacking-selective self-intercalation in epitaxial Nb1+xSe2 films

Two-dimensional (2D) van der Waals (vdW) materials offer rich tuning opportunities generated by different stacking configurations or by introducing intercalants into the vdW gaps. Current knowledge of the interplay between stacking polytypes and intercalation often relies on macroscopically averaged probes, which fail to pinpoint the exact atomic position and chemical state of the intercalants in real space. Here, by using atomic-resolution electron energy-loss spectroscopy in a scanning transmission electron microscope, we visualize a stacking-selective self-intercalation phenomenon in thin films of the transition-metal dichalcogenide (TMDC) Nb1+xSe2. We observe robust contrasts between 180°-stacked layers with large amounts of Nb intercalants inside their vdW gaps and 0°-stacked layers with little detectable intercalants inside their vdW gaps, coexisting on the atomic scale. First-principles calculations suggest that the films lie at the boundary of a phase transition from 0° to 180° stacking when the intercalant concentration x exceeds ~0.25, which we could attain in our films due to specific kinetic pathways. Our results offer not only renewed mechanistic insights into stacking and intercalation, but also open up prospects for engineering the functionality of TMDCs via stacking-selective self-intercalation.

Visualization of Alternating Triangular Domains of Charge Density Waves in 2H-NbSe_{2} by Scanning Tunneling Microscopy

The charge density wave (CDW) state of 2H-NbSe_{2} features commensurate domains separated by domain boundaries accompanied by phase slips known as discommensurations. We have unambiguously visualized the structure of CDW domains using a displacement-field measurement algorithm on a scanning tunneling microscopy image. Each CDW domain is delimited by three vertices and three edges of discommensurations and is designated by a triplet of integers whose sum identifies the types of commensurate structure. The observed structure is consistent with the alternating triangular tiling pattern predicted by a phenomenological Landau theory. The domain shape is affected by crystal defects and also by topological defects in the CDW phase factor. Our results provide a foundation for a complete understanding of the CDW state and its relation to the superconducting state.

Enhanced Superconductivity and Critical Current Density Due to the Interaction of InSe2 Bonded Layer in (InSe2)0.12NbSe2

Superconductivity was discovered in (InSe2)xNbSe2. The materials are crystallized in a unique layered structure where bonded InSe2 layers are intercalated into the van der Waals gaps of 2H-phase NbSe2. The (InSe2)0.12NbSe2 superconductor exhibits a superconducting transition at 11.6 K and critical current density of 8.2 × 105 A/cm2. Both values are the highest among all transition metal dichalcogenide superconductors at ambient pressure. The present finding provides an ideal material platform for further investigation of superconducting-related phenomena in transition metal dichalcogenides.

Precursor region with full phonon softening above the charge-density-wave phase transition in 2H-TaSe2

Research on charge-density-wave (CDW) ordered transition-metal dichalcogenides continues to unravel new states of quantum matter correlated to the intertwined lattice and electronic degrees of freedom. Here, we report an inelastic x-ray scattering investigation of the lattice dynamics of the canonical CDW compound 2H-TaSe2 complemented by angle-resolved photoemission spectroscopy and density functional perturbation theory. Our results rule out the formation of a central-peak without full phonon softening for the CDW transition in 2H-TaSe2 and provide evidence for a novel precursor region above the CDW transition temperature TCDW, which is characterized by an overdamped phonon mode and not detectable in our photoemission experiments. Thus, 2H-TaSe2 exhibits structural before electronic static order and emphasizes the important lattice contribution to CDW transitions. Our ab-initio calculations explain the interplay of electron-phonon coupling and Fermi surface topology triggering the CDW phase transition and predict that the CDW soft phonon mode promotes emergent superconductivity near the pressure-driven CDW quantum critical point.

Phase Engineering of 2D Materials

Polymorphic 2D materials allow structural and electronic phase engineering, which can be used to realize energy-efficient, cost-effective, and scalable device applications. The phase engineering covers not only conventional structural and metal-insulator transitions but also magnetic states, strongly correlated band structures, and topological phases in rich 2D materials. The methods used for the local phase engineering of 2D materials include various optical, geometrical, and chemical processes as well as traditional thermodynamic approaches. In this Review, we survey the precise manipulation of local phases and phase patterning of 2D materials, particularly with ideal and versatile phase interfaces for electronic and energy device applications. Polymorphic 2D materials and diverse quantum materials with their layered, vertical, and lateral geometries are discussed with an emphasis on the role and use of their phase interfaces. Various phase interfaces have demonstrated superior and unique performance in electronic and energy devices. The phase patterning leads to novel homo- and heterojunction structures of 2D materials with low-dimensional phase boundaries, which highlights their potential for technological breakthroughs in future electronic, quantum, and energy devices. Accordingly, we encourage researchers to investigate and exploit phase patterning in emerging 2D materials.

Observations of Charge-Density-Wave States in W6Te6 Wires

Determining the electronic ground state of a one-dimensional system is crucial to understanding the underlying physics of electronic behavior. Here, we demonstrate the discovery of charge-density wave states in few-wire W6Te6 arrays using scanning tunneling microscopy/spectroscopy. We directly visualize incommensurate charge orders, energy gaps with prominent coherence peaks, and the picometer-scale lattice distortion in nearly disorder-free double-wire systems, thereby demonstrating the existence of Peierls-type charge density waves. In the presence of disorder-induced charge order fluctuations, the coherence peaks resulting from phase correlation disappear and gradually transform the system into the pseudogap states. The power-law zero-bias anomaly and quasi-particle interference analysis further suggest the Tomonaga-Luttinger liquid behavior in such pseudogap region. In addition, we explicitly determined the evolution of the CDW energy gap as a function of stacking-wire numbers. The present study demonstrates the existence of electron-phonon interactions in few-wire W6Te6 that can be tuned by disorders and van der Waals stacking.

Signatures of the exciton gas phase and its condensation in monolayer 1T-ZrTe2

The excitonic insulator (EI) is a Bose-Einstein condensation (BEC) of excitons bound by electron-hole interaction in a solid, which could support high-temperature BEC transition. The material realization of EI has been challenged by the difficulty of distinguishing it from a conventional charge density wave (CDW) state. In the BEC limit, the preformed exciton gas phase is a hallmark to distinguish EI from conventional CDW, yet direct experimental evidence has been lacking. Here we report a distinct correlated phase beyond the 2×2 CDW ground state emerging in monolayer 1T-ZrTe₂ and its investigation by angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy (STM). The results show novel band- and energy-dependent folding behavior in a two-step process, which is the signatures of an exciton gas phase prior to its condensation into the final CDW state. Our findings provide a versatile two-dimensional platform that allows tuning of the excitonic effect.

Tunable Photoresponse in a Two-Dimensional Superconducting Heterostructure

The photo-induced superconducting phase transition is widely used in probing the physical properties of correlated electronic systems and to realize broadband photodetection with extremely high responsivity. However, such photoresponse is usually insensitive to electrostatic doping due to the high carrier density of the superconductor, restricting its applications in tunable optoelectronic devices. In this work, we demonstrate the gate voltage modulation to the photoresponsivity in a two-dimensional NbSe₂-graphene heterojunction. The superconducting critical current of the NbSe₂ relies on the gate-dependent hot carrier generation in graphene via the Joule heating effect, leading to the observed shift of both the magnitude and peak position of the photoresponsivity spectra as the gate voltage changes. This heating effect is further confirmed by the temperature and laser-power-dependent characterization of the photoresponse. In addition, we investigate the spatially-resolved photocurrent, finding that the superconductivity is inhomogeneous across the junction area. Our results provide a new platform for designing tunable superconducting photodetector and indicate that the photoresponse could be a powerful tool in studying the local electronic properties and phase transitions in low-dimensional superconducting systems.

Observation of a Yu-Shiba-Rusinov state originating from the magnetic moment in a curved monolayer island of 1T-phase NbSe2

We report the finding of a 1T phase island of NbSe₂ on a cleaved surface and its magnetic properties. Tunneling spectroscopy at 400 mK shows robust peaks in the superconducting gap, which we assign to the Yu-Shiba-Rusinov (YSR) state originating from the magnetic moment placed in the superconducting state. The YSR peak appears on a specific position of an island of the 1T phase, not on the surrounding 2H phase area, and shows an anisotropic decay behavior. In addition, we found a close relationship between the enhancement of the YSR peak and the local curvature of the film. We assign the origin of the magnetic moment to the curvature of the 1T phase island, which can form a magnetic moment through a rotation of the wave function by a robust spin-orbit coupling, as indicated by a recent theoretical study.

Charge density wave in a SnSe2 layer on and the effect of surface hydrogenation

We have carried out an investigation using density functional theory (DFT) of the atomic and electronic structures of SnSe₂ layers on the surface and hydrogenation of this surface. We have considered a (2 × 2) SnSe₂ superstructure oriented along the diagonal direction of the surface periodicity, for which scanning tunneling microscopy (STM) measurements have recently been reported. In the band structure calculations, while the s-p character surface state originating from each SnSe₂ layer is determined, there is an additional half-filled surface state in the fundamental band gap region due to the Sn adatom. At the M̄ point in the Brillouin zone, a charge density wave (CDW) partial gap opening of ∼0.1 eV occurs between these surface states close to the Fermi level. Here, the CDW gap is caused by two reasons; (i) Fermi surface nesting, due to the inequivalent electron pockets at the M̄ point, and (ii) the out of plane weak electron-phonon coupling regime due to the mean-field (MF) theory (2Δ/k_BT^MF = 3.52). Upon hydrogen adsorption on the surface, we have obtained a β-phase SnSe layer and SeH₂ molecule with a bond angle of ∼90°. The hydrogenated surface pushes the surface state associated with the SnSe₂ layer into the Si projected bulk band continuum. After SeH₂ desorption, the work function drops from 5.20 eV to 4.39 eV.

Order-Disorder Transitions in (Ca_{x}Sr_{1-x})_{3}Rh_{4}Sn_{13}

The classification of structural phase transitions as displacive or order-disorder in character is usually based on spectroscopic data above the transition. We use single crystal x-ray diffraction to investigate structural correlations in the quasiskutterudites, (Ca_{x}Sr_{1-x})_{3}Rh_{4}Sn_{13}, which have a quantum phase transition at x∼0.9. Three-dimensional pair distribution functions show that the amplitudes of local atomic displacements are temperature independent below the transition and persist to well above the transition, a signature of order-disorder behavior. The implications for the associated electronic transitions are discussed.

Size Dependence of Charge-Density-Wave Orders in Single-Layer NbSe2 Hetero/Homophase Junctions

Controlling charge-density-wave (CDW) orders in two-dimensional (2D) crystals has attracted a great deal of interest because of their fundamental physics and their demand inse in miniaturized devices. In this work, we systematically studied the size-dependent CDW orders in single-layer hetero/homo-NbSe₂ stacking junctions. We found that the CDW orders in the top 1T-NbSe₂ layer of the junctions are highly dependent on its lateral size. For the 1T/2H-NbSe₂ heterojunction, the critical lateral size of 1T-NbSe₂ islands for the formation of well-defined CDW orders is ∼26 nm, whereas below 15 nm, the CDW orders melt. However, for the 1T/1T-NbSe₂ homojunction, the CDW orders in the islands can persist even with a lateral size of <11 nm. Our findings illuminate the fresh phenomenon of size-dependent CDW orders existing in 2D van der Waals hetero/homojunctions and provide useful information for the control of CDW orders.

Coexisting Charge-Ordered States with Distinct Driving Mechanisms in Monolayer VSe2

Thinning crystalline materials to two dimensions (2D) creates a rich playground for electronic phases, including charge, spin, superconducting, and topological order. Bulk materials hosting charge density waves (CDWs), when reduced to ultrathin films, have shown CDW enhancement and tunability. However, charge order confined to only 2D remains elusive. Here we report a distinct charge ordered state emerging in the monolayer limit of 1T-VSe₂. Systematic scanning tunneling microscopy experiments reveal that bilayer VSe₂ largely retains the bulk electronic structure, hosting a tridirectional CDW. However, monolayer VSe₂ ─consistently across distinct substrates─exhibits a dimensional crossover, hosting two CDWs with distinct wavelengths and transition temperatures. Electronic structure calculations reveal that while one CDW is bulk-like and arises from the well-known Peierls mechanism, the other is decidedly unconventional. The observed CDW-lattice decoupling and the emergence of a flat band suggest that the second CDW could arise from enhanced electron-electron interactions in the 2D limit. These findings establish monolayer-VSe₂ as a host of coexisting charge orders with distinct origins, and enable the tailoring of electronic phenomena via emergent interactions in 2D materials.

Role of Equilibrium Fluctuations in Light-Induced Order

Engineering novel states of matter with light is at the forefront of materials research. An intensely studied direction is to realize broken-symmetry phases that are "hidden" under equilibrium conditions but can be unleashed by an ultrashort laser pulse. Despite a plethora of experimental discoveries, the nature of these orders and how they transiently appear remain unclear. To this end, we investigate a nonequilibrium charge density wave (CDW) in rare-earth tritellurides, which is suppressed in equilibrium but emerges after photoexcitation. Using a pump-pump-probe protocol implemented in ultrafast electron diffraction, we demonstrate that the light-induced CDW consists solely of order parameter fluctuations, which bear striking similarities to critical fluctuations in equilibrium despite differences in the length scale. By calculating the dynamics of CDW fluctuations in a nonperturbative model, we further show that the strength of the light-induced order is governed by the amplitude of equilibrium fluctuations. These findings highlight photoinduced fluctuations as an important ingredient for the emergence of transient orders out of equilibrium. Our results further suggest that materials with strong fluctuations in equilibrium are promising platforms to host hidden orders after laser excitation.

Experimental and Theoretical Study of Possible Collective Electronic States in Exfoliable Re-Doped NbS2

Metallic transition-metal dichalcogenides (TMDs) are rich material systems in which the interplay between strong electron-electron and electron-phonon interactions often results in a variety of collective electronic states, such as charge density waves (CDWs) and superconductivity. While most metallic group V TMDs exhibit coexisting superconducting and CDW phases, 2H-NbS₂ stands out with no charge ordering. Further, due to strong interlayer interaction, the preparation of ultrathin samples of 2H-NbS₂ has been challenging, limiting the exploration of presumably rich quantum phenomena in reduced dimensionality. Here, we demonstrate experimentally and theoretically that light substitutional doping of NbS₂ with heavy atoms is an effective approach to modify both interlayer interaction and collective electronic states in NbS₂. Very low concentrations of Re dopants (<1%) make NbS₂ exfoliable (down to monolayer) while maintaining its 2H crystal structure and superconducting behavior. In addition, first-principles calculations suggest that Re dopants can stabilize some native CDW patterns that are not stable in pristine NbS₂.

Superconducting 2D NbS2 Grown Epitaxially by Chemical Vapor Deposition

Metallic two-dimensional (2D) transition metal dichalcogenides (TMDCs) are attracting great attention because of their interesting low-temperature properties such as superconductivity, magnetism, and charge density waves (CDW). However, further studies and practical applications are being slowed down by difficulties in synthesizing high-quality materials with a large grain size and well-determined thickness. In this work, we demonstrate epitaxial chemical vapor deposition (CVD) growth of 2D NbS₂ crystals on a sapphire substrate, with a thickness-dependent structural phase transition. NbS₂ crystals are epitaxially aligned by the underlying c-plane sapphire resulting in high-quality growth. The thickness of NbS₂ is well controlled by growth parameters to be between 1.5 and 10 nm with a large grain size of up to 500 μm. As the thickness increases, we observe in our NbS₂ a transition from a metallic 3R-polytype to a superconducting 2H-polytype, confirmed by Raman spectroscopy, aberration-corrected scanning transmission electron microscopy (STEM) and electrical transport measurements. A Berezinskii-Kosterlitz-Thouless (BKT) superconducting transition occurs in the CVD-grown 2H-phase NbS₂ below the transition temperature (T_c) of 3 K. Our work demonstrates thickness and phase-controllable synthesis of high-quality superconducting 2D NbS₂, which is imperative for its practical applications in next-generation TMDC-based electrical devices.

Visualizing Spatial Evolution of Electron-Correlated Interface in Two-Dimensional Heterostructures

Microscopically visualizing the evolution of electronic structures at the interface between two electron-correlated domains shows fundamental importance in both material science and physics. Here, we report scanning tunneling microscopy and spectroscopy studies of the interfacial electronic structures evolution in a phase-engineered monolayer NbSe₂ heterostructure. The H-NbSe₂ metallic state penetrates the Mott insulating T-NbSe₂ at the H/T phase interface, with a prominent 2D charge density wave (CDW) proximity effect. Moreover, an insulating Mott gap collapse with the disappearance of the upper Hubbard band is detected at the electronic phase transition region. Theoretical calculations reveal that such insulating Mott gap collapse can be attributed to the electron doping effect induced by the interface. Our findings promote a microscopical understanding of the interactions between different electron-correlated systems and provide an effective method for controlling the Mott insulating states with phase engineering.

Visualizing the Anomalous Charge Density Wave States in Graphene/NbSe2 Heterostructures

Metallic layered transition metal dichalcogenides (TMDs) host collective many-body interactions, including the competing superconducting and charge density wave (CDW) states. Graphene is widely employed as a heteroepitaxial substrate for the growth of TMD layers and as an ohmic contact, where the graphene/TMD heterostructure is naturally formed. The presence of graphene can unpredictably influence the CDW order in 2D CDW conductors. This work reports the CDW transitions of 2H-NbSe₂ layers in graphene/NbSe₂ heterostructures. The evolution of Raman spectra demonstrates that the CDW phase transition temperatures (T_CDW ) of NbSe₂ are dramatically decreased when capped by graphene. The induced anomalous short-range CDW state is confirmed by scanning tunneling microscopy measurements. The findings propose a new criterion to determine the T_CDW through monitoring the line shape of the A_1g mode. Meanwhile, the 2D band is also discovered as an indicator to observe the CDW transitions. First-principles calculations imply that interfacial electron doping suppresses the CDW states by impeding the lattice distortion of 2H-NbSe₂ . The extraordinary random CDW lattice suggests deep insight into the formation mechanism of many collective electronic states and possesses great potential in modulating multifunctional devices.

Defect-Selective Charge-Density-Wave Condensation in 2H-NbSe_{2}

Defects have been known to substantially affect quantum states of materials including charge density wave (CDW). However, the microscopic mechanism of the influence of defects is often elusive due partly to the lack of atomic scale characterization of defects themselves. We investigate native defects of a prototypical CDW material 2H-NbSe_{2} and their microscopic interaction with CDW. Three prevailing types of atomic scale defects are classified by scanning tunneling microscope, and their atomic structures are identified by density functional theory calculations as Se vacancies and Nb intercalants. Above the transition temperature, two distinct CDW structures are found to be induced selectively by different types of defects. This intriguing phenomenon is explained by competing CDW ground states and local lattice strain fields induced by defects, providing a clear microscopic mechanism of the defect-CDW interaction.

Inelastic Electron Tunneling in 2H-Ta_{x}Nb_{1-x}Se_{2} Evidenced by Scanning Tunneling Spectroscopy

We report a detailed study of tunneling spectra measured on 2H-Ta_{x}Nb_{1-x}Se_{2} (x=0∼0.1) single crystals using a low-temperature scanning tunneling microscope. The prominent gaplike feature, which has not been understood for a long time, was found to be accompanied by some "in-gap" fine structures. By investigating the second-derivative spectra and their temperature and magnetic field dependencies, we were able to prove that inelastic electron tunneling is the origin of these features and obtain the Eliashberg function of 2H-Ta_{x}Nb_{1-x}Se_{2} at an atomic scale, providing a potential way to study the local Eliashberg function and the phonon spectra of the related transition-metal dichalcogenides.

Distinction between pristine and disorder-perturbed charge density waves in ZrTe3

Charge density waves (CDWs) in the cuprate high-temperature superconductors have evoked much interest, yet their typical short-range nature has raised questions regarding the role of disorder. Here we report a resonant X-ray diffraction study of ZrTe[Formula: see text], a model CDW system, with focus on the influence of disorder. Near the CDW transition temperature, we observe two independent signals that arise concomitantly, only to become clearly separated in momentum while developing very different correlation lengths in the well-ordered state that is reached at a distinctly lower temperature. Anomalously slow dynamics of mesoscopic charge domains are further found near the transition temperature, in spite of the expected strong thermal fluctuations. Our observations signify the presence of distinct experimental fingerprints of pristine and disorder-perturbed CDWs. We discuss the latter also in the context of Friedel oscillations, which we argue might promote CDW formation via a self-amplifying process.

Dielectric Properties of NbxW1-xSe2 Alloys

The growth of transition metal dichalcogenide (TMDC) alloys provides an opportunity to experimentally access information elucidating how optical properties change with gradual substitutions in the lattice compared with their pure compositions. In this work, we performed growths of alloyed crystals with stoichiometric compositions between pure forms of NbSe₂ and WSe₂, followed by an optical analysis of those alloys by utilizing Raman spectroscopy and spectroscopic ellipsometry.

Disorder raises the critical temperature of a cuprate superconductor

With the discovery of charge-density waves (CDWs) in most members of the cuprate high-temperature superconductors, the interplay between superconductivity and CDWs has become a key point in the debate on the origin of high-temperature superconductivity. Some experiments in cuprates point toward a CDW state competing with superconductivity, but others raise the possibility of a CDW-superconductivity intertwined order or more elusive pair-density waves (PDWs). Here, we have used proton irradiation to induce disorder in crystals of [Formula: see text] and observed a striking 50% increase of [Formula: see text], accompanied by a suppression of the CDWs. This is in sharp contrast with the behavior expected of a d-wave superconductor, for which both magnetic and nonmagnetic defects should suppress [Formula: see text] Our results thus make an unambiguous case for the strong detrimental effect of the CDW on bulk superconductivity in [Formula: see text] Using tunnel diode oscillator (TDO) measurements, we find indications for potential dynamic layer decoupling in a PDW phase. Our results establish irradiation-induced disorder as a particularly relevant tuning parameter for the many families of superconductors with coexisting density waves, which we demonstrate on superconductors such as the dichalcogenides and [Formula: see text].

Enhancement of superconducting properties and flux pinning mechanism on Cr0.0005NbSe2 single crystal under Hydrostatic pressure

Superconducting properties of Cr_0.0005NbSe₂ (T_c~6.64 K) single crystals have been investigated through the temperature dependent resistivity (~8 GPa) and DC magnetization (~1 GPa) measurements. Further, the critical current density (J_c) as a function of applied magnetic field has been studied from magnetic isotherms. The vortex pinning mechanisms have also been systematically analyzed using weak collective pinning theory as a function of pressure. The J_c corresponds to the flux flow enhanced by the application of pressure due to increase of T_c and vortex changes. We found that the pressure is responsible for the spatial variations in the charge carrier mean free path (δl pinning). We find that core point pinning is more dominant than surface pinning which is caused by the application of pressure. In addition, J_c(H = 0) increases from 3.9 × 10⁵ (0 GPa) to 1.3 × 10⁶ (1.02 GPa) A/cm² at 2 K as the pressure is increased from normal pressure to 1.02 GPa. The pressure dependence of T_c (dT_c/dP) becomes 0.91 K/GPa and 0.75 K/GPa from magnetization and resistivity measurements respectively. We found that the pressure promotes the anisotropy nature, and decrease of coherence length and resulting in pathetic interface of the vortex core with pinning centers.

Surface-Limited Superconducting Phase Transition on 1 T-TaS2

Controlling superconducting phase transition on a two-dimensional (2D) material is of great fundamental and technological interest from the viewpoint of making 2D resistance-free electronic circuits. Here, we demonstrate that a 1 T-to-2 H phase transition can be induced on the topmost monolayer of bulk (<100 nm thick) 1 T-TaS₂ by thermal annealing. The monolayer 2 H-TaS₂ on bulk 1 T-TaS₂ exhibits a superconducting transition temperature ( T_c) of 2.1 K, which is significantly enhanced compared to that of bulk 2 H-TaS₂. Scanning tunneling microscopy measurements reveal a 3 × 3 charge density wave (CDW) in the phase-switched monolayer at 4.5 K. The enhanced T_c is explained by the suppressed 3 × 3 CDW and a charge-transfer doping from the 1 T substrate. We further show that the monolayer 2 H-TaS₂ could be switched back to 1 T phase by applying a voltage pulse. The observed surface-limited superconducting phase transition offers a convenient way to prepare robust 2D superconductivity on bulk 1 T-TaS₂ crystal, thereby bypassing the need to exfoliate monolayer samples.

Edge-Epitaxial Growth of 2D NbS2 -WS2 Lateral Metal-Semiconductor Heterostructures

2D metal-semiconductor heterostructures based on transition metal dichalcogenides (TMDs) are considered as intriguing building blocks for various fields, such as contact engineering and high-frequency devices. Although, a series of p-n junctions utilizing semiconducting TMDs have been constructed hitherto, the realization of such a scheme using 2D metallic analogs has not been reported. Here, the synthesis of uniform monolayer metallic NbS2 on sapphire substrate with domain size reaching to a millimeter scale via a facile chemical vapor deposition (CVD) route is demonstrated. More importantly, the epitaxial growth of NbS2 -WS2 lateral metal-semiconductor heterostructures via a "two-step" CVD method is realized. Both the lateral and vertical NbS2 -WS2 heterostructures are achieved here. Transmission electron microscopy studies reveal a clear chemical modulation with distinct interfaces. Raman and photoluminescence maps confirm the precisely controlled spatial modulation of the as-grown NbS2 -WS2 heterostructures. The existence of the NbS2 -WS2 heterostructures is further manifested by electrical transport measurements. This work broadens the horizon of the in situ synthesis of TMD-based heterostructures and enlightens the possibility of applications based on 2D metal-semiconductor heterostructures.

Using controlled disorder to probe the interplay between charge order and superconductivity in NbSe2

The interplay between superconductivity and charge-density wave (CDW) in 2H-NbSe₂ is not fully understood despite decades of study. Artificially introduced disorder can tip the delicate balance between two competing long-range orders, and reveal the underlying interactions that give rise to them. Here we introduce disorder by electron irradiation and measure in-plane resistivity, Hall resistivity, X-ray scattering, and London penetration depth. With increasing disorder, the superconducting transition temperature, T_c, varies non-monotonically, whereas the CDW transition temperature, T_CDW, monotonically decreases and becomes unresolvable above a critical irradiation dose where T_c drops sharply. Our results imply that the CDW order initially competes with superconductivity, but eventually assists it. We argue that at the transition where the long-range CDW order disappears, the cooperation with superconductivity is dramatically suppressed. X-ray scattering and Hall resistivity measurements reveal that the short-range CDW survives above the transition. Superconductivity persists to much higher dose levels, consistent with fully gapped superconductivity and moderate interband pairing.

Atomic-scale strain manipulation of a charge density wave

Charge density waves (CDWs) are simple periodic reorganizations of charge in a crystal, and yet they are still poorly understood and continue to bear surprises. External perturbations, such as strain or pressure, can in principle push a CDW phase into a different ordering geometry. However, engineering this type of quantum criticality has been experimentally challenging. Here, we implement a simple method for straining bulk materials. By applying it to 2H-NbSe₂, a prototypical CDW system studied for decades, we discover two dramatic strain-induced CDW phase transitions. Our atomic-scale spectroscopic imaging measurements, combined with theory, reveal the distinct roles of electrons and phonons in forming these emergent states, thus opening a window into the rich phenomenology of CDWs.

A charge density wave (CDW) is one of the fundamental instabilities of the Fermi surface occurring in a wide range of quantum materials. In dimensions higher than one, where Fermi surface nesting can play only a limited role, the selection of the particular wavevector and geometry of an emerging CDW should in principle be susceptible to controllable manipulation. In this work, we implement a simple method for straining materials compatible with low-temperature scanning tunneling microscopy/spectroscopy (STM/S), and use it to strain-engineer CDWs in 2H-NbSe₂. Our STM/S measurements, combined with theory, reveal how small strain-induced changes in the electronic band structure and phonon dispersion lead to dramatic changes in the CDW ordering wavevector and geometry. Our work unveils the microscopic mechanism of a CDW formation in this system, and can serve as a general tool compatible with a range of spectroscopic techniques to engineer electronic states in any material where local strain or lattice symmetry breaking plays a role.

Photoemission perspective on pseudogap, superconducting fluctuations, and charge order in cuprates: a review of recent progress

In the course of seeking the microscopic mechanism of superconductivity in cuprate high temperature superconductors, the pseudogap phase- the very abnormal 'normal' state on the hole-doped side- has proven to be as big of a quandary as superconductivity itself. Angle-resolved photoemission spectroscopy (ARPES) is a powerful tool for assessing the momentum-dependent phenomenology of the pseudogap, and recent technological developments have permitted a more detailed understanding. This report reviews recent progress in understanding the relationship between superconductivity and the pseudogap, the Fermi arc phenomena, and the relationship between charge order and pseudogap from the perspective of ARPES measurements.

Local Real-Space View of the Achiral 1T-TiSe_{2} 2×2×2 Charge Density Wave

The transition metal dichalcogenide 1T-TiSe_{2}-two-dimensional layered material undergoing a commensurate 2×2×2 charge density wave (CDW) transition with a weak periodic lattice distortion (PLD) below ≈200  K. Scanning tunneling microscopy (STM) combined with intentionally introduced interstitial Ti atoms allows us to go beyond the usual spatial resolution of STM and to intimately probe the three-dimensional character of the PLD. Furthermore, the inversion-symmetric achiral nature of the CDW in the z direction is revealed, contradicting the claimed existence of helical CDW stacking and associated chiral order. This study paves the way to a simultaneous real-space probing of both charge and structural reconstructions in CDW compounds.

Comprehensive optical characterization of atomically thin NbSe2

Transition-metal dichalcogenides (TMDCs) have offered experimental access to quantum confinement in one dimension. In recent years, metallic TMDCs like NbSe₂ have taken center stage with many of them exhibiting interesting temperature-dependent properties such as charge density waves and superconductivity. In this paper, we perform a comprehensive optical analysis of NbSe₂ by utilizing Raman spectroscopy, differential reflectance contrast, and spectroscopic ellipsometry. These analyses, when coupled with Kramers-Kronig analysis, allow us to extract the dielectric functions of bulk and atomically thin NbSe₂ and relate them to the resonant behavior of the Raman spectra.

High-temperature charge density wave correlations in La1.875Ba0.125CuO4 without spin-charge locking

Although all superconducting cuprates display charge-ordering tendencies, their low-temperature properties are distinct, impeding efforts to understand the phenomena within a single conceptual framework. While some systems exhibit stripes of charge and spin, with a locked periodicity, others host charge density waves (CDWs) without any obviously related spin order. Here we use resonant inelastic X-ray scattering to follow the evolution of charge correlations in the canonical stripe-ordered cuprate La_1.875Ba_0.125CuO₄ across its ordering transition. We find that high-temperature charge correlations are unlocked from the wavevector of the spin correlations, signaling analogies to CDW phases in various other cuprates. This indicates that stripe order at low temperatures is stabilized by the coupling of otherwise independent charge and spin density waves, with important implications for the relation between charge and spin correlations in the cuprates.

Inter-Layer Coupling Induced Valence Band Edge Shift in Mono- to Few-Layer MoS2

Recent progress in the synthesis of monolayer MoS2, a two-dimensional direct band-gap semiconductor, is paving new pathways toward atomically thin electronics. Despite the large amount of literature, fundamental gaps remain in understanding electronic properties at the nanoscale. Here, we report a study of highly crystalline islands of MoS2 grown via a refined chemical vapor deposition synthesis technique. Using high resolution scanning tunneling microscopy and spectroscopy (STM/STS), photoemission electron microscopy/spectroscopy (PEEM) and μ-ARPES we investigate the electronic properties of MoS2 as a function of the number of layers at the nanoscale and show in-depth how the band gap is affected by a shift of the valence band edge as a function of the layer number. Green's function based electronic structure calculations were carried out in order to shed light on the mechanism underlying the observed bandgap reduction with increasing thickness, and the role of the interfacial Sulphur atoms is clarified. Our study, which gives new insight into the variation of electronic properties of MoS2 films with thickness bears directly on junction properties of MoS2, and thus impacts electronics application of MoS2.

Superconducting ferecrystals: turbostratically disordered atomic-scale layered (PbSe)1.14(NbSe2)n thin films

Hybrid electronic heterostructure films of semi- and superconducting layers possess very different properties from their bulk counterparts. Here, we demonstrate superconductivity in ferecrystals: turbostratically disordered atomic-scale layered structures of single-, bi- and trilayers of NbSe2 separated by PbSe layers. The turbostratic (orientation) disorder between individual layers does not destroy superconductivity. Our method of fabricating artificial sequences of atomic-scale 2D layers, structurally independent of their neighbours in the growth direction, opens up new possibilities of stacking arbitrary numbers of hybrid layers which are not available otherwise, because epitaxial strain is avoided. The observation of superconductivity and systematic Tc changes with nanostructure make this synthesis approach of particular interest for realizing hybrid systems in the search of 2D superconductivity and the design of novel electronic heterostructures.

Pseudogaps and Emergence of Coherence in Two-Dimensional Electron Liquids in SrTiO_{3}

Using tunneling spectroscopy, we show that pseudogaps emerge in strongly correlated, two-dimensional electron liquids in SrTiO_{3} quantum wells that are tuned near a quantum critical point. Coherence peaks emerge at low temperatures in quantum wells embedded in antiferromagnetic SmTiO_{3} that remain itinerant to the lowest thickness. Quantum wells embedded in ferrimagnetic GdTiO_{3} that become ferromagnetic at low temperatures show no indication of quasiparticle coherence. They undergo a symmetry-lowering metal-to-insulator transition at the lowest thicknesses that coincides with a vanishing single-particle density of states (DOS) around the Fermi level. Both types of quantum wells show a power-law depletion of the DOS at high energies. The results show that the different pseudogap behaviors are closely correlated with the type of magnetism in the proximity of the quantum wells and thus provide insights into the microscopic mechanisms.

Paramagnetic magnetization signals and curious metastable behaviour in field-cooled magnetization of a single crystal of superconductor 2H-NbSe2

We present here some newer characteristics pertaining to paramagnetic Meissner effect like response in a single crystal of the low [Formula: see text] superconducting compound 2H-[Formula: see text] via a detailed study of effects of perturbation on the field-cooled magnetization response. In the temperature range, where an anomalous paramagnetic magnetization occurs, the field-cooled magnetization response is found to be highly metastable: it displays a curious tendency to switch randomly from a given paramagnetic value to a diamagnetic or to a different paramagnetic value, when the system is perturbed by an impulse of an externally applied ac magnetic field. The new facets revealed in a single crystal of 2H-[Formula: see text] surprisingly bear a marked resemblance with the characteristics of magnetization behaviour anticipated for the giant vortex states with multiple flux quanta ([Formula: see text], [Formula: see text], [Formula: see text]) predicted to occur in mesoscopic-sized superconducting specimen and possible transitions amongst such states.

Charge order from orbital-dependent coupling evidenced by NbSe2

Niobium diselenide has long served as a prototype of two-dimensional charge ordering, believed to arise from an instability of the electronic structure analogous to the one-dimensional Peierls mechanism. Despite this, various anomalous properties have recently been identified experimentally, which cannot be explained by Peierls-like weak-coupling theories. Here, we consider instead a model with strong electron-phonon coupling, taking into account both the full momentum and orbital dependence of the coupling matrix elements. We show that both are necessary for a consistent description of the full range of experimental observations. We argue that NbSe2 is typical in this sense, and that any charge-ordered material in more than one dimension will generically be shaped by the momentum and orbital dependence of its electron-phonon coupling as well as its electronic structure. The consequences will be observable in many charge-ordered materials, including cuprate superconductors.