Pressure induced superconductivity in pristine 1T-TiSe2

Direct Visualization of Trimerized States in 1T^{'}-TaTe_{2}

Transition-metal dichalcogenides containing tellurium anions show remarkable charge-lattice modulated structures and prominent interlayer character. Using cryogenic scanning transmission electron microscopy (STEM), we map the atomic-scale structures of the high temperature (HT) and low temperature (LT) modulated phases in 1T^{'}-TaTe_{2}. At HT, we directly show in-plane metal distortions which form trimerized clusters and staggered, three-layer stacking. In the LT phase at 93 K, we visualize an additional trimerization of Ta sites and subtle distortions of Te sites by extracting structural information from contrast modulations in plan-view STEM data. Coupled with density functional theory calculations and image simulations, this approach opens the door for atomic-scale visualizations of low temperature phase transitions and complex displacements in a variety of layered systems.

Unusual Pressure-Induced Quantum Phase Transition from Superconducting to Charge-Density Wave State in Rare-Earth-Based Heusler LuPd_{2}In Compound

We investigate the pressure effects on the electronic structures and phonon properties of rare-earth-based cubic-Heusler compound LuPd_{2}In, on the basis of ab initio density functional theory. We find the occurrence of intriguing phase transition from the superconducting (SC) to charge-density wave (CDW) state under pressure (P), which is quite unusual in that the pressure is detrimental to the CDW state in usual systems. The SC transition temperature T_{C} of LuPd_{2}In increases first with increasing pressure, up to P_{C}≈28  GPa, above which a quantum phase transition into the CDW state takes place. This extraordinary transition originates from the occurrence of phonon softening instability at a special q=M in the Brillouin zone. We thus propose that LuPd_{2}In is a quite unique material, in which the CDW quantum critical point is realized under the SC dome by applying the pressure.

Weak Dimensionality Dependence and Dominant Role of Ionic Fluctuations in the Charge-Density-Wave Transition of NbSe_{2}

Contradictory experiments have been reported about the dimensionality effect on the charge-density-wave transition in 2H NbSe_{2}. While scanning tunneling experiments on single layers grown by molecular beam epitaxy measure a charge-density-wave transition temperature in the monolayer similar to the bulk, around 33 K, Raman experiments on exfoliated samples observe a large enhancement of the transition temperature up to 145 K. By employing a nonperturbative approach to deal with anharmonicity, we calculate from first principles the temperature dependence of the phonon spectra both for bulk and monolayer. In both cases, the charge-density-wave transition temperature is estimated as the temperature at which the phonon energy of the mode driving the structural instability vanishes. The obtained transition temperature in the bulk is around 59 K, in rather good agreement with experiments, and it is just slightly increased in the single-layer limit to 73 K, showing the weak dependence of the transition on dimensionality. Environmental factors could motivate the disagreement between the transition temperatures reported by experiments. Our analysis also demonstrates the predominance of ionic fluctuations over electronic ones in the melting of the charge-density-wave order.

Inversion-Protected Higher-Order Topological Superconductivity in Monolayer WTe_{2}

Monolayer WTe_{2}, a centrosymmetric transition metal dichacogenide, has recently been established as a quantum spin Hall insulator and found superconducting upon gating. Here we study the pairing symmetry and topological nature of superconducting WTe_{2} with a microscopic model at mean-field level. Surprisingly, we find that the spin-triplet phases in our phase diagram all host Majorana modes localized on two opposite corners. Even when the conventional pairing is favored, we find that an intermediate in-plane magnetic field exceeding the Pauli limit stabilizes an unconventional equal-spin pairing aligning with the field, which also hosts Majorana corner modes. Motivated by our findings, we obtain a recipe for two-dimensional superconductors featuring "higher-order topology" from the boundary perspective. Generally, a superconducting inversion-symmetric quantum spin Hall material whose normal-state Fermi surface is away from high-symmetry points, such as gated monolayer WTe_{2}, hosts Majorana corner modes if the superconductivity is parity-odd. We further point out that this higher-order phase is an inversion-protected topological crystalline superconductor and study the bulk-boundary correspondence. Finally, we discuss possible experiments for probing the Majorana corner modes. Our findings suggest superconducting monolayer WTe_{2} is a playground for higher-order topological superconductivity and possibly the first material realization for inversion-protected Majorana corner modes without utilizing proximity effect.

Signatures of nontrivial Rashba metal states in a transition metal dichalcogenides Josephson junction

Nontrivial Rashba metal states in conventional semiconductor materials generated by both Rashba spin-orbit coupling and ferromagnetic exchange coupling coexisting were recently predicted and exploited. Single layered transition metal dichalcogenides (TMDC) featuring those states and their potential applications have been less focused. We find that, in the materials with Rashba spin-orbit coupling only, nontrivial Rashba metallic states can be manipulated by an external gate voltage. Based on extensive numerical simulations, the relationships between the supercurrent and nontrivial Rashba metallic states in the TMDC Josephson junction have been investigated. It is shown that, in the absence of the Rashba spin-orbit coupling, the critical supercurrent exhibits a stark difference between normal Rashba metal state and anomalous Rashba metal state in the finite junction as compared to the case of the short junction. While in the case of the finite Rashba spin-orbit coupling, the critical supercurrent demonstrates a reentrant behavior when Fermi level sweeps from anomalous Rashba metal state to Rashba ring metal state. Intriguingly, not only at the conversion of the nontrivial Rashba metallic states but also in the Rashba ring metal state the reentrant behavior exhibits again, which could be well explained by the mixing of spin-triplet Cooper pairs with spin-singlet Cooper pairs in Ising superconductor. Such a reentrant effect offers a new way to detect Ising superconductivity based on the TMDC systems. Meanwhile our study also clarified that the nontrivial Rashba metallic state plays an important role in controlling the supercurrent in the TMDC Josephson junction, which is useful for designing future superconducting devices.

Molecular Beam Epitaxy of Transition Metal (Ti-, V-, and Cr-) Tellurides: From Monolayer Ditellurides to Multilayer Self-Intercalation Compounds

Material growth by van der Waals epitaxy has the potential to isolate monolayer (ML) materials and synthesize ultrathin films not easily prepared by exfoliation or other growth methods. Here, the synthesis of the early transition metal (Ti, V, and Cr) tellurides by molecular beam epitaxy (MBE) in the mono- to few-layer regime is investigated. The layered ditellurides of these materials are known for their intriguing quantum- and layer dependent- properties. Here we show by a combination of in situ sample characterization and comparison with computational predictions that ML ditellurides with octahedral 1T structure are readily grown, but for multilayers, the transition metal dichalcogenide (TMDC) formation competes with self-intercalated compounds. CrTe₂, a TMDC that is known to be metastable in bulk and easily decomposes into intercalation compounds, has been synthesized successfully in the ML regime at low growth temperatures. At elevated growth temperatures or for multilayers, only the intercalation compound, equivalent to a bulk Cr₃Te₄, could be obtained. ML VTe₂ is more stable and can be synthesized at higher growth temperatures in the ML regime, but multilayers also convert to a bulk-equivalent V₃Te₄ compound. TiTe₂ is the most stable of the TMDCs studied; nevertheless, a detailed analysis of multilayers also indicates the presence of intercalated metals. Computation suggests that the intercalation-induced distortion of the TMDC-layers is much reduced in Ti-telluride compared to V-, and Cr-telluride. This makes the identification of intercalated materials by scanning tunneling microscopy more challenging for Ti-telluride. The identification of self-intercalation compounds in MBE grown multilayer chalcogenides may explain observed lattice distortions in previously reported MBE grown early transition metal chalcogenides. On the other hand, these intercalation compounds in their ultrathin limit can be considered van der Waals materials in their own right. This class of materials is only accessible by direct growth methods but may be used as "building blocks" in MBE-grown van der Waals heterostructures. Controlling their growth is an important step for understanding and studying the properties of these materials.

Superconductivity related to the suppression of exciton formation in 1T-TiSe2

In strongly correlated electron system, the impact of elementary substitution or intercalation plays a crucial role in determining electronic ground state among various macroscopic quantum phases such as charge order and superconductivity. Here, we report that simultaneous Cu intercalation and Ta substitution at Ti site in 1T-CuxTi0.8Ta0.2Se2induce an intrinsic electronic phase diagram, characterized by an inherent superconducting transition in thexregion of 0 ⩽x⩽ 0.12, with a maximum superconducting transition temperatureTcof 2.5 K forx= 0.04, in contrast to the non-superconducting sample 1T-Cu0.04TiSe2. The increased density of free charge carriers screen the Coulomb interaction between electron-hole pairs effectively, promoting the occurrence of superconductivity favourably. Present results suggest that the Cu intercalation and the Ta substitution-induced suppression of the exciton condensation boost the superconductivity, shedding new light on the fundamental physics of the interplay between superconductivity, charge order, and electron correlation.

Charge disproportionate molecular redox for discrete memristive and memcapacitive switching

Electronic symmetry breaking by charge disproportionation results in multifaceted changes in the electronic, magnetic and optical properties of a material, triggering ferroelectricity, metal/insulator transition and colossal magnetoresistance. Yet, charge disproportionation lacks technological relevance because it occurs only under specific physical conditions of high or low temperature or high pressure. Here we demonstrate a voltage-triggered charge disproportionation in thin molecular films of a metal-organic complex occurring in ambient conditions. This provides a technologically relevant molecular route for simultaneous realization of a ternary memristor and a binary memcapacitor, scalable down to a device area of 60 nm². Supported by mathematical modelling, our results establish that multiple memristive states can be functionally non-volatile, yet discrete-a combination perceived as theoretically prohibited. Our device could be used as a binary or ternary memristor, a binary memcapacitor or both concomitantly, and unlike the existing 'continuous state' memristors, its discrete states are optimal for high-density, ultra-low-energy digital computing.

Fermi Surface Reconstruction and Electron Dynamics at the Charge-Density-Wave Transition in TiSe_{2}

The evolution of the charge carrier concentrations and mobilities are examined across the charge-density-wave (CDW) transition in TiSe_{2}. Combined quantum oscillation and magnetotransport measurements show that a small electron pocket dominates the electronic properties at low temperatures while an electron and hole pocket contribute at room temperature. At the CDW transition, an abrupt Fermi surface reconstruction and a minimum in the electron and hole mobilities are extracted from two-band and Kohler analysis of magnetotransport measurements. The minimum in the mobilities is associated with the overseen role of scattering from the softening CDW mode. With the carrier concentrations and dynamics dominated by the CDW and the associated bosonic mode, our results highlight TiSe_{2} as a prototypical system to study the Fermi surface reconstruction at a density-wave transition.

Recent progress of TMD nanomaterials: phase transitions and applications

Transition metal dichalcogenides (TMDs) show wide ranges of electronic properties ranging from semiconducting, semi-metallic to metallic due to their remarkable structural differences. To obtain 2D TMDs with specific properties, it is extremely important to develop particular strategies to obtain specific phase structures. Phase engineering is a traditional method to achieve transformation from one phase to another controllably. Control of such transformations enables the control of properties and access to a range of properties, otherwise inaccessible. Then extraordinary structural, electronic and optical properties lead to a broad range of potential applications. In this review, we introduce the various electronic properties of 2D TMDs and their polymorphs, and strategies and mechanisms for phase transitions, and phase transition kinetics. Moreover, the potential applications of 2D TMDs in energy storage and conversion, including electro/photocatalysts, batteries/supercapacitors and electronic devices, are also discussed. Finally, opportunities and challenges are highlighted. This review may further promote the development of TMD phase engineering and shed light on other two-dimensional materials of fundamental interest and with potential ranges of applications.

Novel Superstructure-Phase Two-Dimensional Material 1T-VSe2 at High Pressure

A superstructure can elicit versatile new properties in materials by breaking their original geometrical symmetries. It is an important topic in the layered graphene-like two-dimensional transition metal dichalcogenides, but its origin remains unclear. Using diamond-anvil cell techniques, synchrotron X-ray diffraction, X-ray absorption, and first-principles calculations, we show that the evolution from weak van der Waals bonding to Heisenberg covalent bonding between layers induces an isostructural transition in quasi-two-dimensional 1T-type VSe₂ at high pressure. Furthermore, our results show that high pressure induces a novel superstructure at 15.5 GPa rather than suppresses it as it would normally, which is unexpected. It is driven by Fermi-surface nesting, enhanced by pressure-induced distortion. The results suggest that the superstructure not only appears in the two-dimensional structure but also can emerge in the pressure-tuned three-dimensional structure with new symmetry and develop superconductivity.

NbSeTe-a new layered transition metal dichalcogenide superconductor

Transition metal dichalcogenides (TMDCs) usually exhibit layered polytypic structures due to the weak interlayer coupling. 2H-NbSe₂ is one of the most widely studied in the pristine TMDC family due to its high superconducting transition temperature (T _c  =  7.3 K) and the occurrence of a charge-density wave (CDW) order below 33 K. The coexistence of CDW with superconductivity poses an intriguing open question about the relationship between Fermi surface nesting and Cooper pairing. Past studies of this issue have mostly been focused on doping 2H-NbSe₂ by 3d transition metals without significantly changing its crystal structure. Here we replaced the Se by Te in 2H-NbSe₂ in order to design a new 1T polytype layered TMDC NbSeTe, which adopts a trigonal structure with space group P [Formula: see text] m1. We successfully grew large size and high-quality single crystals of 1T-NbSeTe via the vapor transport method using I ₂ as the transport agent. Temperature-dependent resistivity and specific heat data revealed a bulk T _c at 1.3 K, which is the first observation of superconductivity in pure 1T-NbSeTe phase. This compound enlarged the family of superconducting TMDCs and provides an opportunity to study the interplay between CDW and superconductivity in the trigonal structure.

Ultrafast charge ordering by self-amplified exciton-phonon dynamics in TiSe2

The origin of charge density waves (CDWs) in TiSe\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${}_{2}$$\end{document}2 has long been debated, mainly due to the difficulties in identifying the timescales of the excitonic pairing and electron–phonon coupling (EPC). Without a time-resolved and microscopic mechanism, one has to assume simultaneous appearance of CDW and periodic lattice distortions (PLD). Here, we accomplish a complete separation of ultrafast exciton and PLD dynamics and unravel their interplay in our real-time time-dependent density functional theory simulations. We find that laser pulses knock off the exciton order and induce a homogeneous bonding–antibonding transition in the initial 20 fs, then the weakened electronic order triggers ionic movements antiparallel to the original PLD. The EPC comes into play after the initial 20 fs, and the two processes mutually amplify each other leading to a complete inversion of CDW ordering. The self-amplified dynamics reproduces the evolution of band structures in agreement with photoemission experiments. Hence we resolve the key processes in the initial dynamics of CDWs that help elucidate the underlying mechanism.

The physical origins of charge density waves in 1T-TiSe2 and their response to ultrafast excitation have long been a topic of theoretical and experimental debate. Here the authors present an ab initio theory that successfully captures the observed dynamics of charge density wave formation.

Magnetoelastoresistance in WTe2: Exploring electronic structure and extremely large magnetoresistance under strain

Strain describes the deformation of a material as a result of applied stress. It has been widely employed to probe transport properties of materials, ranging from semiconductors to correlated materials. In order to understand, and eventually control, transport behavior under strain, it is important to quantify the effects of strain on the electronic bandstructure, carrier density, and mobility. Here, we demonstrate that much information can be obtained by exploring magnetoelastoresistance (MER), which refers to magnetic field-driven changes of the elastoresistance. We use this powerful approach to study the combined effect of strain and magnetic fields on the semimetallic transition metal dichalcogenide [Formula: see text] We discover that WTe₂ shows a large and temperature-nonmonotonic elastoresistance, driven by uniaxial stress, that can be tuned by magnetic field. Using first-principle and analytical low-energy model calculations, we provide a semiquantitative understanding of our experimental observations. We show that in [Formula: see text], the strain-induced change of the carrier density dominates the observed elastoresistance. In addition, the change of the mobilities can be directly accessed by using MER. Our analysis also reveals the importance of a heavy-hole band near the Fermi level on the elastoresistance at intermediate temperatures. Systematic understanding of strain effects in single crystals of correlated materials is important for future applications, such as strain tuning of bulk phases and fabrication of devices controlled by strain.

Strongly Compressed Few-Layered SnSe2 Films Grown on a SrTiO3 Substrate: The Coexistence of Charge Ordering and Enhanced Interfacial Superconductivity

High pressure has been demonstrated to be a powerful approach of producing novel condensed-matter states, particularly in tuning the superconducting transition temperature (T_c) of the superconductivity in a clean fashion without involving the complexity of chemical doping. However, the challenge of high-pressure experiment hinders further in-depth research for underlying mechanisms. Here, we have successfully synthesized continuous layer-controllable SnSe₂ films on SrTiO₃ substrate using molecular beam epitaxy. By means of scanning tunneling microscopy/spectroscopy (STM/S) and Raman spectroscopy, we found that the strong compressive strain is intrinsically built in few-layers films, with a largest equivalent pressure up to 23 GPa in the monolayer. Upon this, unusual 2 × 2 charge ordering is induced at the occupied states in the monolayer, accompanied by prominent decrease in the density of states (DOS) near the Fermi energy (E_F), resembling the gap states of CDW reported in transition metal dichalcogenide (TMD) materials. Subsequently, the coexistence of charge ordering and the interfacial superconductivity is observed in bilayer films as a result of releasing the compressive strain. In conjunction with spatially resolved spectroscopic study and first-principles calculation, we find that the enhanced interfacial superconductivity with an estimated T_c of 8.3 K is observed only in the 1 × 1 region. Such superconductivity can be ascribed to a combined effect of interfacial charge transfer and compressive strain, which leads to a considerable downshift of the conduction band minimum and an increase in the DOS at E_F. Our results provide an attractive platform for further in-depth investigation of compression-induced charge ordering (monolayer) and the interplay between charge ordering and superconductivity (bilayer). Meanwhile, it has opened up a pathway to prepare strongly compressed two-dimensional materials by growing onto a SrTiO₃ substrate, which is promising to induce superconductivity with a higher T_c.

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].

Pressure induced topological and structural phase transitions in 1T-TiSe2: a Raman study

High pressure Raman spectroscopy studies on 1T-TiSe₂ were carried out up to ~20.5 GPa. Based on the anomalies in phonon linewidth (lifetime) and phonon frequency of A _1g mode, we observe three transitions at ~2.5 GPa, ~6.0 GPa and ~15 GPa. The transitions at ~2.5 and ~6.0 GPa are the two topological phase transitions consistent with the theoretical prediction by Zhu et al in 1T-TiSe₂ under pressure, namely, a topological trivial to non-trivial transition (Z ₂  =  1) and topological non-trivial to trivial transition (Z ₂  =  0). The trigonal (1T) phase of TiSe₂ is stable up to ~15 GPa beyond which it undergoes structural transition as seen from the appearance of new Raman modes. There is a coexistence of the 1T and the new high-pressure phase up to ~19 GPa. The structural transition is completely reversible as seen from the appearance of 1T phase Raman spectra upon release of the pressure.

Pressure-Induced Collapse of the Charge Density Wave and Higgs Mode Visibility in 2H-TaS_{2}

The pressure evolution of the Raman active electronic excitations of the transition metal dichalcogenides 2H-TaS_{2} is followed through the pressure phase diagram embedding incommensurate charge-density-wave and superconducting states. At high pressure, the charge-density wave is found to collapse at 8.5 GPa. In the coexisting charge-density-wave and superconducting orders, we unravel a strong in-gap superconducting mode, attributed to a Higgs mode, coexisting with the expected incoherent Cooper-pair breaking signature. The latter remains in the pure superconducting state reached above 8.5 GPa. Our report constitutes a new observation of such Raman active Higgs mode since the long-standing unique case 2H-NbSe_{2}.

Reproduction of the Charge Density Wave Phase Diagram in 1T-TiSe_{2} Exposes its Excitonic Character

Recent experiments suggest that excitonic degrees of freedom play an important role in precipitating the charge density wave (CDW) transition in 1T-TiSe_{2}. Through systematic calculations of the electronic and phonon spectrum based on density functional perturbation theory, we show that the predicted critical doping of the CDW phase overshoots the experimental value by 1 order of magnitude. In contrast, an independent self-consistent many-body calculation of the excitonic order parameter and renormalized band structure is able to capture the experimental phase diagram in extremely good qualitative and quantitative agreement. This demonstrates that electron-electron interactions and the excitonic instability arising from direct electron-hole coupling are pivotal to accurately describe the nature of the CDW in this system. This has important implications to understand the emergence of superconductivity within the CDW phase of this and related systems.

Structural, vibrational and electronic properties of the superconductor CuxTiSe2: theoretical and experimental insights

The crystal/electronic structure and vibrational properties of the CuxTiSe2 intercalation compounds were studied combining experimental and theoretical techniques. The Cu added into the TiSe2 matrix was characterized as an intercalant atom into van der Waals gaps from Raman spectroscopy analysis. Theoretical and experimental data indicate the Cu-intercalation effect on the crystalline structure as a local disorder affecting [TiSe6] clusters from SeSe layers, which results in a volume expansion. A significant charge transfer from Cu atoms to the host lattice results in a change from Ti4+ to Ti3+ species, narrowing the band-gap and increasing the superconductivity of the material.

Gate-induced superconductivity in a monolayer topological insulator

The layered semimetal tungsten ditelluride (WTe₂) has recently been found to be a two-dimensional topological insulator (2D TI) when thinned down to a single monolayer, with conducting helical edge channels. We found that intrinsic superconductivity can be induced in this monolayer 2D TI by mild electrostatic doping at temperatures below 1 kelvin. The 2D TI-superconductor transition can be driven by applying a small gate voltage. This discovery offers possibilities for gate-controlled devices combining superconductivity and nontrivial topological properties, and could provide a basis for quantum information schemes based on topological protection.

Unusual Pressure-Induced Periodic Lattice Distortion in SnSe_{2}

We performed high-pressure x-ray diffraction (XRD), Raman, and transport measurements combined with first-principles calculations to investigate the behavior of tin diselenide (SnSe_{2}) under compression. The obtained single-crystal XRD data indicate the formation of a (1/3,1/3,0)-type superlattice above 17 GPa. According to our density functional theory results, the pressure-induced transition to the commensurate periodic lattice distortion (PLD) phase is due to the combined effect of strong Fermi surface nesting and electron-phonon coupling at a momentum wave vector q=(1/3,1/3,0). In contrast, similar PLD transitions associated with charge density wave (CDW) orderings in transition metal dichalcogenides (TMDs) do not involve significant Fermi surface nesting. The discovered pressure-induced PLD is quite remarkable, as pressure usually suppresses CDW phases in related materials. Our findings, therefore, provide new playgrounds to study the intricate mechanisms governing the emergence of PLD in TMD-related materials.

van der Waals Metallic Transition Metal Dichalcogenides

Transition metal dichalcogenides are layered materials which are composed of transition metals and chalcogens of the group VIA in a 1:2 ratio. These layered materials have been extensively investigated over synthesis and optical and electrical properties for several decades. It can be insulators, semiconductors, or metals revealing all types of condensed matter properties from a magnetic lattice distorted to superconducting characteristics. Some of these also feature the topological manner. Instead of covering the semiconducting properties of transition metal dichalcogenides, which have been extensively revisited and reviewed elsewhere, here we present the structures of metallic transition metal dichalcogenides and their synthetic approaches for not only high-quality wafer-scale samples using conventional methods (e.g., chemical vapor transport, chemical vapor deposition) but also local small areas by a modification of the materials using Li intercalation, electron beam irradiation, light illumination, pressures, and strains. Some representative band structures of metallic transition metal dichalcogenides and their strong layer-dependence are reviewed and updated, both in theoretical calculations and experiments. In addition, we discuss the physical properties of metallic transition metal dichalcogenides such as periodic lattice distortion, magnetoresistance, superconductivity, topological insulator, and Weyl semimetal. Approaches to overcome current challenges related to these materials are also proposed.

Unveiling the charge density wave inhomogeneity and pseudogap state in 1T-TiSe2

By using scanning tunneling microscopy (STM)/spectroscopy (STS), we systematically characterize the electronic structure of lightly doped 1T-TiSe₂, and demonstrate the existence of the electronic inhomogeneity and the pseudogap state. It is found that the intercalation induced lattice distortion impacts the local band structure and reduce the size of the charge density wave (CDW) gap with the persisted 2 × 2 spatial modulation. On the other hand, the delocalized doping electrons promote the formation of pseudogap. Domination by either of the two effects results in the separation of two characteristic regions in real space, exhibiting rather different electronic structures. Further doping electrons to the surface confirms that the pseudogap may be the precursor for the superconducting gap. This study suggests that the competition of local lattice distortion and the delocalized doping effect contribute to the complicated relationship between charge density wave and superconductivity for intercalated 1T-TiSe₂.

Large-Area Atomic Layers of the Charge-Density-Wave Conductor TiSe2

Layered transition metal (Ti, Ta, Nb, etc.) dichalcogenides are important prototypes for the study of the collective charge density wave (CDW). Reducing the system dimensionality is expected to lead to novel properties, as exemplified by the discovery of enhanced CDW order in ultrathin TiSe₂ . However, the syntheses of monolayer and large-area 2D CDW conductors can currently only be achieved by molecular beam epitaxy under ultrahigh vacuum. This study reports the growth of monolayer crystals and up to 5 × 10⁵ µm² large films of the typical 2D CDW conductor-TiSe₂ -by ambient-pressure chemical vapor deposition. Atomic resolution scanning transmission electron microscopy indicates the as-grown samples are highly crystalline 1T-phase TiSe₂ . Variable-temperature Raman spectroscopy shows a CDW phase transition temperature of 212.5 K in few layer TiSe₂ , indicative of high crystal quality. This work not only allows the exploration of many-body state of TiSe₂ in 2D limit but also offers the possibility of utilizing large-area TiSe₂ in ultrathin electronic devices.

Nature and evolution of incommensurate charge order in manganites visualized with cryogenic scanning transmission electron microscopy

Charge order is a modulation of the electron density and is associated with unconventional phenomena, including colossal magnetoresistance and metal–insulator transitions. Determining how the lattice responds provides insights into the nature and symmetry of the ordered state. Scanning transmission electron microscopy can measure lattice displacements with picometer precision, but its use has been limited to room-temperature phases only. Here, we demonstrate high-resolution imaging at cryogenic temperature and map the nature and evolution of charge order in a manganite. We uncover picometer-scale displacive modulations whose periodicity is strongly locked to the lattice and visualize temperature-dependent phase inhomogeneity in the modulations. These results pave the way to understanding the underlying structure of charge-ordered states and other complex phenomena.

Incommensurate charge order in hole-doped oxides is intertwined with exotic phenomena such as colossal magnetoresistance, high-temperature superconductivity, and electronic nematicity. Here, we map, at atomic resolution, the nature of incommensurate charge–lattice order in a manganite using scanning transmission electron microscopy at room temperature and cryogenic temperature (∼93 K). In diffraction, the ordering wave vector changes upon cooling, a behavior typically associated with incommensurate order. However, using real space measurements, we discover that the ordered state forms lattice-locked regions over a few wavelengths interspersed with phase defects and changing periodicity. The cations undergo picometer-scale (∼6 pm to 11 pm) transverse displacements, suggesting that charge–lattice coupling is strong. We further unearth phase inhomogeneity in the periodic lattice displacements at room temperature, and emergent phase coherence at 93 K. Such local phase variations govern the long-range correlations of the charge-ordered state and locally change the periodicity of the modulations, resulting in wave vector shifts in reciprocal space. These atomically resolved observations underscore the importance of lattice coupling and phase inhomogeneity, and provide a microscopic explanation for putative “incommensurate” order in hole-doped oxides.

Pressure-induced metallization in layered ReSe2

The evolution of the crystal structure and electrical transport properties of distorted layered transition metal dichalcogenide ReSe₂ was studied under high pressure up to ~90 GPa by Raman spectroscopy and electrical resistivity measurements accompanied by ab initio electronic band structure calculations. Raman spectroscopy studies indicate an isostructural phase transition due to layer sliding at ~7 GPa, to the distorted 1T-phase which remains stable up to the highest pressures employed in these experiments. From a direct band gap semiconductor at ambient pressure, ReSe₂ undergoes pressure-induced metallization at pressures ~35 GPa, in agreement with the ab initio calculations. Resistivity measurements performed with different loading conditions reveal the possible emergence of superconductivity, which is most likely not an intrinsic property of ReSe₂, but is rather conditioned by internal stresses upon compression.

Superconductivity in Pristine 2H_{a}-MoS_{2} at Ultrahigh Pressure

As a follow-up of our previous work on pressure-induced metallization of the 2H_{c}-MoS_{2} [Chi et al., Phys. Rev. Lett. 113, 036802 (2014)PRLTAO0031-900710.1103/PhysRevLett.113.036802], here we extend pressure beyond the megabar range to seek after superconductivity via electrical transport measurements. We found that superconductivity emerges in the 2H_{a}-MoS_{2} with an onset critical temperature T_{c} of ca. 3 K at ca. 90 GPa. Upon further increasing the pressure, T_{c} is rapidly enhanced beyond 10 K and stabilized at ca. 12 K over a wide pressure range up to 220 GPa. Synchrotron x-ray diffraction measurements evidenced no further structural phase transition, decomposition, and amorphization up to 155 GPa, implying an intrinsic superconductivity in the 2H_{a}-MoS_{2}. DFT calculations suggest that the emergence of pressure-induced superconductivity is intimately linked to the emergence of a new flat Fermi pocket in the electronic structure. Our finding represents an alternative strategy for achieving superconductivity in 2H-MoS_{2} in addition to chemical intercalation and electrostatic gating.

van der Waals Layered Materials: Opportunities and Challenges

Since graphene became available by a scotch tape technique, a vast class of two-dimensional (2D) van der Waals (vdW) layered materials has been researched intensively. What is more intriguing is that the well-known physics and chemistry of three-dimensional (3D) bulk materials are often irrelevant, revealing exotic phenomena in 2D vdW materials. By further constructing heterostructures of these materials in the planar and vertical directions, which can be easily achieved via simple exfoliation techniques, numerous quantum mechanical devices have been demonstrated for fundamental research and technological applications. It is, therefore, necessary to review the special features in 2D vdW materials and to discuss the remaining issues and challenges. Here, we review the vdW materials library, technology relevance, and specialties of vdW materials covering the vdW interaction, strong Coulomb interaction, layer dependence, dielectric screening engineering, work function modulation, phase engineering, heterostructures, stability, growth issues, and the remaining challenges.

Critical Role of the Exchange Interaction for the Electronic Structure and Charge-Density-Wave Formation in TiSe_{2}

We show that the inclusion of screened exchange via hybrid functionals provides a unified description of the electronic and vibrational properties of TiSe_{2}. In contrast to local approximations in density functional theory, the explicit inclusion of exact, nonlocal exchange captures the effects of the electron-electron interaction needed to both separate the Ti-d states from the Se-p states and stabilize the charge-density-wave (CDW) (or low-T) phase through the formation of a p-d hybridized state. We further show that this leads to an enhanced electron-phonon coupling that can drive the transition even if a small gap opens in the high-T phase. Finally, we demonstrate that the hybrid functionals can generate a CDW phase where the electronic bands, the geometry, and the phonon frequencies are in agreement with experiments.

Influence of Domain Walls in the Incommensurate Charge Density Wave State of Cu Intercalated 1T-TiSe_{2}

We report a low-temperature scanning tunneling microscopy study of the charge density wave (CDW) order in 1T-TiSe_{2} and Cu_{0.08}TiSe_{2}. In pristine 1T-TiSe_{2} we observe a long-range coherent commensurate CDW (CCDW) order. In contrast, Cu_{0.08}TiSe_{2} displays an incommensurate CDW (ICDW) phase with localized CCDW domains separated by domain walls. Density of states measurements indicate that the domain walls host an extra population of fermions near the Fermi level which may play a role in the emergence of superconductivity in this system. Fourier transform scanning tunneling spectroscopy studies suggest that the dominant mechanism for CDW formation in the ICDW phase may be electron-phonon coupling.

Raman Characterization of the Charge Density Wave Phase of 1T-TiSe2: From Bulk to Atomically Thin Layers

Raman scattering is a powerful tool for investigating the vibrational properties of two-dimensional materials. Unlike the 2H phase of many transition metal dichalcogenides, the 1T phase of TiSe₂ features a Raman-active shearing and breathing mode, both of which shift toward lower energy with increasing number of layers. By systematically studying the Raman signal of 1T-TiSe₂ in dependence of the sheet thickness, we demonstrate that the charge density wave transition of this compound can be reliably determined from the temperature dependence of the peak position of the E_g mode near 136 cm^-1. The phase transition temperature is found to first increase with decreasing thickness of the sheets, followed by a decrease due to the effect of surface oxidation. The Raman spectroscopy-based method is expected to be applicable also to other 1T-phase transition metal dichalcogenides featuring a charge density wave transition and represents a valuable complement to electrical transport-based approaches.

Observation of a Charge Density Wave Incommensuration Near the Superconducting Dome in Cu_{x}TiSe_{2}

X-ray diffraction was employed to study the evolution of the charge density wave (CDW) in Cu_{x}TiSe_{2} as a function of copper intercalation in order to clarify the relationship between the CDW and superconductivity. The results show a CDW incommensuration arising at an intercalation value coincident with the onset of superconductivity at around x=0.055(5). Additionally, it was found that the charge density wave persists to higher intercalant concentrations than previously assumed, demonstrating that the CDW does not terminate inside the superconducting dome. A charge density wave peak was observed in samples up to x=0.091(6), the highest copper concentration examined in this study. The phase diagram established in this work suggests that charge density wave incommensuration may play a role in the formation of the superconducting state.

Hidden Order and Dimensional Crossover of the Charge Density Waves in TiSe2

Charge density wave (CDW) formation, a key physics issue for materials, arises from interactions among electrons and phonons that can also lead to superconductivity and other competing or entangled phases. The prototypical system TiSe₂, with a particularly simple (2 × 2 × 2) transition and no Kohn anomalies caused by electron-phonon coupling, is a fascinating but unsolved case after decades of research. Our angle-resolved photoemission measurements of the band structure as a function of temperature, aided by first-principles calculations, reveal a hitherto undetected but crucial feature: a (2 × 2) electronic order in each layer sets in at ~232 K before the widely recognized three-dimensional structural order at ~205 K. The dimensional crossover, likely a generic feature of such layered materials, involves renormalization of different band gaps in two stages.

Suppression and inducement of the charge-density-wave state in Cr x TiSe2

The x-ray diffraction, electrical resistivity and thermal expansion measurements have been employed to study how the intercalation of Cr atoms into TiSe2 matrix affects the crystal structure, formation of the charge density wave (CDW) and electrical properties. The intercalation of a small amount of Cr atoms (up to x ~ 0.03) is observed to suppress the CDW formation. The electrical resistivity of Cr x TiSe2 compounds with the Cr concentrations 0.03  ⩽  x  ⩽  0.20 shows a metallic-type behavior; while in the concentration range 0.25  ⩽  x  ⩽  0.5, the resistivity shows an anomalous behavior indicating the reappearance of the transition to a CDW-like state; further growth of the Cr content up to x  =  0.6 again leads to the metallic-type resistivity. For the compound Cr0.25TiSe2, the phase transition below 160 K together with abnormal change in the electrical resistivity is found to be accompanied by anomalies in the lattice parameters and thermal expansion behavior; this transition is classified as first-order type. It has been found that despite the intercalation of Cr atoms some Ti-Se bonds in the Se-Ti-Se tri-layers of Cr x TiSe2 with x  ⩽  0.5 have nearly the same lengths as in the host lattice TiSe2, which apparently allows the transition to be returned to the CDW-like state.

Charge density waves in strongly correlated electron systems

Strong electron correlations are at the heart of many physical phenomena of current interest to the condensed matter community. Here we present a survey of the mechanisms underlying such correlations in charge density wave (CDW) systems, including the current theoretical understanding and experimental evidence for CDW transitions. The focus is on emergent phenomena that result as CDWs interact with other charge or spin states, such as magnetism and superconductivity. In addition to reviewing the CDW mechanisms in 1D, 2D, and 3D systems, we pay particular attention to the prevalence of this state in two particular classes of compounds, the high temperature superconductors (cuprates) and the layered transition metal dichalcogenides. The possibilities for quantum criticality resulting from the competition between magnetic fluctuations and electronic instabilities (CDW, unconventional superconductivity) are also discussed.

Interplay of charge density wave and multiband superconductivity in 2H-PdxTaSe2

2H-TaSe2 has been one of unique transition metal dichalcogenides exhibiting several phase transitions due to a delicate balance among competing electronic ground states. An unusual metallic state at high-T is sequentially followed by an incommensurate charge density wave (ICDW) state at ≈122 K and a commensurate charge density wave (CCDW) state at ≈90 K, and superconductivity at TC ~ 0.14 K. Upon systematic intercalation of Pd ions into TaSe2, we find that CCDW order is destabilized more rapidly than ICDW to indicate a hidden quantum phase transition point at x ~ 0.09-0.10. Moreover, TC shows a dramatic enhancement up to 3.3 K at x = 0.08, ~24 times of TC in 2H-TaSe2, in proportional to the density of states N(EF). Investigations of upper critical fields Hc2 in single crystals reveal evidences of multiband superconductivity as temperature-dependent anisotropy factor γH = , quasi-linear increase of , and an upward, positive-curvature in near TC. Furthermore, analysis of temperature-dependent electronic specific heat corroborates the presence of multiple superconducting gaps. Based on above findings and electronic phase diagram vs x, we propose that the increase of N(EF) and effective electron-phonon coupling in the vicinity of CDW quantum phase transition should be a key to the large enhancement of TC in PdxTaSe2.

Superconductivity in Potassium-Doped Metallic Polymorphs of MoS2

Superconducting layered transition metal dichalcogenides (TMDs) stand out among other superconductors due to the tunable nature of the superconducting transition, coexistence with other collective electronic excitations (charge density waves), and strong intrinsic spin-orbit coupling. Molybdenum disulfide (MoS2) is the most studied representative of this family of materials, especially since the recent demonstration of the possibility to tune its critical temperature, Tc, by electric-field doping. However, just one of its polymorphs, band-insulator 2H-MoS2, has so far been explored for its potential to host superconductivity. We have investigated the possibility to induce superconductivity in metallic polytypes, 1T- and 1T'-MoS2, by potassium (K) intercalation. We demonstrate that at doping levels significantly higher than that required to induce superconductivity in 2H-MoS2, both 1T and 1T' phases become superconducting with Tc = 2.8 and 4.6 K, respectively. Unusually, K intercalation in this case is responsible both for the structural and superconducting phase transitions. By adding new members to the family of superconducting TMDs, our findings open the way to further manipulate and enhance the electronic properties of these technologically important materials.

Chemical bond in FexTiSe2 intercalation compounds: dramatic influence of Fe concentration

iThe changes in the electronic structure and nature of the chemical bonds due to the ordering of the intercalated atoms inside the van der Waals gap were observed for the first time.

Modulation of doping and biaxial strain on the transition temperature of the charge density wave transition in 1T-TiSe2

We study the effects of charge doping and biaxial strains on the transition temperature of charge density wave (CDW) transition in TiSe₂.

Charge density wave transition in single-layer titanium diselenide

A single molecular layer of titanium diselenide (TiSe₂) is a promising material for advanced electronics beyond graphene—a strong focus of current research. Such molecular layers are at the quantum limit of device miniaturization and can show enhanced electronic effects not realizable in thick films. We show that single-layer TiSe₂ exhibits a charge density wave (CDW) transition at critical temperature T_C=232±5 K, which is higher than the bulk T_C=200±5 K. Angle-resolved photoemission spectroscopy measurements reveal a small absolute bandgap at room temperature, which grows wider with decreasing temperature T below T_C in conjunction with the emergence of (2 × 2) ordering. The results are rationalized in terms of first-principles calculations, symmetry breaking and phonon entropy effects. The observed Bardeen-Cooper-Schrieffer (BCS) behaviour of the gap implies a mean-field CDW order in the single layer and an anisotropic CDW order in the bulk.

Single molecular layers of TiSe₂ are promising for advanced electronic applications, and it is therefore important to characterize their phases. Here, the authors use ARPES to detect a charge density wave transition without Fermi surface nesting and that takes place at a temperature higher than in bulk.

Sub-Kelvin magnetic and electrical measurements in a diamond anvil cell with in situ tunability

We discuss techniques for performing continuous measurements across a wide range of pressure-field-temperature phase space, combining the milli-Kelvin temperatures of a helium dilution refrigerator with the giga-Pascal pressures of a diamond anvil cell and the Tesla magnetic fields of a superconducting magnet. With a view towards minimizing remnant magnetic fields and background magnetic susceptibility, we characterize high-strength superalloy materials for the pressure cell assembly, which allows high fidelity measurements of low-field phenomena such as superconductivity below 100 mK at pressures above 10 GPa. In situ tunability and measurement of the pressure permit experiments over a wide range of pressure, while at the same time making possible precise steps across abrupt phase transitions such as those from insulator to metal.

Ferromagnetism in layered metastable 1T-CrTe2

We have synthesized for the first time the metastable compound 1T-CrTe2. We have done its complete structural characterization and measured its magnetization, specific heat and electrical resistivity between 4 and 330 K. We have also performed detailed band structure calculations. We have found that it crystallizes in the CdI2 structure type and that its electrical resistance follows a metallic behaviour below room temperature. Its magnetization and specific heat curves show that the compound has a transition to a ferromagnetic state at TC = 310 K, with the magnetic moments ordered parallel to the basal plane. From the specific heat measurements and the ferromagnetic solutions obtained from our DFT calculations, we conclude that the ferromagnetism is of itinerant nature.

Enhanced thermoelectric properties of selenium-deficient layered TiSe(2-x): a charge-density-wave material

In the present work, we report on the investigation of low-temperature (300-5 K) thermoelectric properties of hot-pressed TiSe2, a charge-density-wave (CDW) material. We demonstrate that, with increasing hot-pressing temperature, the density of TiSe2 increases and becomes nonstoichiometric owing to the loss of selenium. X-ray diffraction, scanning electron microscopy, and transimission electron microscopy results show that the material consists of a layered microstructure with several defects. Increasing the hot-press temperature in nonstoichiometric TiSe2 leads to a reduction of the resistivity and enhancement of the Seebeck coefficient in concomitent with suppression of CDW. Samples hot-pressed at 850 °C exhibited a minimum thermal conductivity (κ) of 1.5 W/m·K at 300 K that, in turn, resulted in a figure-of-merit (ZT) value of 0.14. This value is higher by 6 orders of magnitude compared to 1.49 × 10(-7) obtained for cold-pressed samples annealed at 850 °C. The enhancement of ZT in hot-pressed samples is attributed to (i) a reduced thermal conductivity owing to enhanced phonon scattering and (ii) improved power factor (α(2)σ).

Non-thermal separation of electronic and structural orders in a persisting charge density wave

The simultaneous ordering of different degrees of freedom in complex materials undergoing spontaneous symmetry-breaking transitions often involves intricate couplings that have remained elusive in phenomena as wide ranging as stripe formation, unconventional superconductivity or colossal magnetoresistance. Ultrafast optical, X-ray and electron pulses can elucidate the microscopic interplay between these orders by probing the electronic and lattice dynamics separately, but a simultaneous direct observation of multiple orders on the femtosecond scale has been challenging. Here we show that ultrabroadband terahertz pulses can simultaneously trace the ultrafast evolution of coexisting lattice and electronic orders. For the example of a charge density wave (CDW) in 1T-TiSe2, we demonstrate that two components of the CDW order parameter--excitonic correlations and a periodic lattice distortion (PLD)--respond very differently to 12-fs optical excitation. Even when the excitonic order of the CDW is quenched, the PLD can persist in a coherently excited state. This observation proves that excitonic correlations are not the sole driving force of the CDW transition in 1T-TiSe2, and exemplifies the sort of profound insight that disentangling strongly coupled components of order parameters in the time domain may provide for the understanding of a broad class of phase transitions.