Dimensional Effects on the Charge Density Waves in Ultrathin Films of TiSe2

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.

Titanium Self-Intercalation Induced Formation of Orthogonal (1 × 1) Edge/Surface Reconstruction in 1T-TiSe2: Atomic Scale Dynamics and Mechanistic Study

Edges and surfaces play indispensable roles in affecting the chemical-physical properties of materials, particularly in two-dimensional transition metal dichalcogenides (TMDCs) with reduced dimensionality. Herein, we report a novel edge/surface structure in multilayer 1T-TiSe2, i.e., the orthogonal (1 × 1) reconstruction, induced by the self-intercalation of Ti atoms into interlayer octahedral sites of the host TiSe2 at elevated temperature. Formation dynamics of the reconstructed edge/surface are captured at the atomic level by in situ scanning transmission electron microscopy (STEM) and further validated by density functional theory (DFT), which enables the proposal of the nucleation mechanism and two growth routes (zigzag and armchair). Via STEM-electron energy loss spectroscopy (STEM-EELS), a chemical shift of 0.6 eV in Ti L3,2 is observed in the reconstructed edge/surface, which is attributed to the change of the coordination number and lattice distortion. The present work provides insights to tailor the atomic/electronic structures and properties of 2D TMDC materials.

Fast and scalable quantum Monte Carlo simulations of electron-phonon models

We introduce methodologies for highly scalable quantum Monte Carlo simulations of electron-phonon models, and we report benchmark results for the Holstein model on the square lattice. The determinant quantum Monte Carlo (DQMC) method is a widely used tool for simulating simple electron-phonon models at finite temperatures, but it incurs a computational cost that scales cubically with system size. Alternatively, near-linear scaling with system size can be achieved with the hybrid Monte Carlo (HMC) method and an integral representation of the Fermion determinant. Here, we introduce a collection of methodologies that make such simulations even faster. To combat "stiffness" arising from the bosonic action, we review how Fourier acceleration can be combined with time-step splitting. To overcome phonon sampling barriers associated with strongly bound bipolaron formation, we design global Monte Carlo updates that approximately respect particle-hole symmetry. To accelerate the iterative linear solver, we introduce a preconditioner that becomes exact in the adiabatic limit of infinite atomic mass. Finally, we demonstrate how stochastic measurements can be accelerated using fast Fourier transforms. These methods are all complementary and, combined, may produce multiple orders of magnitude speedup, depending on model details.

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.

Semiconductor-Metal Phase Transition and Emergent Charge Density Waves in 1T-ZrX2 (X = Se, Te) at the Two-Dimensional Limit

A charge density wave (CDW) is a collective quantum phenomenon in metals and features a wavelike modulation of the conduction electron density. A microscopic understanding and experimental control of this many-body electronic state in atomically thin materials remain hot topics in materials physics. By means of material engineering, we realized a dimensionality and Zr intercalation induced semiconductor-metal phase transition in 1T-ZrX₂ (X = Se, Te) ultrathin films, accompanied by a commensurate 2 × 2 CDW order. Furthermore, we observed a CDW energy gap of up to 22 meV around the Fermi level. Fourier-transformed scanning tunneling microscopy and angle-resolved photoemission spectroscopy reveal that 1T-ZrX₂ films exhibit the simplest Fermi surface among the known CDW materials in TMDCs, consisting only of a Zr 4d derived elliptical electron conduction band at the corners of the Brillouin zone.

Magnetic Doping Induced Superconductivity-to-Incommensurate Density Waves Transition in a 2D Ultrathin Cr-Doped Mo2C Crystal

In the vicinity of a competing electronic order, superconductivity emerges within a superconducting dome in the phase diagram, which has been demonstrated in unconventional superconductors and transition-metal dichalcogenides (TMDs), suggesting a scenario where fluctuations or a partial melting of a parent order are essential for inducing superconductivity. Here, we present a contrary example, the two-dimensional (2D) superconductivity in transition-metal carbide can be readily turned into charge density wave (CDW) phases via dilute magnetic doping. Low temperature scanning tunneling microscopy/spectroscopy (STM/STS), transport measurements, and density functional theory (DFT) calculations were employed to investigate Cr-doped superconducting Mo₂C crystals in the 2D limit. With ultralow Cr doping (2.7 atom %), the superconductivity of Mo₂C is heavily suppressed. Strikingly, an incommensurate density wave (IDW) and a related partially opened gap are observed at a temperature above the superconducting regime. The wave vector of IDW agrees well with the calculated Fermi surface nesting vectors. By further increasing the Cr doping level to 9.4 atom %, a stronger IDW with a smaller periodicity and a larger partial gap appear concurrently. The resistance anomaly implies the onset of the CDW phase. Spatial-resolved and temperature-dependent spectroscopy reveals that such CDW phases exist only in a nonsuperconducting regime and could form long-range orders uniformly. The results provide the understanding for the interplay between charge ordered states and superconductivity in 2D transition-metal carbide.

Influence of the choice of precursors on the synthesis of two-dimensional transition metal dichalcogenides

The interest in transition metal dichalcogenides (TMDCs; MEy/2; M = transition metal; E = chalcogenide, y = valence of the metal) has grown exponentially across various science and engineering disciplines due to their unique structural chemistry manifested in a two-dimensional lattice that results in extraordinary electronic and transport properties desired for applications in sensors, energy storage and optoelectronic devices. Since the properties of TMDCs can be tailored by changing the stacking sequence of 2D monolayers with similar or dis-similar materials, a number of synthetic routes essentially based on the disintegration of bulk (e.g., chemical exfoliation) or the integration of atomic constituents (e.g., vapor phase growth) have been explored. Despite a large body of data available on the chemical synthesis of TMDCs, experimental strategies with high repeatability of control over film thickness, phase and compositional purity remain elusive, which calls for innovative synthetic concepts offering, for instance, self-limited growth in the z-direction and homogeneous lateral topography. This review summarizes the recent conceptual advancements in the growth of layered van der Waals TMDCs from both mixtures of metal and chalcogen sources (multi-source precursors; MSPs) and from molecular compounds containing metals and chalcogens in one starting material (single-source precursor; SSPs). The critical evaluation of the strengths, limitations and opportunities of MSP and SSP approaches is provided as a guideline for the fabrication of TMDCs from commercial and customized molecular precursors. For example, alternative synthetic pathways using tailored molecular precursors circumvent the challenges of differential nucleation and crystal growth kinetics that are invariably associated with conventional gas phase chemical vapor transport (CVT) and chemical vapor deposition (CVD) of a mixture of components. The aspects of achieving high compositional purity and alternatives to minimize competing reactions or side products are discussed in the context of efficient chemical synthesis of TMDCs. Moreover, a critical analysis of the potential opportunities and existing bottlenecks in the synthesis of TMDCs and their intrinsic properties is provided.

Enhanced photocurrent response speed in charge-density-wave phase of TiSe2-metal junctions

Group IVB transition metal dichalcogenides (TMDCs) have attracted significant attention due to their predicted high charge carrier mobility, large sheet current density, and enhanced thermoelectric power. Here, we investigate the electrical and optoelectronic properties of few-layer titanium diselenide (TiSe2)-metal junctions through spatial-, wavelength-, temperature-, power- and temporal-dependent scanning photocurrent measurements. Strong photocurrent responses have been detected at TiSe2-metal junctions, which is likely attributed to both photovoltaic and photothermoelectric effects. A fast response time of 31 μs has been achieved, which is two orders of magnitude better than HfSe2 based devices. More importantly, our experimental results reveal a significant enhancement in the response speed upon cooling to the charge-density-wave (CDW) phase transition temperature (TCDW = 206 K), which may result from dramatic reduction in carrier scattering that occurs as a result of the switching between the normal and CDW phases of TiSe2. Additionally, the photoresponsivity at 145 K is up to an order of magnitude higher than that obtained at room temperature. These fundamental studies not only offer insight for the photocurrent generation mechanisms of group IVB TMDC materials, but also provide a route to engineering future temperature-dependent, two-dimensional, fast electronic and optoelectronic devices.

Coherent Electronic Band Structure of TiTe2/TiSe2 Moiré Bilayer

A van der Waals bonded moiré bilayer formed by sequential growth of TiSe₂ and TiTe₂ monolayers exhibits emergent electronic structure as evidenced by angle-resolved photoemission band mapping. The two monolayers adopt the same lattice orientation but incommensurate lattice constants. Despite the lack of translational symmetry, sharp dispersive bands are observed. The dispersion relations appear distinct from those for the component monolayers alone. Theoretical calculations illustrate the formation of composite bands by coherent electronic coupling despite the weak interlayer bonding, which leads to band renormalization and energy shifts.

Experimental observations and density functional simulations on the structural transition behavior of a two-dimensional transition-metal dichalcogenide

In this work, we show an obvious evidence of nondestructive Raman spectra for the structural transition, i.e., the existence of a charge density wave (CDW) in monolayer 2H-TaS₂, which can exhibit a much higher transition temperature than bulk and results in additional vibrational modes, indicating strong interactions with light. Furthermore, we reveal that the degenerate breath and wiggle modes of 2H-TaS₂ originated from the periodic lattice distortion can be probed using the optical methods. Since recently several light-tunable devices have been proposed based on the CDW phase transition of 1 T-TaS₂, our study and in particular, the theoretical results will be very helpful for understanding and designing electronic devices based on the CDW of 2H-TaS₂.

Charge Instability in Single-Layer TiTe_{2} Mediated by van der Waals Bonding to Substrates

Single layers of transition metal dichalcogenides are of interest for emergent properties; an often-neglected issue is substrate effects. Our experiments show that the charge density wave in a single-layer TiTe_{2} grown on PtTe_{2} films is strongly suppressed by increasing the PtTe_{2} substrate thickness. Given that the interfacial bonding remains of the weak incommensurate van der Waals type, the observed changes are correlated with a thickness-dependent metallicity transformation in the PtTe_{2} substrate. The results illustrate the crucial role of the substrate in single-layer physics.

Charge density waves and degenerate modes in exfoliated monolayer 2H-TaS2

Charge density waves spontaneously breaking lattice symmetry through periodic lattice distortion, and electron-electron and electron-phonon inter-actions, can lead to a new type of electronic band structure. Bulk 2H-TaS2 is an archetypal transition metal dichalcogenide supporting charge density waves with a phase transition at 75 K. Here, it is shown that charge density waves can exist in exfoliated monolayer 2H-TaS2 and the transition temperature can reach 140 K, which is much higher than that in the bulk. The degenerate breathing and wiggle modes of 2H-TaS2 originating from the periodic lattice distortion are probed by optical methods. The results open an avenue to investigating charge density wave phases in two-dimensional transition metal dichalcogenides and will be helpful for understanding and designing devices based on charge density waves.

Anharmonicity and Doping Melt the Charge Density Wave in Single-Layer TiSe2

Low-dimensional systems with a vanishing band gap and a large electron-hole interaction have been proposed to be unstable toward exciton formation. As the exciton binding energy increases in low dimension, conventional wisdom suggests that excitonic insulators should be more stable in 2D than in 3D. Here we study the effects of the electron-hole interaction and anharmonicity in single-layer TiSe₂. We find that, contrary to the bulk case and to the generally accepted picture, in single-layer TiSe₂, the electron-hole exchange interaction is much smaller in 2D than in 3D and it has weak effects on phonon spectra. By calculating anharmonic phonon spectra within the stochastic self-consistent harmonic approximation, we obtain T_CDW ≈ 440 K for an isolated and undoped single layer and T_CDW ≈ 364 K for an electron-doping n = 4.6 × 10¹³ cm^-2, close to the experimental result of 200-280 K on supported samples. Our work demonstrates that anharmonicity and doping melt the charge density wave in single-layer TiSe₂.

Dimensionality-Mediated Semimetal-Semiconductor Transition in Ultrathin PtTe_{2} Films

Platinum ditelluride (PtTe_{2}), a type-II Dirac semimetal, remains semimetallic in ultrathin films down to just two triatomic layers (TLs) with a negative gap of -0.36  eV. Further reduction of the film thickness to a single TL induces a Lifshitz electronic transition to a semiconductor with a large positive gap of +0.79  eV. This transition is evidenced by experimental band structure mapping of films prepared by layer-resolved molecular beam epitaxy, and by comparing the data to first-principles calculations using a hybrid functional. The results demonstrate a novel electronic transition at the two-dimensional limit through film thickness control.

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.

The transformation of anatase TiO2 to TiSe2 to form TiO2–TiSe2 composites for Li+/Na+ storage with improved capacities

We discovered and explored the basic conditions for the conversion of TiO₂-A to TiSe₂ and tested its electrochemical performance.

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.

Unique Gap Structure and Symmetry of the Charge Density Wave in Single-Layer VSe_{2}

Single layers of transition metal dichalcogenides (TMDCs) are excellent candidates for electronic applications beyond the graphene platform; many of them exhibit novel properties including charge density waves (CDWs) and magnetic ordering. CDWs in these single layers are generally a planar projection of the corresponding bulk CDWs because of the quasi-two-dimensional nature of TMDCs; a different CDW symmetry is unexpected. We report herein the successful creation of pristine single-layer VSe_{2}, which shows a (sqrt[7]×sqrt[3]) CDW in contrast to the (4×4) CDW for the layers in bulk VSe_{2}. Angle-resolved photoemission spectroscopy from the single layer shows a sizable (sqrt[7]×sqrt[3]) CDW gap of ∼100  meV at the zone boundary, a 220 K CDW transition temperature twice the bulk value, and no ferromagnetic exchange splitting as predicted by theory. This robust CDW with an exotic broken symmetry as the ground state is explained via a first-principles analysis. The results illustrate a unique CDW phenomenon in the two-dimensional limit.

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.

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.

S-Doped TiSe2 Nanoplates/Fe3 O4 Nanoparticles Heterostructure

2D Sulfur-doped TiSe₂ /Fe₃ O₄ (named as S-TiSe₂ /Fe₃ O₄ ) heterostructures are synthesized successfully based on a facile oil phase process. The Fe₃ O₄ nanoparticles, with an average size of 8 nm, grow uniformly on the surface of S-doped TiSe₂ (named as S-TiSe₂ ) nanoplates (300 nm in diameter and 15 nm in thickness). These heterostructures combine the advantages of both S-TiSe₂ with good electrical conductivity and Fe₃ O₄ with high theoretical Li storage capacity. As demonstrated potential applications for energy storage, the S-TiSe₂ /Fe₃ O₄ heterostructures possess high reversible capacities (707.4 mAh g^-1 at 0.1 A g^-1 during the 100th cycle), excellent cycling stability (432.3 mAh g^-1 after 200 cycles at 5 A g^-1 ), and good rate capability (e.g., 301.7 mAh g^-1 at 20 A g^-1 ) in lithium-ion batteries. As for sodium-ion batteries, the S-TiSe₂ /Fe₃ O₄ heterostructures also maintain reversible capacities of 402.3 mAh g^-1 at 0.1 A g^-1 after 100 cycles, and a high rate capacity of 203.3 mAh g^-1 at 4 A g^-1 .

Emergence of charge density waves and a pseudogap in single-layer TiTe2

Two-dimensional materials constitute a promising platform for developing nanoscale devices and systems. Their physical properties can be very different from those of the corresponding three-dimensional materials because of extreme quantum confinement and dimensional reduction. Here we report a study of TiTe₂ from the single-layer to the bulk limit. Using angle-resolved photoemission spectroscopy and scanning tunneling microscopy and spectroscopy, we observed the emergence of a (2 × 2) charge density wave order in single-layer TiTe₂ with a transition temperature of 92 ± 3 K. Also observed was a pseudogap of about 28 meV at the Fermi level at 4.2 K. Surprisingly, no charge density wave transitions were observed in two-layer and multi-layer TiTe₂, despite the quasi-two-dimensional nature of the material in the bulk. The unique charge density wave phenomenon in the single layer raises intriguing questions that challenge the prevailing thinking about the mechanisms of charge density wave formation.

Due to reduced dimensionality, the properties of 2D materials are often different from their 3D counterparts. Here, the authors identify the emergence of a unique charge density wave (CDW) order in monolayer TiTe₂ that challenges the current understanding of CDW formation.

Angle-resolved photoemission spectroscopy for the study of two-dimensional materials

Quantum systems in confined geometries allow novel physical properties that cannot easily be attained in their bulk form. These properties are governed by the changes in the band structure and the lattice symmetry, and most pronounced in their single layer limit. Angle-resolved photoemission spectroscopy (ARPES) is a direct tool to investigate the underlying changes of band structure to provide essential information for understanding and controlling such properties. In this review, recent progresses in ARPES as a tool to study two-dimensional atomic crystals have been presented. ARPES results from few-layer and bulk crystals of material class often referred as “beyond graphene” are discussed along with the relevant developments in the instrumentation.