Charge Density Wave Structure Research Articles

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

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

In operando cryo-STEM of pulse-induced charge density wave switching in TaS2

The charge density wave material 1T-TaS2 exhibits a pulse-induced insulator-to-metal transition, which shows promise for next-generation electronics such as memristive memory and neuromorphic hardware. However, the rational design of TaS2 devices is hindered by a poor understanding of the switching mechanism, the pulse-induced phase, and the influence of material defects. Here, we operate a 2-terminal TaS2 device within a scanning transmission electron microscope at cryogenic temperature, and directly visualize the changing charge density wave structure with nanoscale spatial resolution and down to 300 μs temporal resolution. We show that the pulse-induced transition is driven by Joule heating, and that the pulse-induced state corresponds to the nearly commensurate and incommensurate charge density wave phases, depending on the applied voltage amplitude. With our in operando cryogenic electron microscopy experiments, we directly correlate the charge density wave structure with the device resistance, and show that dislocations significantly impact device performance. This work resolves fundamental questions of resistive switching in TaS2 devices, critical for engineering reliable and scalable TaS2 electronics.

The Structure of Charge Density Waves in TaS2 across Temperature and Dimensionality.

The Structure of Charge Density Waves in TaS2 across Temperature and Dimensionality.

Charge density wave-templated spin cycloid in topological semimetal NdSbxTe2−x−δ

Magnetic topological semimetals present open questions regarding the interplay of crystal symmetry, magnetism, band topology, and electron correlations. Ln${\mathrm{Sb}}_{x}{\mathrm{Te}}_{2\text{\ensuremath{-}}x\text{\ensuremath{-}}\ensuremath{\delta}}$ (Ln denotes Lanthanide) is a family of square-net-derived topological semimetals that allows compositional control of band filling, and access to different topological states via an evolving charge density wave (CDW) distortion. Previously studied Gd and Ce members containing a CDW have shown complex magnetic phase diagrams, which implied that spins localized on Ln interact with the CDW, but to this date no magnetic structures have been solved within the CDW regime of this family of compounds. Here, we report on the interplay of the CDW with magnetism in ${\mathrm{NdSb}}_{x}{\mathrm{Te}}_{2\text{\ensuremath{-}}x\text{\ensuremath{-}}\ensuremath{\delta}}$ by comparing the undistorted square net member ${\mathrm{NdSb}}_{0.94}{\mathrm{Te}}_{0.92}$ with the CDW-distorted phase ${\mathrm{NdSb}}_{0.48}{\mathrm{Te}}_{1.37}$, via single-crystal x-ray diffraction, magnetometry, heat capacity, and neutron powder diffraction. ${\mathrm{NdSb}}_{0.94}{\mathrm{Te}}_{0.92}$ is a collinear antiferromagnet with ${T}_{N}\ensuremath{\sim}2.7\phantom{\rule{4pt}{0ex}}\mathrm{K}$, where spins align antiparallel to each other, but parallel to the square net of the nuclear structure. ${\mathrm{NdSb}}_{0.48}{\mathrm{Te}}_{1.37}$ exhibits a nearly fivefold-modulated CDW (${q}_{\text{CDW}}=0.18$), isostructural to other Ln${\mathrm{Sb}}_{x}{\mathrm{Te}}_{2\text{\ensuremath{-}}x\text{\ensuremath{-}}\ensuremath{\delta}}$ at similar $x$. ${\mathrm{NdSb}}_{0.48}{\mathrm{Te}}_{1.37}$ displays more complex magnetism with ${T}_{N}=2.3\phantom{\rule{0.28em}{0ex}}\mathrm{K}$, additional metamagnetic transitions, and an elliptical cycloid magnetic structure with ${q}_{\text{mag}}=\ensuremath{-}0.41{\mathrm{b}}^{*}$. The magnitudes of ${q}_{\text{CDW}}$ and ${q}_{\text{mag}}$ exhibit an integer relationship, $1+2{q}_{\text{mag}}={q}_{\text{CDW}}$, implying a coupling between the CDW and magnetic structure. Given that the CDW is localized within the nonmagnetic distorted square net, we propose that conduction electrons ``template'' the spin modulation via the Ruderman-Kittel-Kasuya-Yosida interaction.

Emergent charge density wave featuring quasi-one-dimensional chains in Ta-intercalated bilayer 2H−TaS2 with coexisting superconductivity

Recently, intercalation emerges as an effective way to manipulate ground-state properties and enrich quantum phase diagrams of layered transition metal dichalcogenides (TMDCs). In this work, we focus on fully Ta-intercalated bilayer $2H\text{\ensuremath{-}}{\mathrm{TaS}}_{2}$ with a stoichiometry of ${\mathrm{Ta}}_{3}{\mathrm{S}}_{4}$, which has recently been experimentally synthesized. Based on first-principles calculations, we computationally show the suppression of an intrinsic $3\ifmmode\times\else\texttimes\fi{}3$ charge-density wave (CDW) in the ${\mathrm{TaS}}_{2}$ layer, and the emergence of a $2\ifmmode\times\else\texttimes\fi{}1$ CDW in intercalated Ta layer. The formation of the CDW in ${\mathrm{Ta}}_{3}{\mathrm{S}}_{4}$ is triggered by strong electron-phonon coupling (EPC) between the $d$-like orbitals of intercalated Ta atoms via the imaginary phonon modes at $M$ point. A $2\ifmmode\times\else\texttimes\fi{}1$ CDW structure is identified, featuring quasi-one-dimensional Ta chains, attributable to the competition between the CDW displacements associated with potential CDW vectors (${\mathbit{q}}_{\text{CDW}}\mathrm{s}$). Superconductivity is found to coexist with the $2\ifmmode\times\else\texttimes\fi{}1$ CDW in ${\mathrm{Ta}}_{3}{\mathrm{S}}_{4}$, with an estimated superconducting transition temperature (${T}_{\mathrm{c}}$) of 3.0 K, slightly higher than that of bilayer ${\mathrm{TaS}}_{2}$. The ${\mathrm{Ta}}_{3}{\mathrm{S}}_{4}$ structures of non-CDW, $2\ifmmode\times\else\texttimes\fi{}1$ CDW, and $2\ifmmode\times\else\texttimes\fi{}2$ CDW can be switched by strain. Our work enriches the phase diagram of ${\mathrm{TaS}}_{2}$, offers a candidate material for studying the interplay between CDW and superconductivity, and highlights intercalation as an effective way to tune the physical properties of layered materials.

Charge density wave and superconductivity in the kagome metal CsV3Sb5 around a pressure-induced quantum critical point

Using first-principles density functional theory calculations, we investigate the pressure-induced quantum phase transition (QPT) from the charge density wave (CDW) to the pristine phase in the layered kagome metal CsV$_3$Sb$_5$ consisting of three-atom-thick Sb$-$V$_3$Sb$-$Sb and one-atom-thick Cs layers. The CDW structure having the formation of trimeric and hexameric V atoms with buckled Sb honeycomb layers features an increase in the lattice parameter along the $c$ axis, compared to its counterpart pristine structure having the ideal V$_3$Sb kagome and planar Sb honeycomb layers. Consequently, as pressure increases, the relatively smaller volume of the pristine phase contributes to reducing the enthalpy difference between the CDW and pristine phases, yielding a pressure-induced QPT at a critical pressure $P_c$ of ${\sim}$2 GPa. Furthermore, we find that (i) the superconducting transition temperature $T_c$ increases around $P_c$ due to a phonon softening associated with the periodic lattice distortion of V trimers and hexamers and that (ii) above $P_c$, optical phonon modes are hardened with increasing pressure, leading to monotonous decreases in the electron-phonon coupling constant and $T_c$. Our findings not only demonstrate that the uniaxial strain along the $c$ axis plays an important role in the QPT observed in CsV$_3$Sb$_5$, but also provide an explanation for the observed superconductivity around $P_c$ in terms of a phonon-mediated superconducting mechanism.

Competing magnetic and nonmagnetic states in monolayer VSe2 with charge density wave

The field of two-dimensional ferromagnets has been reinvigorated by the discovery of ${\mathrm{VSe}}_{2}$ monolayer grown on van der Waals substrates, which is reported to be ferromagnetic with a Curie point higher than 330 K. However, the ferromagnetic and nonmagnetic states of pristine monolayer ${\mathrm{VSe}}_{2}$ are highly debated. Here, employing density functional theory, Wannier function calculations, and the band unfolding method, we explore the electronic structure of monolayer ${\mathrm{VSe}}_{2}$ with a $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{7}$ charge density wave (CDW). Certain qualitative aspects of the calculated unfolded band dispersion and unfolded Fermi surface of monolayer ${\mathrm{VSe}}_{2}$ with the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{7}$ CDW in the nonmagnetic state agree well with previous angle-resolved photoemission spectroscopy results, albeit with uncertainty about whether these experiments probed single or multiple domains. Specifically, we find that an isolated CDW domain naturally induces a strong breaking of the threefold symmetry of the electronic structure. In addition we find that, relative to the undistorted structure, the CDW structure shows a strong competition between nonmagnetic and various magnetic states, with an energy difference less than 5 meV/f.u. For the CDW structure in the antiferromagnetic state, the band dispersions and Fermi surface are similar to those in the nonmagnetic state, while the unfolded bands of the ferromagnetic CDW state display a sizable exchange splitting. These results indicate the possibility of various antiferromagnetic fluctuations in ${\mathrm{VSe}}_{2}$ to coexist and compete with ferromagnetic order and the experimentally reported CDW order. Our calculations build insights for exploring the interplay between magnetism and CDW behaviors more generally in transition metal dichalcogenides.

Charge Density Wave Order and Fluctuations above T_{CDW} and below Superconducting T_{c} in the Kagome Metal CsV_{3}Sb_{5}.

The phase diagram of the kagome metal family AV_{3}Sb_{5} (A=K, Rb, Cs) features both superconductivity and charge density wave (CDW) instabilities, which have generated tremendous recent attention. Nonetheless, significant questions remain. In particular, the temperature evolution and demise of the CDW state has not been extensively studied, and little is known about the coexistence of the CDW with superconductivity at low temperatures. We report an x-ray scattering study of CsV_{3}Sb_{5} over a broad range of temperatures from 300 to ∼2 K, below the onset of its superconductivity at T_{c}∼2.9 K. Order parameter measurements of the 2×2×2 CDW structure show an unusual and extended linear temperature dependence onsetting at T^{*}∼160 K, much higher than the susceptibility anomaly associated with CDW order at T_{CDW}=94 K. This implies strong CDW fluctuations exist to ∼1.7×T_{CDW}. The CDW order parameter is observed to be constant from T=16 to 2K, implying that the CDW and superconducting order coexist below T_{c}, and, at ambient pressure, any possible competition between the two order parameters is manifested at temperatures well below T_{c}, if at all. Anomalies in the temperature dependence in the lattice parameters coincide with T_{CDW} for c(T) and with T^{*} for a(T).

Insulator-to-metal transition in ultrathin rutile VO2/TiO2(001)

An insulator-to-metal transition (IMT) is an emergent characteristic of quantum materials. When the IMT occurs in materials with interacting electronic and lattice degrees of freedom, it is often difficult to determine if the energy gap in the insulating state is formed by Mott electron–electron correlation or by Peierls charge-density wave (CDW) ordering. To solve this problem, we investigate a representative material, vanadium dioxide (VO2), which exhibits both strong electron–electron interaction and CDW ordering. For this research, VO2 films of different thicknesses on rutile (001) TiO2 substrates have been fabricated. X-ray diffraction (XRD) data show that ultrathin VO2 films with thickness below 7.5 nm undergo the IMT between rutile insulator below Tc and rutile metal above Tc, while an ultrathin VO2 film with a thickness of 8 nm experiences the structural phase transition from the monoclinic structure below Tc to the rutile structure above Tc. Infrared and optical measurements on a film of 7.2 nm thickness, below Tc, reveal the energy gap of 0.6 eV in the rutile insulator phase and the absence of the 2.5 eV bonding-antibonding CDW structure. Above Tc, a Drude feature in the optical conductivity reveals the IMT to a metallic phase. These results suggest that for VO2 films below a critical thickness of about 7.5 nm, the IMT occurs in the rutile structure of VO2 without the Peierls lattice distortion.

Intrinsic and doping-enhanced superconductivity in monolayer 1H−TaS2 : Critical role of charge ordering and spin-orbit coupling

The interplay of superconductivity with charge density wave (CDW) in metallic transition-metal dichalcogenides has been widely debated, and viable strategies manipulating these quantum states in the two-dimensional (2D) limit remain unclear. Using the ab initio anisotropic Migdal-Eliashberg theory, we successfully explain the superconductivity observed in monolayer $1H\text{\ensuremath{-}}{\mathrm{TaS}}_{2}$ by simultaneously determining its precise CDW structure and treating the marked modification of electron-phonon interaction and critical temperature ${T}_{\mathrm{c}}$ by spin-orbit coupling effects. With this paradigm, we further show that electron doping weakens the CDW order leading to increased ${T}_{\mathrm{c}}$ up to 11 K, along with a single-gap to two-gap superconductivity transition due to the suppression of the CDW gap. By contrast, a low hole doping barely affects the CDW but still yields a significantly enhanced superconducting order, implying their good coexistence. Combined with the synergistic behavior of CDW and superconductivity, which cooperate upon ${\mathrm{TaS}}_{2}$ thickness reduction causing an unusual rise of ${T}_{\mathrm{c}}$, our results unravel diversified interactions between the two collective orders in ultrathin ${\mathrm{TaS}}_{2}$, being competition, coexistence or cooperation depending on external stimuli, which provide key clues for controlling correlated states in devices based on 2D CDW superconductors.

Realization of Coexisting Charge Density Wave and Quantum Spin/Anomalous Hall State in Monolayer NbTe2

AbstractThe combination of nontrivial topology and charge density wave (CDW) has been proposed as a powerful resource for realizing novel quantum phenomena such as axion electrodynamics and the anomalous Hall effect. Hence, topological materials with CDW states attract great interest, yet they are still very rare, particularly in the 2D limit. Here, it is predicted that monolayer NbTe2 in its high‐symmetry 1T phase stabilized by anharmonicity at room temperature exhibits nontrivial topology sensitive to electronic interactions: it changes from a quantum spin Hall (QSH) state to a quantum anomalous Hall (QAH) state when the Hubbard potential U exceeds a critical value. At low temperature, a 4 × 4 CDW order emerges and coexists with the nontrivial topology. Meanwhile, the critical U increases because CDW reduces density of states at Fermi level. More interestingly, in contrast to the high‐symmetry structure that actually is a topologically nontrivial metal, the CDW structure shows an insulating nontrivial gap either in the QSH or the QAH phase, indicating CDW is an effective means to modulate the topological state for developing new functions and devices. These discoveries establish NbTe2 as a promising candidate to explore exotic quantum states at the confluence of nontrivial topology, electronic correlation, and CDW.

Quantum phases and spin liquid properties of 1T-TaS2

Quantum materials exhibiting magnetic frustration are connected to diverse phenomena, including high Tc superconductivity, topological order, and quantum spin liquids (QSLs). A QSL is a quantum phase (QP) related to a quantum-entangled fluid-like state of matter. Previous experiments on QSL candidate materials are usually interpreted in terms of a single QP, although theories indicate that many distinct QPs are closely competing in typical frustrated spin models. Here we report on combined temperature-dependent muon spin relaxation and specific heat measurements for the triangular-lattice QSL candidate material 1T-TaS2 that provide evidence for competing QPs. The measured properties are assigned to arrays of individual QSL layers within the layered charge density wave structure of 1T-TaS2 and their characteristic parameters can be interpreted as those of distinct Z2 QSL phases. The present results reveal that a QSL description can extend beyond the lowest temperatures, offering an additional perspective in the search for such materials.

Origin of the large magnetoresistance in the candidate chiral superconductor 4Hb−TaS2

The intriguing electronic phase diagram involving charge density wave (CDW) transitions in the $\mathrm{Ta}{\mathrm{S}}_{2}$ system has been widely investigated over the past decade, especially for the $1T$ and $2H$ phases. $4{H}_{b}\text{\ensuremath{-}}\mathrm{Ta}{\mathrm{S}}_{2}$, regarded as the natural heterostructure that combines the characteristics of $1T$ and $2H\text{\ensuremath{-}}\mathrm{Ta}{\mathrm{S}}_{2}$, has also been the focus recently, due to the prospects for fundamental research and device applications. Here, we have systematically investigated the electrical transport properties of $4{H}_{b}\text{\ensuremath{-}}\mathrm{Ta}{\mathrm{S}}_{2}$ single crystals combined with the band structure calculations and found that the low-temperature phase of candidate chiral superconductor $4{H}_{b}\text{\ensuremath{-}}\mathrm{Ta}{\mathrm{S}}_{2}$ (${T}_{c}\ensuremath{\sim}3.5$ K) at normal state is not the simple CDW but exhibits a strong magnetic field dependence. The most significant result is the emergence of the large magnetoresistance (MR), which may originate from the high mobility of holes and partial compensation. In addition, the symmetry of MR under the low magnetic field has also changed significantly in $4{H}_{b}\text{\ensuremath{-}}\mathrm{Ta}{\mathrm{S}}_{2}$, which is closely related to the CDW structures formed in the $H$ layers at 22 K. The results are conducive to the understanding of the mechanism of MR appearing in layered CDW compounds, and the presence of MR in $4{H}_{b}\text{\ensuremath{-}}\mathrm{Ta}{\mathrm{S}}_{2}$ suggests the potential applications for functional devices in the future.

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.

Atomic-Scale Chemical Conversion of Single-Layer Transition Metal Dichalcogenides.

Chemical conversion by atomic substitution offers a powerful route toward the creation of unusual structures and functionalities. Here, we demonstrate the progressive transformation of single-layer TiTe2 into TiSe2 by reaction with a Se flux in vacuum. Angle-resolved photoemission spectroscopy and scanning tunneling microscopy reveal intriguing reaction patterns involving TiSe2 island ingrowth starting from the TiTe2 island edges, while the band structure and core level signatures of TiSe2 grow in intensity at the expense of those corresponding to TiTe2. Lattice mismatch between TiTe2 and TiSe2 results in misfit holes and lattice distortions over a distance behind a seamless fingerlike reaction front. The regions of TiSe2 and TiTe2 are distinguished by a height difference and a charge density wave (CDW) at different transition temperatures. The method of in situ chemical conversion offers opportunities for atomic-scale engineering of layered transition metal dichalcogenides that host useful properties arising from CDW, Dirac, Weyl, superconducting, spin-valley, and magnetic structures.

Tunable phase transition in single-layer TiSe2 via electric field

Phase transition represents an intriguing physical phenomenon that exists in a number of single-layer transition-metal dichalcogenides. This phenomenon often occurs below a critical temperature and breaks the long-range crystalline order leading to a reconstructed superstructure called the charge-density wave (CDW) structure, which can therefore be recovered by external stimuli such as temperature. Alternatively, we show here that another external stimulation, electric field can also result in the phase transition between the regular and CDW structures of a single-layer transition-metal dichalcogenide. We used single-layer TiSe2 as an example to elucidate the mechanism of the CDW followed by calculations of the electronic structure using a hybrid density functional. We found that applying electric field can tune the phase transition between the 1T and CDW phases of single-layer TiSe2. Our work opens up a route of tuning the phase transition of single-layer materials via electric field.

First principles analysis of the CDW instability of single-layer 1T-TiSe2 and its evolution with charge carrier density

We present a density functional theory study of the electronic structure of single-layer TiSe2, and focus on the charge density wave (CDW) instability present on this 2D material. We explain the periodicity of the CDW from the phonon band structure of the undistorted crystal, which is unstable under one of the phonon modes at the M point. This can be understood in terms of a partial band gap opening at the Fermi level, which we describe on the basis of the symmetry of the involved crystal orbitals, leading to an energy gain upon the displacement of the atoms following the phonon mode in a 2 × 1 structure. Furthermore, the combination of the corresponding phonons for the three inequivalent M points of the Brillouin zone leads to the 2 × 2 distortion characteristic of the CDW state. This leads to a further opening of a full gap, which reduces the energy of the 2 × 2 structure compared to the 2 × 1 one of a single M point phonon, and makes the CDW structure the most stable one. We also analyze the effect of charge injection into the layer on the structural instability. We predict that the 2 × 2 structure only survives for a certain range of doping levels, both for electrons and for holes, as doping reduces the energy gain due to the gap opening. We predict the transition from the commensurate 2 × 2 distortion to an incommensurate one with increasing wavelength upon increasing the doping level, followed by the appearance of the undistorted 1 × 1 structure for larger carrier concentrations.

Dynamic instabilities in strongly correlated VSe2 monolayers and bilayers

With the emergence of graphene and other two-dimensional (2D) materials, transition-metal dichalcogenides have been investigated intensely as potential 2D materials using experimental and theoretical methods. ${\mathrm{VSe}}_{2}$ is an especially interesting material since its bulk modification exhibits a charge-density wave (CDW), the CDW is retained even for few-layer nanosheets, and monolayers of ${\mathrm{VSe}}_{2}$ are predicted to be ferromagnetic. In this work, we show that electron correlation has a profound effect on the magnetic properties and dynamic stability of ${\mathrm{VSe}}_{2}$ monolayers and bilayers. Including a Hubbard-$U$ term in the density-functional-theory calculations strongly affects the magnetocrystalline anisotropy in the $1T\ensuremath{-}{\mathrm{VSe}}_{2}$ structure while leaving the $2H$-polytype virtually unchanged. This demonstrates the importance of electronic correlations for the electrical and magnetic properties of $1T\ensuremath{-}{\mathrm{VSe}}_{2}$. The Hubbard-$U$ term changes the dynamic stability and the presence of imaginary modes of ferromagnetic $1T\ensuremath{-}{\mathrm{VSe}}_{2}$ while affecting only the amplitudes in the nonmagnetic phase. The Fermi surface of nonmagnetic $1T\ensuremath{-}{\mathrm{VSe}}_{2}$ allows for nesting along the CDW vector, but it plays no role in ferromagnetic $1T\ensuremath{-}{\mathrm{VSe}}_{2}$. Following the eigenvectors of the soft modes in nonmagnetic $1T\ensuremath{-}{\mathrm{VSe}}_{2}$ monolayers yields a CDW structure with a $4\ifmmode\times\else\texttimes\fi{}4$ supercell and Peierls-type distortion in the atomic positions and electronic structure. The magnetic order indicates the potential for spin-density-wave structures.

Doping-controlled phase transitions in single-layer MoS2

The electronic properties of single-layer ${\mathrm{MoS}}_{2}$ make it an ideal two-dimensional (2D) material for application in electronic devices. Experiments show that ${\mathrm{MoS}}_{2}$ can undergo structural phase transitions. Applications of single-layer ${\mathrm{MoS}}_{2}$ will require firm laboratory control over the phase formation. Here we compare the stability and electronic structure of the three experimentally observed single-layer ${\mathrm{MoS}}_{2}$ phases, $2H,\phantom{\rule{0.28em}{0ex}}1T$, and $1{T}^{\ensuremath{'}}$, and an in-plane metal/semiconductor heterostructure. We reveal by density-functional theory calculations that charge doping can induce the phase transition of single-layer ${\mathrm{MoS}}_{2}$ from the $2H$ to the $1T$ structure. Further, the $1T$ structure undergoes a second phase transition due to the occurrence of a charge-density wave (CDW). By comparing the energies of several possible resulting CDW structures, we find that the $1{T}^{\ensuremath{'}}$ orthorhombic structure is the most stable one, consistent with experimental observations and previous theoretical studies. We show that the underlying CDW transition mechanism is not due to Fermi surface nesting, but nonetheless, can be controlled by charge doping. In addition, the stability landscape is highly sensitive to charge doping, which can be used as a practical phase selector. We also provide a prescription for obtaining the $1{T}^{\ensuremath{'}}$ structure via growth or deposition of ${\mathrm{MoS}}_{2}$ on a Hf substrate, which transfers electrons uniformly and with minimal structural distortion. Finally, we show that lateral heterostructures formed by the $2H$ and $1{T}^{\ensuremath{'}}$ structures exhibit a low interfacial energy of 0.17 eV/\AA{}, a small Schottky barrier of 0.3 eV for holes, and a large barrier of 1.6 eV for electrons.

Strain Engineering a 4a×√3a Charge Density Wave Phase in Transition Metal Dichalcogenide 1T-VSe2.

We report a rectangular charge density wave (CDW) phase in strained 1T-VSe2 thin films synthesized by molecular beam epitaxy on c-sapphire substrates. The observed CDW structure exhibits an unconventional rectangular 4a×√3a periodicity, as opposed to the previously reported hexagonal 4a×4a structure in bulk crystals and exfoliated thin layered samples. Tunneling spectroscopy shows a strong modulation of the local density of states of the same 4a×√3a CDW periodicity and an energy gap of 2ΔCDW = (9.1 ± 0.1) meV. The CDW energy gap evolves into a full gap at temperatures below 500 mK, indicating a transition to an insulating phase at ultra-low temperatures. First-principles calculations confirm the stability of both 4a×4a and 4a×√3a structures arising from soft modes in the phonon dispersion. The unconventional structure becomes preferred in the presence of strain, in agreement with experimental findings.