Commensurate Charge Density Wave Research Articles

Locally commensurate charge-density wave with three-unit-cell periodicity in YBa2Cu3Oy

In order to identify the mechanism responsible for the formation of charge-density waves (CDW) in cuprate superconductors, it is important to understand which aspects of the CDW’s microscopic structure are generic and which are material-dependent. Here, we show that, at the local scale probed by NMR, long-range CDW order in YBa2Cu3Oy is unidirectional with a commensurate period of three unit cells (λ = 3b), implying that the incommensurability found in X-ray scattering is ensured by phase slips (discommensurations). Furthermore, NMR spectra reveal a predominant oxygen character of the CDW with an out-of-phase relationship between certain lattice sites but no specific signature of a secondary CDW with λ = 6b associated with a putative pair-density wave. These results shed light on universal aspects of the cuprate CDW. In particular, its spatial profile appears to generically result from the interplay between an incommensurate tendency at long length scales, possibly related to properties of the Fermi surface, and local commensuration effects, due to electron-electron interactions or lock-in to the lattice.

Room temperature depinning of the charge-density waves in quasi-two-dimensional 1T-TaS2 devices

We report on the depinning of nearly commensurate charge-density waves in 1T-TaS2 thin films at room temperature. A combination of the differential current–voltage measurements with the low-frequency noise spectroscopy provides unambiguous means for detecting the depinning threshold field in quasi-2D materials. The depinning process in 1T-TaS2 is not accompanied by an observable abrupt increase in electric current—in striking contrast to depinning in the conventional charge-density-wave materials with quasi-1D crystal structure. We explained it by the fact that the current density from the charge-density waves in the 1T-TaS2 devices is orders of magnitude smaller than the current density of the free carriers available in the discommensuration network surrounding the commensurate charge-density wave islands. The depinning fields in 1T-TaS2 thin-film devices are several orders of magnitude larger than those in quasi-1D van der Waals materials. Obtained results are important for the proposed applications of the charge-density wave devices in electronics.

Strongly coupled charge, orbital, and spin order in TbTe3

We report a ground state with strongly coupled magnetic and charge density wave orders mediated via orbital ordering in the layered compound \tbt. In addition to the commensurate antiferromagnetic (AFM) and charge density wave (CDW) orders, new magnetic peaks are observed whose propagation vector equals the sum of the AFM and CDW propagation vectors, revealing an intricate and highly entwined relationship. This is especially interesting given that the magnetic and charge orders lie in different layers of the crystal structure where the highly localized magnetic moments of the Tb$^{3+}$ ions are netted in the Tb-Te stacks, while the charge order is formed by the conduction electrons of the adjacent Te-Te layers. Our results, based on neutron diffraction and resonant x-ray scattering reveal that the charge and magnetic subsystems mutually influence each other via the orbital ordering of Tb$^{3+}$ ions.

Enhanced anisotropic superconductivity in the topological nodal-line semimetal InxTaS2

Coexistence of topological bands and a charge density wave (CDW) in topological materials has attracted immense attention because of their fantastic properties, such as an axionic CDW, the three-dimensional quantum Hall effect, etc. In this work, the nodal-line semimetal ${\mathrm{In}}_{x}{\mathrm{TaS}}_{2}$ characterized by a CDW and superconductivity is successfully synthesized, whose structure and topological bands (two separated Weyl rings) are similar to ${\mathrm{In}}_{0.58}{\mathrm{TaSe}}_{2}$. A $2\ifmmode\times\else\texttimes\fi{}2$ commensurate CDW is observed at low temperature in ${\mathrm{In}}_{x}{\mathrm{TaS}}_{2}$, identified by transport properties and scanning tunneling microscopy measurements. Moreover, superconductivity emerges below 0.69 K, and the anisotropy ratio of the upper critical field $[\mathrm{\ensuremath{\Gamma}}={H}_{c2}^{||ab}(0)/{H}_{c2}^{||c}(0)]$ is significantly enhanced compared to 2H-${\mathrm{TaS}}_{2}$, which shares the same essential layer unit. According to the Lawrence-Doniach model, the enhanced $\mathrm{\ensuremath{\Gamma}}$ may be explained by the reduced effective mass in the ${k}_{x}\text{\ensuremath{-}}{k}_{y}$ plane, where Weyl rings locate. Therefore, this type of layered topological systems may offer a platform to investigate highly anisotropic superconductivity and to understand the extremely large upper critical field in the bulk or in the two-dimensional limit.

Layer-dependent charge density wave phase transition stiffness in 1T-TaS2 nanoflakes evidenced by ultrafast carrier dynamics

Novel physical properties emerge when the thickness of charge density wave (CDW) materials is reduced to the atomic level, owing to the significant modification of the electronic band structure and correlation effects. Here, we investigate the layer-dependent CDW phase transition and evolution of the nonequilibrium state of 1T-TaS2 nanoflakes using pump-probe spectroscopy. Both the low-energy single-particle and collective excitation relaxations exhibit sharp changes at ~ 210 K, indicating a phase transition from commensurate CDW to nearly commensurate CDW state. The single particle process reveals that the phase transition stiffness (PTS) is thickness-dependent. Moreover, a small PTS is observed in thin nanoflakes, which is attributed to the reduced thickness that increases the fluctuation and inhibits the nucleation and growth of discommensurations. In addition, the phase mode vanishes when the discommensuration network appears. Our results suggest that the carrier dynamics could be an efficient operational approach to measuring the quantum phase transition in correlated materials.

Charge density wave instability and pressure-induced superconductivity in bulk 1T−NbS2

Charge-density-wave (CDW) instability and pressure-induced superconductivity in bulk 1T-NbS2 are predicted theoretically by first-principles calculations. We reveal a CDW instability towards the formation of a stable commensurate CDW order, resulting in a sqart(13)*sqart(13) structural reconstruction featured with star-of-David clusters. The CDW phase exhibits one-dimensional metallic behavior with in-plane flat-band characteristics, and coexists with an orbital-density-wave order predominantly contributed by 4d_(z^2-r^2 ) orbital from the inner Nb atoms of the star-of-David cluster. By doubling the cell of the CCDW phase along the layer stacking direction, a metal-insulator transition may be realized in the CDW phase in case the interlayer antiferromagnetic ordering and Coulomb correlation effect have been considered simultaneously. Bare electron susceptibility, phonon linewidth and electron-phonon coupling calculations suggest that the CDW instability is driven by softened phonon modes due to the strong electron-phonon coupling interactions. CDW order can be suppressed by pressure, concomitant with appearance of superconductivity. Our theoretical predictions call for experimental investigations to further clarify the transport and magnetic properties of 1T-NbS2. Furthermore, it would also be very interesting to explore the possibility to realize the CDW order coexisting with the superconductivity in bulk 1T-NbS2.

Phase‐Dependent Band Gap Engineering in Alloys of Metal‐Semiconductor Transition Metal Dichalcogenides

AbstractBandgap engineering plays a critical role in optimizing the electrical, optical and (photo)‐electrochemical applications of semiconductors. Alloying has been a historically successful way of tuning bandgaps by making solid solutions of two isovalent semiconductors. In this work, a novel form of bandgap engineering involving alloying non‐isovalent cations in a 2D transition metal dichalcogenide (TMDC) is presented. By alloying semiconducting MoSe2 with metallic NbSe2, two structural phases of Mo0.5Nb0.5Se2, the 1T and 2H phases, are produced each with emergent electronic structure. At room temperature, it is observed that the 1T and 2H phases are semiconducting and metallic, respectively. For the 1T structure, scanning tunneling microscopy/spectroscopy (STM/STS) is used to measure band gaps in the range of 0.42–0.58 at 77 K. Electron diffraction patterns of the 1T structure obtained at room temperature show the presence of a nearly commensurate charge density wave (NCCDW) phase with periodic lattice distortions that result in an uncommon 4 × 4 supercell, rotated approximately 4° from the lattice. Density‐functional‐theory calculations confirm that local distortions, such as those in a NCCDW, can open up a band gap in 1T‐Mo0.5Nb0.5Se2, but not in the 2H phase. This work expands the boundaries of alloy‐based bandgap engineering by introducing a novel technique that facilitates CDW phases through alloying.

Anisotropic gapping of topological Weyl rings in the charge-density-wave superconductor InxTaSe2

Topological materials and topological phases have recently become a hot topic in condensed matter physics. In this work, we report an In-intercalated transition-metal dichalcogenide InxTaSe2 (named 112 system), a topological nodal-line semimetal in the presence of both charge density wave (CDW) and superconductivity. In the x = 0.58 sample, the 2×3 commensurate CDW (CCDW) and the 2×2 CCDW are observed below 116 and 77 K, respectively. Consistent with theoretical calculations, the spin–orbital coupling gives rise to two twofold-degenerate nodal rings (Weyl rings) connected by drumhead surface states, confirmed by angle-resolved photoemission spectroscopy. Our results suggest that the 2×2 CCDW ordering gaps out one Weyl ring in accordance with the CDW band folding, while the other Weyl ring remains gapless with intact surface states. In addition, superconductivity emerges at 0.91 K, with the upper critical field deviating from the s-wave behavior at low temperature, implying possibly unconventional superconductivity. Therefore, we think this type of the 112 system may possess abundant physical states and offer a platform to investigate the interplay between CDW, nontrivial band topology and superconductivity.

Charge density waves beyond the Pauli paramagnetic limit in 2D systems

Two-dimensional materials are ideal candidates to host Charge Density Waves (CDWs) that exhibit paramagnetic limiting behavior, similar to the well-known case of superconductors. Here, we study how CDWs in two-dimensional systems can survive beyond the Pauli limit when they are subjected to a strong magnetic field by developing a generalized mean-field theory of CDWs under Zeeman fields that includes incommensurability, imperfect nesting, and temperature effects and the possibility of a competing or coexisting Spin Density Wave (SDW) order. Our numerical calculations yield rich phase diagrams with distinct high-field phases above the Pauli limiting field. For perfectly nested commensurate CDWs, a q-modulated CDW phase that is completely analogous to the superconducting Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) phase appears at high fields. In the more common case of imperfect nesting, the commensurate CDW ground state undergoes a series of magnetic-field-induced phase transitions first into a phase where commensurate CDW and SDW coexist and subsequently into another phase where CDW and SDW acquire a q-modulation that is, however, distinct from the pure FFLO CDW phase. The commensurate CDW + SDW phase occurs for fields comparable to but less than the Pauli limit and survives above it. Thus, this phase provides a plausible mechanism for the CDW to survive at high fields without the need for forming the more fragile FFLO phase. We suggest that the recently discovered 2D materials like the transition metal dichalcogenides offer a promising platform for observing such exotic field-induced CDW phenomena.

Electron-phonon interactions and two-phonon modes associated with charge density wave in single crystalline1T−VSe2

Charge density wave (CDW) is a unique phenomenon mostly realized in two-dimensional (2D) metallic layered transition metal dichalcogenides (TMDCs). Here, we report on Raman spectroscopy of single crystal 1T-VSe2 and observed signature of commensurate CDW (C-CDW) and incommensurate (I-CDW) transition, in the temperature range of 50-120 K. The room temperature Raman spectra showed a sharp A1g mode ~ 206 cm-1 along with two new weak and broad Raman modes associated to Eg mode ~ 257 cm-1 and two-phonon mode (2ph) ~ 332 cm-1. The onset of I-CDW and C-CDW is estimated from resistance measurements supported by magnetic measurements. Remarkably, at the onset of I-CDW ~ 115 K, a significant enhancement in the intensity of weak Eg mode is observed along with emergence of a doubly degenerate Eg(2) mode ~ 144 cm-1. Below 70 K, a weak A1g mode ~ 170 cm-1 emerged signifying the onset of C-CDW. Anomalous phonon softening of Eg mode ~ 257 cm-1 and 2ph process mode below I-CDW has been also observed, which is signifying the involvement of electron-phonon coupling.

Structural dynamics of incommensurate charge-density waves tracked by ultrafast low-energy electron diffraction.

We study the non-equilibrium structural dynamics of the incommensurate and nearly commensurate charge-density wave (CDW) phases in 1T-. Employing ultrafast low-energy electron diffraction with 1 ps temporal resolution, we investigate the ultrafast quench and recovery of the CDW-coupled periodic lattice distortion (PLD). Sequential structural relaxation processes are observed by tracking the intensities of main lattice as well as satellite diffraction peaks and the diffuse scattering background. Comparing distinct groups of diffraction peaks, we disentangle the ultrafast quench of the PLD amplitude from phonon-related reductions of the diffraction intensity. Fluence-dependent relaxation cycles reveal a long-lived partial suppression of the order parameter for up to 60 ps, far outlasting the initial amplitude recovery and electron-phonon scattering times. This delayed return to a quasi-thermal level is controlled by lattice thermalization and coincides with the population of zone-center acoustic modes, as evidenced by a structured diffuse background. The long-lived non-equilibrium order parameter suppression suggests hot populations of CDW-coupled lattice modes. Finally, a broadening of the superlattice peaks is observed at high fluences, pointing to a non-linear generation of phase fluctuations.

The electric pulses induced multi-resistance states in the hysteresis temperature range of 1T-TaS2 and 1T-TaS1.6Se0.4

The electric pulse-induced responses of 1T-TaS2 and 1T-TaS1.6Se0.4 crystals in the commensurate charge-density-wave (CCDW) phase in the hysteresis temperature range have been investigated. We observed that abrupt multi-steps of the resistance are excited by electric pulses at a fixed temperature forming multi-metastable like states. We propose that the response of the system corresponds to the rearrangements of the textures of CCDW domains and the multi-resistance states or the nonvolatile resistance properties excited simply by electric pulses have profound significance for the exploration of solid-state devices.

Stable Flatbands, Topology, and Superconductivity of Magic Honeycomb Networks.

We propose a new principle to realize flatbands which are robust in real materials, based on a network superstructure of one-dimensional segments. This mechanism is naturally realized in the nearly commensurate charge-density wave of 1T-TaS_{2} with the honeycomb network of conducting domain walls, and the resulting flatband can naturally explain the enhanced superconductivity. We also show that corner states, which are a hallmark of the higher-order topological insulators, appear in the network superstructure.

Room Temperature Commensurate Charge Density Wave on Epitaxially Grown Bilayer 2H-Tantalum Sulfide on Hexagonal Boron Nitride.

The breaking of multiple symmetries by periodic lattice distortion at a commensurate charge density wave (CDW) state is expected to give rise to intriguing interesting properties. However, accessing the commensurate CDW state on bulk TaS2 crystals typically requires cryogenic temperatures (77 K), which precludes practical applications. Here, we found that heteroepitaxial growth of a 2H-tantalum disulfide bilayer on a hexagonal-boron nitride (h-BN) substrate produces a robust commensurate CDW order at room temperature, characterized by a Moiré superlattice of 3 × 3 TaS2 on a 4 × 4 h-BN unit cell. The CDW order is confirmed by scanning transmission electron microscopy and Raman measurements. Theoretical calculations reveal that the stabilizing energy for the CDW phase of the monolayer and bilayer 2H-TaS2-on-h-BN substrates arises primarily from interfacial electrostatic interactions and, to a lesser extent, interfacial strain. Our work shows that engineering interfacial electrostatic interactions in an ultrathin van der Waals heterostructure constitutes an effective way to enhance CDW order in two-dimensional materials.

Scanning tunneling spectroscopic study of monolayer 1T-TaS2 and 1T-TaSe2

The isostructural and isoelectronic transition-metal-dichalcogenides 1T-TaS2 and 1T-TaSe2 are layered materials with intricate electronic structures. Combining the molecular beam epitaxy growth, scanning tunneling microscopy measurements and first-principles calculations, we prepare monolayer 1T-TaS2 and TaSe2 and explore their electronic structures at the atomic scale. Both two-dimensional (2D) compounds exhibit commensurate charge density wave phase at low temperature. The conductance mapping identifies the contributions from different Ta atoms to the local density of states with spatial and energy resolution. Both 1T-TaS2 and 1T-TaSe2 monolayer are shown to be insulators, while the former has a Mott gap and the latter is a regular band insulator.

Suppression of the commensurate charge density wave phase in ultrathin 1T−TaS2 evidenced by Raman hyperspectral analysis

Using temperature dependent Raman spectroscopy we address the question of how the transition from bulk to few atomic layers affects the charge density wave (CDW) phases in 1T-TaS2. We find that for crystals with thickness larger than approx 10nm the transition temperatures between the different phases as well as the hysteresis that occurs in the thermal cycle correspond to the ones expected for a bulk sample. However, when the crystals become thinner than $\approx 10nm$, the commensurate CDW phase is suppressed down to the experimentally accessible temperatures. In addition, the nearly commensurate CDW phase is diminished below approx 4nm. These findings suggest that the interlayer coupling plays a significant role in determining the properties of CDW systems consisting of a few unit cells in the vertical direction.

Impeded phase transition in 1T-TaS2: Thermoelectric fingerprint of long-lived mixed states

1T-TaS2 is a material that belongs to the family of transition metal dichalcogenides and features a rich phase diagram including different charge density wave states. So far, most techniques used to study this material focus on either very local properties on the atomic scale or use global measurements of the whole sample like the electrical resistance. Here, we report on the influence of micrometer scale laser illumination on the global electric properties of a bulk sample. Thermoelectric effects are found to be responsible for a large electric response to the laser illumination. This effect is used to develop a method that allows to spatially map the thermoelectric properties of a 1T-TaS2 sample on the millimeter scale with micrometer resolution. We show that a specific temperature sweep can impede the phase transition, allowing to study long-lived mixed states, consisting of two phases. With this method we are able to image metastable states occurring in the transition between the nearly commensurate and commensurate charge density wave state in bulk 1T-TaS2 and compare the results to Raman spectroscopy.

Surface structure and stacking of the commensurate (13×13)R13.9∘ charge density wave phase of 1T−TaS2(0001)

By quantitative low-energy electron diffraction (LEED) we investigate the extensively studied commensurate charge density wave (CDW) phase of trigonal tantalum disulphide (1T-TaS$_2$), which develops at low temperatures with a $\left(\sqrt{13}\times\sqrt{13}\right)$R13.9{\deg} periodicity. A full-dynamical analysis of the energy dependence of diffraction spot intensities reveals the entire crystallographic surface structure, i.e. the detailed atomic positions within the outermost two trilayers consisting of 78 atoms as well as the CDW stacking. The analysis is based on an unusually large data set consisting of spectra for 128 inequivalent beams taken in the energy range 20-250 eV and an excellent fit quality expressed by a bestfit Pendry R-factor of R=0.110. The LEED intensity analysis reveals that the well-accepted model of star-of-David-shaped clusters of Ta atoms for the bulk structure also holds for the outermost two TaS$_2$ trilayers. Specifically, in both layers the clusters of Ta atoms contract laterally by up to 0.25 $\r{A}$ and also slightly rotate within the superstructure cell, causing respective distortions as well as heavy bucklings (up to 0.23 $\r{A}$) in the adjacent sulphur layers. Most importantly, our analysis finds that the CDWs of the 1$^{\text{st}}$ and 2$^{\text{nd}}$ trilayer are vertically aligned, while there is a lateral shift of two units of the basic hexagonal lattice (6.71 $\r{A}$) between the 2$^{\text{nd}}$ and 3$^{\text{rd}}$ trilayer. The results may contribute to a better understanding of the intricate electronic structure of the reference compound 1T-TaS$_2$ and guide the way to the analysis of complex structures in similar quantum materials.

Direct Synthesis of Large-Scale Multilayer TaSe2 on SiO2/Si Using Ion Beam Technology.

The multilayer 1T-TaSe2 is successfully synthesized by annealing a Se-implanted Ta thin film on the SiO2/Si substrate. Material analyses confirm the 1T (octahedral) structure and the quasi-2D nature of the prepared TaSe2. Temperature-dependent resistivity reveals that the multilayer 1T-TaSe2 obtained by our method undergoes a commensurate charge-density wave (CCDW) transition at around 500 K. This synthesis process has been applied to synthesize MoSe2 and HfSe2 and expanded for synthesis of one more transition-metal dichalcogenide (TMD) material. In addition, the main issue of the process, that is, the excess metal capping on the TMD layers, is solved by the reduction of thickness of the as-deposited metal thin film in this work.

Superconductivity related to local electronic and atomic structures in layered chalcogenide 1T-TaS2-xSex

We have performed temperature-dependent synchrotron radiation x-ray absorption fine structure (XAFS) spectra of layered transition metal dichalcogenide 1T-TaS2-xSex to elucidate the local electronic and atomic structure especially associated with the occurrence of superconductivity for the first time. We observed a corresponding temperature-dependent phase transition from nearly commensurate to commensurate charge density wave, as well as a characteristic of p-d hybridization between Ta 5d and Se 4p states, which is favorable to boost superconductivity, determined by x-ray absorption near edge structure (XANES) spectra at the Ta L3-edge and Se K-edge, respectively. And also, the periodic lattice distortion accompanied by the occurrence of charge density wave is clearly demonstrated by extended XAFS (EXAFS) spectra at the Ta L3-edge of the pristine sample 1T-TaS2, which is clearly suppressed in the Se-doping sample 1T-TaSSe with a maximum transition temperature . The present results reveal that the p-d hybridization and the loss of long-range coherence of the CDW state play an important role in manipulating the superconductivity, shedding new light on the physics mechanism of the interplay between superconductivity, charge order, and electron correlation.