Study Of Charge Density Waves Research Articles

Optical response from charge-density waves in Weyl semimetals

The study of charge-density wave (CDW) distortions in Weyl semimetals has recently returned to the forefront, inspired by experimental interest in materials such as ${\text{(TaSe}}_{4}{\text{)}}_{2}\text{I}$. However, the interplay between collective phonon excitations and charge transport in Weyl-CDW systems has not been systematically studied. In this paper, we examine the longitudinal electromagnetic response due to collective modes in a Weyl semimetal gapped by a quasi-one-dimensional CDW order, using both continuum and lattice-regularized models. We systematically compute the contributions of the collective modes to the linear and nonlinear optical conductivity of our models, both with and without tilting of the Weyl cones. We discover that, unlike in a single-band CDW, the gapless CDW collective mode does not contribute to the conductivity unless the Weyl cones are tilted. Going further, we show that the lowest nontrivial collective mode contribution to charge transport with untilted Weyl cones comes in the third-order conductivity for a single collective mode. This third-order process is mediated by the gapped amplitude mode. We show that this leads to a sharply peaked third-harmonic response at frequencies below the single-particle energy gap. We discuss the implications of our findings for transport experiments in Weyl-CDW systems.

Study of charge density waves in suspended 2H-TaS2 and 2H-TaSe2 by nanomechanical resonance

The charge density wave (CDW) state in van der Waals systems shows interesting scaling phenomena as the number of layers can significantly affect the CDW transition temperature, TCDW. However, it is often difficult to use conventional methods to study the phase transition in these systems due to their small size and sensitivity to degradation. Degradation is an important parameter, which has been shown to greatly influence the superconductivity in layered systems. Since the CDW state competes with the onset of superconductivity, it is expected that TCDW will also be affected by the degradation. Here, we probe the CDW phase transition by the mechanical resonances of suspended 2H-TaS2 and 2H-TaSe2 membranes and study the effect of disorder on the CDW state. Pristine flakes show the transition near the reported values of 75 K and 122 K, respectively. We then study the effect of degradation on 2H-TaS2, which displays an enhancement of TCDW up to 129 K after degradation in ambient air. Finally, we study a sample with local degradation and observe that multiple phase transitions occur at 87 K, 103 K, and 118 K with a hysteresis in temperature in the same membrane. The observed spatial variations in the Raman spectra suggest that variations in crystal structure cause domains with different transition temperatures, which could result in the hysteresis. This work shows the potential of using nanomechanical resonance to characterize the CDW in suspended 2D materials and demonstrates that the degradation can have a large effect on transition temperatures.

Nuclear magnetic resonance study of charge density waves under hydrostatic pressure in YBa2Cu3Oy

The effect of hydrostatic pressure ($P$) on charge density waves (CDWs) in ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{\mathrm{y}}$ has recently been controversial. Using NMR, we find that both the short-range CDW in the normal state and the long-range CDW in high fields are, at most, slightly weakened at $P=1.9$ GPa. This result is in contradiction with x-ray-scattering results finding complete suppression of the CDW at $\ensuremath{\approx}1$ GPa and we discuss possible explanations of this discrepancy. Quantitative analysis, however, shows that the NMR data are not inconsistent with a disappearance of the CDW on a larger pressure scale, typically $\ensuremath{\approx}10$--20 GPa. We also propose a simple model reconciling transport data with such a hypothesis, provided the pressure-induced change in doping is taken into account. We conclude that it is therefore possible that most of the spectacular increase in ${T}_{c}$ upon increasing pressure up to $\ensuremath{\approx}15$ GPa arises from a concomitant decrease of CDW strength.

Charge density wave modulation and gap measurements inCeTe3

We present a study of charge density wave (CDW) ordering in CeTe$_3$ at room temperature using a scanning tunneling microscope and Raman spectroscopy. Two characteristic CDW ordering wavevectors obtained from the Fourier analysis are assessed to be $|{\bf \textbf{c}}^\ast-{\bf q}|=4.19\,{\rm nm}^{-1}$ and $|{\bf q}|=10.26\,{\rm nm}^{-1}$ where $|{\bf c}^\ast| = 2\pi/c$ is the reciprocal lattice vector. The scanning tunneling spectroscopy measurements, along with inelastic light (Raman) scattering measurements, show a CDW gap $\Delta_{\rm max}$ of approximately 0.37 eV. In addition to the CDW modulation, we observe an organization of the Te sheet atoms in an array of alternating V- and N- groups along the CDW modulation, as predicted in the literature.

Resonant x-ray scattering study of charge-density wave correlations inYBa2Cu3O6+x

We report the results a comprehensive study of charge density wave (CDW) correlations in untwinned YBCO6+x single crystals with 0.4<x<0.99 using Cu-L3 edge resonant x-ray scattering (RXS). Evidence of CDW formation is found for 0.45<x<0.93, but not for samples with x<0.44 that exhibit incommensurate spin-density-wave order, and in slightly overdoped samples with x=0.99. This suggests the presence of two proximate zero-temperature CDW critical points at doping pc1~0.08 and pc2~0.18. The CDW reflections are observed at incommensurate in-plane wave vectors (d_a, 0) and (0, d_b). Both decrease linearly with increasing doping, in agreement with recent reports on Bi-based high-Tc superconductors, but in sharp contrast to the behavior of the 214 family. The CDW intensity and correlation length exhibit maxima at p~0.12, coincident with a plateau in the superconducting transition temperature Tc. The onset temperature of the CDW reflections depends non-monotonically on p, with a maximum of~160 K for p~0.12. The RXS reflections exhibit a uniaxial intensity anisotropy. We further observe a depression of CDW correlations upon cooling below Tc, and (for samples with p> 0.09) an enhancement of the signal when an external magnetic field up to 6 T is applied in the superconducting state. For samples with p~0.08, where prior work has revealed a field-enhancement of incommensurate magnetic order, the RXS signal is field-independent. This supports a previously suggested scenario in which incommensurate charge and spin orders compete against each other, in addition to individually competing against. We discuss the relationship of these results to stripe order 214, the pseudogap phenomenon, superconducting fluctuations, and quantum oscillations.

First-principles study of charge-density waves on Cu surfaces covered by In, Pb, and Bi atoms: Analysis of electronic structure and surface phonons

We performed a first-principles density-functional calculation to investigate the difference in the mechanisms of phase transitions for In/Cu(001) and W(001). We also explain the origins of surface states of In, Pb, and Bi/Cu(001)-0.5 ML having $\text{c}(2\ifmmode\times\else\texttimes\fi{}2)$ structure that cause a phase transition via the generation of a charge-density wave (CDW). The perfect theoretical/experimental agreement for the wave numbers of nesting vectors corresponding to the well-nested surface states of In and Pb/Cu(001)-0.5 ML is reported. Band-structure analysis suggests a common mechanism of CDW transition for In and Pb/Cu(001)-0.5 ML. The absorption of In and Pb on Cu(001) leads to a reduction in the energy of the band composing the edge of bulk band gap. As a result, the band enters the bulk band gap and has the character of the surface state. Since these surface states compose a well-nested Fermi surface, CDW transition would be induced. In addition, we studied the relationship between the lattice distortions and the band dispersions of the surface states of In/Cu(001)-0.5 ML and W(001) in terms of the Jahn-Teller effect (JTE). While we find promoting modes that resolve the degeneracy of surface states of W(001), any surface-localized mode of In/Cu(001) does not split the band of surface state. Therefore, the static electron-phonon interaction of In/Cu(001) is weak. We propose that the dynamic JTE contributes to the CDW transition of In/Cu(001) and the dynamic nature is related to the spatial coherence length of the CDW.

Synchrotron X-ray study of charge density waves in o-TaS3

We report a synchrotron X-ray study of charge density waves (CDW) in an o-TaS3 crystal. CDW of o-TaS3 has been known to undergo a commensurate-incommensurate transition at 100 K, below which the wavevector locks in with the pristine lattice. We exploited the beamline BL02B1 of SPring-8. Temperature dependence of the Bragg peak (002) and satellite peak (1 -1 2)+q⃗ was measured from 7 K to 180 K. We found that a new phase in a temperature range of 130--50 K, where two independent CDWs coexist. These waves are incommensurate and commensurate CDWs with longitudinal wave vectors qc=0.252c* and 0.250c*, respectively. By lowering the temperature, intensity of the incommensurate CDW was decreased, while that of the commensurate CDW was increased. At 50 K, the incommensurate CDW was completely diminished. Based on the concept of discommensuration, we determined the dislocation configuration from the intensity of the two CDWs.

Wide band XRD study of 2H-NbSe2 in a CDW-regime

Albeit rather simple structure and ample experimental study of charge density wave (CDW) superconductor 2H-NbSe2 its behaviour in a CDW regime (TCDW = 32.5 K, TSN = 7.2 K) remains unclear. The relevance of the known mechanisms of CDW formation to this hexagonal modification of the niobium diselenide is not straightforward. Occurrence of the lock-in transition in this compound is still debated despite numerous structural investigations by means of diverse diffraction techniques. Here, we present Debye patterns measured in a detail at temperatures 8–35 K with different sources of X-ray irradiation and energy resolution of about 1eV. New features observed in the temperature range 15–30 K are discussed in terms of fluctuation-mediated phase transition.

Charge Stripes and Superconductivity in La2−x Ba x CuO4 and La1.6−x Nd0.4Sr x CuO4

We report x-ray scattering study of charge density wave (stripe) order in La2−x Ba x CuO4 (LBCO) and La1.6−x Nd0.4Sr x CuO4 (LNSCO). The doping dependence of the charge stripe ordering temperature and the low-temperature correlation length is compared with the bulk superconducting transition temperature. We find that the charge stripe ordering temperature and correlation length are quite different in these two families of cuprates, while there seems to be inverse correlation between the bulk superconducting temperature and the charge stripe correlation length.

Commensurate–incommensurate transition of charge density waves in o-

Abstract We report a synchrotron X-ray study of charge density waves (CDWs) in an o- TaS 3 crystal. CDW of o- TaS 3 has been known to undergo a commensurate–incommensurate transition at 100 K, below which the wavevector locks in with the pristine lattice. However, the details of the commensurate–incommensurate transition remain open problems, the example being whether the discommensuration exists or not in the neighborhood of the transition. We exploited the beamline BL02B1 of SPring-8. A two-dimensional detector was placed at a distance of 1300 mm from the sample, providing an angle resolution of 0.0076°. Temperature dependence of the Bragg peak (0 0 2) and satellite peak ( 1 - 1 2 ) + q was measured from 7 to 180 K. We found that a new phase in the temperature range of 130–50 K, where two independent CDWs coexist. These waves are incommensurate and commensurate CDWs with longitudinal wave vectors q c = 0.252 c * and 0.250 c * , respectively. By lowering the temperature, intensity of the incommensurate CDW was decreased, while that of the commensurate CDW was increased. Below 50 K, the incommensurate CDW was completely diminished. Based on the concept of discommensuration, we suggested the dislocation configuration from the intensity of the two CDWs.

Field-Induced Discommensuration in Charge Density Waves in o-TaS3

We report a synchrotron X-ray study of charge density waves (CDWs) in an o-TaS3 crystal. We found that two independent CDWs coexist in the temperature range of 130 - 50 K. These waves are incommensurate and commensurate CDWs with longitudinal wave vectors qc ¼ 0:252cand 0:250c � , respectively. The temperature and electric current dependences of the intensity of the two CDW satellites were measured. We found that the commensurate CDW was converted to the incommensurate CDW at 80 K by inducing current flow. Our observation was interpreted in terms of the dynamics of topological defects. We determined the edge dislocation configuration from the electric current dependence of the intensity of the two CDWs. The result implies for the first time that discommensurations are induced in the commensurate CDW by applying an electric field.

X-ray scattering study of charge density waves inLa2−xBaxCuO4

We report a comprehensive x-ray scattering study of charge density wave (stripe) ordering in La2-xBaxCuO4 (x{approx}1/8), for which the bulk superconducting Tc is greatly suppressed. Strong superlattice reflections corresponding to static ordering of charge stripes were observed in this sample. The structural modulation at the lowest temperature was deduced based on the intensity of over 70 unique superlattice positions surveyed. We found that the charge order in this sample is described with one-dimensional charge density waves, which have incommensurate wave vectors (0.23, 0, 0.5) and (0, 0.23, 0.5), respectively, on neighboring CuO2 planes. The structural modulation due to the charge density wave order is simply sinusoidal, and no higher harmonics were observed. Just below the structural transition temperature, short-range charge density wave correlation appears, which develops into a large scale charge ordering around 40 K, close to the spin density wave ordering temperature. However, this charge ordering fails to grow into a true long range order, and its correlation length saturates at {approx}230 Angstroms, and slightly decreases below about 15 K, which may be due to the onset of two-dimensional superconductivity.

Revealing Charge Density Wave Formation in theLaTe2System by Angle Resolved Photoemission Spectroscopy

We present the first direct study of charge density wave (CDW) formation in quasi-2D single layer LaTe2 using high-resolution angle resolved photoemission spectroscopy and low energy electron diffraction. CDW formation is driven by Fermi surface (FS) nesting, however, characterized by a surprisingly smaller gap ( approximately 50 meV) than seen in the double layer RTe2 compounds, extending over the entire FS. This establishes LaTe2 as the first reported semiconducting 2D CDW system where the CDW phase is FS nesting driven. In addition, the layer dependence of this phase in the tellurides and the possible transition from a stripe to a checkerboard phase is discussed.

Charge density wave transport in submicron antidot arrays in NbSe

We demonstrate for the first time that a periodic array of submicrometer holes (antidots) can be patterned into thin single NbSe3 crystals. We report on the study of charge density wave (CDW) transport of the network of mesoscopic units between antidots. Size of the elementary unit can be as small as 0.5 micron along the chain axis and (0.2 micron) x (0.3 micron) in cross section. We observe size effects for Ohmic residual resistance and in CDW transport current-voltage characteristics in submicronic networks.

Features of charge density waves in quasi-one-dimensional conductors at low temperatures

The reported study of charge density waves at low temperatures is based on a microscopic theory. One feature of a charge density wave at low temperatures is a large shift in the chemical potential near its defects, such as solitons, dislocations, and pinning centers, which leads to a higher conductivity of material along chains when the charge density wave is immobile, and the wave dynamics is controlled by this shift. Equations describing the dynamics of a charge density wave have been derived and used to estimate the velocity of 2π-solitons along conducting chains. The resulting soliton mobility has proved to be low and makes a small contribution to the conductivity. The large shift in the chemical potential near strong pinning centers can lead to a considerable increase in linear conductivity along conducting chains.

Observation of a high-temperature incommensurate phase transition and discommensurations in TaTe4

In many ways, TaTe4 and NbTe4 are nearly prototypical compounds for the study of charge-density waves (CDW). The compounds have a quasi-one-dimensional crystal structure in which chains of metal atoms are centered within extended cages of Te atoms in square antiprismatic coordination. The observed lattice distortions, involving mainly longitudinal motions of the metal atoms along the chains, correspond to that of the classic CDW model. In addition, the compounds exhibit the full spectrum of possible CDW-driven phase transitions: commensurate-to-incommensurate (C to IC), C to C and IC to IC. The subcell of TaTe4 is tetragonal with axes (a x a x c). At room temperature, the crystal is commensurately modulated giving rise to a supercell with axes (2a x 2a x 3c) and, upon heating, has been observed to undergo a C to C transition at about 450 K. In this paper, we report an additional C to IC transition occurring above 550 K. The evolution of the microstructure upon heating, including the formation of discommensuration arrays in the IC state, has been revealed by satellite dark-field (SDF) imaging.

Study of Charge Density Waves in 4Hb–TaS2 by STM/STS

An investigation of charge-density waves in 4Hb–TaS2 was carried out by scanning tunneling microscopy and scanning tunneling spectroscopy. We succeeded in discriminating of the surface electronic structures of 4Hb–TaS2, octahedral structure and trigonal-prismatic structure in terms of the electronic properties. The measured energy gap of the charge-density waves of 4Hb–TaS2 at room temperature was about 9± 10 meV.

Applications of scanning tunneling microscopy to the study of charge density waves

Scanning tunneling microscopy (STM) studies of the surfaces of transition metal di- and tri-chalcogenides have been used to detect a variety of charge-density-wave (CDW) contributions to the surface charge modulation at 77 and 4.2K. In the 1T phases of TaSe2 and TaS2 strong charge maxima are observed which correspond to the √13 a0 × √13 a0 superlattice generated by the CDWs formed as standing waves from the conduction electrons. The charge-density contours located between the charge maxima show major contributions from the detailed arrangement of surface Se or S atom. The z-deflection observed from the total surface charge-density modulation in the 1T phases is extremely large in the range 1.0 to 2.5Å. The STM scans show the same general structure for the 1T phases at both 77 and 4.2K, but variations in the z-deflection suggest some temperature dependence of the CDW amplitude. The observations are consistent with band structure considerations and the large electron transfer associated with the CDWs. In 2H-TaSe2 at 77K and in 2H-NbSe2 at 4.2K the CDWs are much weaker than in the 1T phases and contribute only small deflections to the STM scans which are mainly dominated by the atomic modulation of the surface charge-density. The linear chain compound NbSe3 has two CDW transitions, one at 144K and one at 59K. The STM scans at 77K with only one CDW present and only 20% of the Fermi surface gapped show no detectable contribution to the surface charge modulation at the CDW wavelength. The z-deflection shows a large surface modulation and resolves the three chains per surface unit cell, but the STM pattern can be matched to the expected height and charge variations of the surface Se atoms. At 4.2K the two CDWs present in NbSe3 gap approximately 80% of the Fermi surface and a modulation at the CDW wavelength of ∼ 4b0 along the chain axis can be analyzed in terms of the band structure and CDW formation. Initial STM scans have also been performed at 77K on the linear chain compound TaS3. The CDW onset occurs at 216K with gapping of the entire Fermi surface and formation of a semiconducting phase at low temperatures. A clear CDW modulation has not yet been observed, but reasonable STM scans can be obtained and improved resolution should make it possible to detect the CDW structure. Technical problems associated with operation of the STMs at both 77 and 4.2K will also be discussed.

Numerical study of Charge Density Waves in nearly quarter-filled one-dimensional electron-photon systems

In order to investigate the structure of the charge density waves in nearly quarter-filled one-dimensional electron-photon systems, the ground states of finite chains are studied numerically by using the SSH and Fröhlich-type models. The structure factor of the CDW is calculated for the two models with different electron concentrations and different constants. The results are discussed in connection to the X-ray or neutron scattering experiments.

X-ray diffraction study of the CDW phase in (TaSe 4) 2I: Determination of the CDW modulation amplitude

An extensive X-ray diffraction study of charge density wave (CDW) phase in (TaSe 4) 2I is reported. We have observed the superstructure satellites at 2 q in addition to those at q reported by Fujishita et al. The results imply a sinusoidal lattice modulation with polarization almost perpendicular to q (i.e. transverse) and the existence of CDW domains. At 15 K we have extracted an approximate value for the amplitude of the lattice modulation perpendicular to q to be μ ⊥ ∽ 0.087 Å.