Charge Density Wave Wave Vector Research Articles

Emergent tetragonality in a fundamentally orthorhombic material.

Symmetry plays a key role in determining the physical properties of materials. By Neumann's principle, the properties of a material remain invariant under the symmetry operations of the space group to which the material belongs. Continuous phase transitions are associated with a spontaneous reduction in symmetry. Less common are examples where proximity to a continuous phase transition leads to an increase in symmetry. We find signatures of an emergent tetragonal symmetry close to a charge density wave (CDW) bicritical point in a fundamentally orthorhombic material, ErTe3, for which the two distinct CDW phase transitions are tuned via anisotropic strain. We first establish that tension along the a axis favors an abrupt rotation of the CDW wave vector from the c to a axis and infer the presence of a bicritical point where the two continuous phase transitions meet. We then observe a divergence of the nematic elastoresistivity approaching this putative bicritical point, indicating an emergent tetragonality in the critical behavior.

Dramatic Plasmon Response to the Charge-Density-Wave Gap Development in 1T-TiSe_{2}.

1T-TiSe_{2} is one of the most studied charge density wave (CDW) systems, not only because of its peculiar properties related to the CDW transition, but also due to its status as a promising candidate of exciton insulator signaled by the proposed plasmon softening at the CDW wave vector. Using high-resolution electron energy loss spectroscopy, we report a systematic study of the temperature-dependent plasmon behaviors of 1T-TiSe_{2}. We unambiguously resolve the plasmon from phonon modes, revealing the existence of Landau damping to the plasmon at finite momentums, which does not support the plasmon softening picture for exciton condensation. Moreover, we discover that the plasmon lifetime at zero momentum responds dramatically to the band gap evolution associated with the CDW transition. The interband transitions near the Fermi energy in the normal phase are demonstrated to serve as a strong damping channel of plasmons, while such a channel in the CDW phase is suppressed due to the CDW gap opening, which results in the dramatic tunability of the plasmon in semimetals or small-gap semiconductors.

Bulk charge density wave and electron-phonon coupling in superconducting copper oxychlorides

Bulk charge density waves are now reported in nearly all high-temperature superconducting cuprates, with the noticeable exception of one particular family: the copper oxychlorides. Here, we used resonant inelastic X-ray scattering to reveal a bulk charge density waves in these materials. Combining resonant inelastic X-ray scattering with non-resonant inelastic X-ray scattering, we investigate the interplay between the lattice excitations and the charge density wave, and evidence the phonon anomalies of the Cu-O bond-stretching mode at the charge density wave wave-vector. We propose that such electron-phonon anomalies occur in the presence of dispersive charge excitations emanating from the charge density wave and interacting with the Cu-O bond-stretching phonon. Our results pave the way for future studies, combining both bulk and surface probes, to investigate the static and dynamical properties of the charge density wave in the copper oxychloride family.

Chirality locking charge density waves in a chiral crystal

In Weyl semimetals, charge density wave (CDW) order can spontaneously break the chiral symmetry, gap out the Weyl nodes, and drive the material into the axion insulating phase. Investigations have however been limited since CDWs are rarely seen in Weyl semimetals. Here, using scanning tunneling microscopy/spectroscopy (STM/S), we report the discovery of a novel unidirectional CDW order on the (001) surface of chiral crystal CoSi – a unique Weyl semimetal with unconventional chiral fermions. The CDW is incommensurate with both lattice momentum and crystalline symmetry directions, and exhibits an intra unit cell π phase shift in the layer stacking direction. The tunneling spectrum shows a particle-hole asymmetric V-shaped energy gap around the Fermi level that modulates spatially with the CDW wave vector. Combined with first-principle calculations, we identify that the CDW is locked to the crystal chirality and is related by a mirror reflection between the two enantiomers of the chiral crystal. Our findings reveal a novel correlated topological quantum state in chiral CoSi crystals and raise the potential for exploring the unprecedented physical behaviors of unconventional chiral fermions.

Гистерезис тензора сопротивления в полителлуридах редкоземельных металлов

Possible reasons for the temperature hysteresis of the Hall and diagonal components of resistivity tensor in tritellurides and tetratellurides of rare-earth metals, respectively, are analyzed. The width of this hysteresis exceeds 100 K in both families. This hysteresis is related to the charge density wave (CDW), but its detailed nature is still being discussed. It is known that it cannot be explained by a temperature variation in the CDW wave vector. In this paper, we discuss various interpretations of the observed hysteresis, present new experimental data showing a strong dependence of the hysteresis value on the temperature range, and propose new experiments (or a detailed analysis of unpublished data from existing ARPES measurements) that can substantiate or refute the proposed explanations for this unusual effect.

Hysteresis of resistivity tensor in rare-earth polytellurides

Possible reasons for the temperature hysteresis of the Hall and diagonal components of resistivity tensor in tritellurides and tetratellurides of rare-earth metals, respectively, are analyzed. The width of this hysteresis exceeds 100 K in both families. This hysteresis is related to the charge density wave (CDW), but its detailed nature is still being discussed. It is known that it cannot be explained by a temperature variation in the CDW wave vector. In this paper, we discuss various interpretations of the observed hysteresis, present new experimental data showing a strong dependence of the hysteresis value on the temperature range, and propose new experiments (or a detailed analysis of unpublished data from existing ARPES measurements) that can substantiate or refute the proposed explanations for this unusual effect. Keywords: charge density wave, hysteresis, conductivity, Hall coefficient, anisotropy.

Observation of Unconventional Charge Density Wave without Acoustic Phonon Anomaly in Kagome Superconductors AV3Sb5 ( A=Rb , Cs)

The combination of non-trivial band topology and symmetry breaking phases gives rise to novel quantum states and phenomena such as topological superconductivity, quantum anomalous Hall effect and axion electrodynamics. Evidence of intertwined charge density wave (CDW) and superconducting order parameters has recently been observed in a novel kagome material AV3Sb5 (A=K,Rb,Cs) that features a Z2 topological invariant in the electronic structure. However, the origin of the CDW and its intricate interplay with topological state has yet to be determined. Here, using hard x-ray scattering, we demonstrate a three-dimensional (3D) CDW with 2*2*2 superstructure in (Rb,Cs)V3Sb5. Unexpectedly, we find that the CDW fails to induce acoustic phonon anomalies at the CDW wavevector but yields a novel Raman mode which quickly damps into a broad continuum below the CDW transition temperature. Our observations exclude strong electron-phonon coupling driven CDW in AV3Sb5 and point to an unconventional and electronic-driven mechanism that couples the CDW and the topological band structure.

Collective electronic excitations in charge density wave systems: The case of CuTe

The study of neutral electronic excitations directly probed by electron energy loss spectroscopy experiments allows obtaining important insight about the physical origin of the charge density wave (CDW) transition in solids. In particular it allows us to disentangle purely phononic mechanisms from the excitonic insulator scenario which is associated to a purely electronic mechanism. As a matter of fact, while the the loss function of the excitonic insulators should display negative dispersive features associated to the softening of neutral electronic excitations at the CDW wave vector above the critical temperature, no softening is expected when the driving force is purely phononic. Here we perform a microscopic analysis of the dynamical charge response of CuTe, a material that displays a low-temperature Peierls-like CDW instability. By means of first-principles time-dependent density functional calculations of the loss function, we characterize the plasmon dispersion along the different directions, highlighting the role of the intrinsic structural anisotropy and the effects of the crystal local fields that are responsible for the periodic reappearance of the spectra of the first Brillouin zone as well as the formation of an acousticlike plasmon. Finally, we demonstrate that also in this system, in analogy with other materials displaying excitonic insulator instability, the low energy region of the loss function presents negative dispersive structures at momentum transfer close to the CDW wave vector. This is a feature common to both excitonic insulator transition and Peierls distortion that further highlights how the difference between the two mechanisms is at most quantitative.

Direct observation of an incommensurate charge density wave in the BiS2 -based superconductor NdO1−xFxBiS2

The nature of superconductivity in ${\mathrm{BiS}}_{2}$-based superconductors has been controversial while ab initio calculations proposed this system in close proximity to a charge-density-wave (CDW) phase. Using high-energy high-flux x-ray diffraction, we reveal an intrinsic and long-range CDW phase coexisting with superconductivity in ${\mathrm{NdO}}_{1\ensuremath{-}x}{\mathrm{F}}_{x}{\mathrm{BiS}}_{2}$ superconductor $(x=0.37 \mathrm{and} 0.3)$. The CDW wave vector in ${\mathrm{NdO}}_{0.63}{\mathrm{F}}_{0.37}{\mathrm{BiS}}_{2}$ correspond ${\mathbf{Q}}_{\mathrm{CDW}}=(0.17, 0.17, 0.5)$ and is associated with transverse atomic displacements. Interestingly, this wave vector does not match theoretical expectations based on either phonon softening or Fermi surface nesting. In ${\mathrm{NdO}}_{0.7}{\mathrm{F}}_{0.3}{\mathrm{BiS}}_{2}$, where the superconducting transition temperature is highest, the CDW satellites are slightly broader and weaker compared to ${\mathrm{NdO}}_{0.63}{\mathrm{F}}_{0.37}{\mathrm{BiS}}_{2}$, possibly suggesting the competition with the superconductivity. Last, we measure a thermal diffuse scattering across the superconducting transition temperature and find no meaningful changes. Our result suggests the importance of understanding CDW which might hold a key to the superconductivity in the ${\mathrm{BiS}}_{2}$-based superconductor.

Van der Waals driven anharmonic melting of the 3D charge density wave in VSe2

Understanding of charge-density wave (CDW) phases is a main challenge in condensed matter due to their presence in high-Tc superconductors or transition metal dichalcogenides (TMDs). Among TMDs, the origin of the CDW in VSe2 remains highly debated. Here, by means of inelastic x-ray scattering and first-principles calculations, we show that the CDW transition is driven by the collapse at 110 K of an acoustic mode at qCDW = (2.25 0 0.7) r.l.u. The softening starts below 225 K and expands over a wide region of the Brillouin zone, identifying the electron-phonon interaction as the driving force of the CDW. This is supported by our calculations that determine a large momentum-dependence of the electron-phonon matrix-elements that peak at the CDW wave vector. Our first-principles anharmonic calculations reproduce the temperature dependence of the soft mode and the TCDW onset only when considering the out-of-plane van der Waals interactions, which reveal crucial for the melting of the CDW phase.

Coexistence of Superconductivity and Charge Density Waves in Tantalum Disulfide: Experiment and Theory

The coexistence of charge density wave (CDW) and superconductivity in tantalum disulfide (2H-TaS_{2}) at low temperature is boosted by applying hydrostatic pressures to study both vibrational and magnetic transport properties. Around P_{c}, we observe a superconducting dome with a maximum superconducting transition temperature T_{c}=9.1 K. First-principles calculations of the electronic structure predict that, under ambient conditions, the undistorted structure is characterized by a phonon instability at finite momentum close to the experimental CDW wave vector. Upon compression, this instability is found to disappear, indicating the suppression of CDW order. The calculations reveal an electronic topological transition (ETT), which occurs before the suppression of the phonon instability, suggesting that the ETT alone is not directly causing the structural change in the system. The temperature dependence of the first vortex penetration field has been experimentally obtained by two independent methods. While a d wave and single-gap BCS prediction cannot describe the lower critical field H_{c1} data, the temperature dependence of the H_{c1} can be well described by a single-gap anisotropic s-wave order parameter.

Unusual Dynamic Charge Correlations in Simple-Tetragonal HgBa2CuO4+δ

The charge-density-wave (CDW) instability in the underdoped, pseudogap part of the cuprate phase diagram has been a major recent research focus, yet measurements of dynamic, energy-resolved CDW correlations are still in their infancy. We report a high-resolution resonant inelastic X-ray scattering (RIXS) study of the underdoped cuprate superconductor HgBa$_{2}$CuO$_{4+\delta}$ ($T_c = 70$ K). At $T=250$ K, above the CDW order temperature $T_\mathrm{CDW} \approx 200$ K, we observe significant dynamic CDW correlations at about 40 meV. This energy scale is comparable to both the superconducting gap and the previously reported low-energy pseudogap. At $T = T_c$, a strong elastic CDW peak appears, but the dynamic correlations around 40 meV remain virtually unchanged. In addition, we observe a new feature: dynamic correlations at significantly higher energy, with a characteristic scale of about 160 meV. A similar scale was previously identified in other experiments as a high-energy pseudogap. The existence of three distinct features in the charge response is highly unusual for a CDW system, and suggests that charge order in the cuprates is closely related to the pseudogap phenomenon and more complex than previously thought. We further observe the paramagnon dispersion along [1,0], across the two-dimensional CDW wavevector $\boldsymbol{q}_\mathrm{CDW}$, which is consistent with magnetic excitations measured by inelastic neutron scattering. Unlike for some other cuprates, our results point to the absence of a discernible coupling between CDW and magnetic excitations.

Phonon spectrum of underdoped HgBa2CuO4+δ investigated by neutron scattering

The cuprates exhibit a prominent charge-density-wave (CDW) instability with wavevector along [100], i.e., the Cu-O bond direction. Whereas CDW order is most prominent at moderate doping and low temperature, there exists increasing evidence for dynamic charge correlations throughout a large portion of the temperature-doping phase diagram. In particular, signatures of incipient charge order have been observed as phonon softening and/or broadening near the CDW wavevector approximately half-way through the Brillouin zone. Most of this work has focused on moderately-doped cuprates, for which the CDW order is robust, or on optimally-doped samples, for which the superconducting transition temperature ($T_c$) attains its maximum. Here we present a time-of-flight neutron scattering study of phonons in simple-tetragonal $\text{HgBa}_2\text{CuO}_{4+\delta}$ ($T_c = 55$ K) at a low doping level where prior work showed the CDW order to be weak. We employ and showcase a new software-based technique that mines the large number of measured Brillouin zones for useful data in order to improve accuracy and counting statistics. Density-functional theory has not provided an accurate description of phonons in $\text{HgBa}_2\text{CuO}_{4+\delta}$, yet we find the right set of parameters to qualitatively reproduce the data. The notable exception is a dispersion minimum in the longitudinal Cu-O bond-stretching branch along [100]. This discrepancy suggests that, while CDW order is weak, there exist significant dynamic charge correlations in the optic phonon range at low doping, near the edge of the superconducting dome.

Evidence of charge density wave with anisotropic gap in a monolayer VTe2 film

We report experimental evidence of charge density wave (CDW) transition in monolayer 1T-VTe$_2$ film. 4$\times$4 reconstruction peaks are observed by low energy electron diffraction below the transition temperature $T_{CDW}$ = 186 K. Angle-resolved photoemission spectroscopy measurements reveal arc-like pockets with anisotropic CDW gaps up to 50 meV. The anisotropic CDW gap is attributed to the imperfect nesting of the CDW wave vector, and first-principles calculations reveal phonon softening at the same vector, suggesting the important roles of Fermi surface nesting and electron-phonon interaction in the CDW mechanism.

Interplay between band crossing and charge density wave instabilities

Our measurements of the Hall coefficient in rare-earth tritelluride compounds reveal a strong hysteresis between cooling and warming in the low temperature range where a second unidirectional charge density wave (CDW) occurs. We show that this effect results from the interplay between two instabilities: band crossing of the Te $p_{x}$ and $p_{y}$ orbitals at the Fermi level and CDW, which have a close energy gain and compete. Calculation of the electron susceptibility at the CDW wave vector with and without band anticrossing reconstruction of the electron spectrum yields a satisfactory estimation of the temperature range of the hysteresis in Hall effect measurements.

Synchrotron x-ray scattering study of charge-density-wave order in HgBa2CuO4+δ

We present a detailed synchrotron x-ray scattering study of the charge-density-wave (CDW) order in simple tetragonal HgBa$_2$CuO$_{4+\delta}$ (Hg1201). Resonant soft x-ray scattering measurements reveal that short-range order appears at a temperature that is distinctly lower than the pseudogap temperature and in excellent agreement with a prior transient reflectivity result. Despite considerable structural differences between Hg1201 and YBa$_2$Cu$_3$O$_{6+\delta}$, the CDW correlations exhibit similar doping dependencies, and we demonstrate a universal relationship between the CDW wave vector and the size of the reconstructed Fermi pocket observed in quantum oscillation experiments. The CDW correlations in Hg1201 vanish already below optimal doping, once the correlation length is comparable to the CDW modulation period, and they appear to be limited by the disorder potential from unit cells hosting two interstitial oxygen atoms. A complementary hard x-ray diffraction measurement, performed on an underdoped Hg1201 sample in magnetic fields along the crystallographic $c$ axis of up to 16 T, provides information about the form factor of the CDW order. As expected from the single-CuO$_2$-layer structure of Hg1201, the CDW correlations vanish at half-integer values of $L$ and appear to be peaked at integer $L$. We conclude that the atomic displacements associated with the short-range CDW order are mainly planar, within the CuO$_2$ layers.

Correlation between Fermi arc and charge order resulting from the momentum-dependent self-energy correction in cuprates

We calculate momentum-dependent self-energies due to self-consistent spin and charge-density fluctuations within a single-band Hubbard model for hole-doped cuprates. We find that the dynamical density instability (mainly paramagnonlike spin fluctuations) arising from the van Hove singularity at the antinodal point produces strongly anisotropic mass renormalization, increasing from the nodal direction to the antinodal one. This gives rise to a coherent Fermi arc pattern in which although the self-energy dressed Green's function has poles at all Fermi momenta, the corresponding spectral weight decreases from the nodal to the antinodal direction. We study the feedback effects of the anisotropic self-energy and Fermi arc on the charge-density wave (CDW) instability by direct computations of charge susceptibility and the quasiparticle interference pattern. We find that that due to the loss of spectral weight at the antinodal points, the CDW nesting weakens, and the corresponding hot spot shifts from the antinodal region to the tip of the Fermi arc below the magnetic Brillouin zone. The results are in good agreement with experiments, reproducing the observed slow doping dependence of the CDW wave vector. Our investigation therefore provides a mechanism for the Fermi arc in cuprates, with various testable predictions such as a sharp, first-order-like phase transition of the CDW order on the higher-doping side.

Dispersive charge density wave excitations in Bi2Sr2CaCu2O8+δ

Experimental evidence on high-Tc cuprates reveals ubiquitous charge density wave (CDW) modulations, which coexist with superconductivity. Although the CDW had been predicted by theory, important questions remain about the extent to which the CDW influences lattice and charge degrees of freedom and its characteristics as functions of doping and temperature. These questions are intimately connected to the origin of the CDW and its relation to the mysterious cuprate pseudogap. Here, we use ultrahigh resolution resonant inelastic x-ray scattering (RIXS) to reveal new CDW character in underdoped Bi2Sr2CaCu2O8+{\delta} (Bi2212). At low temperature, we observe dispersive excitations from an incommensurate CDW that induces anomalously enhanced phonon intensity, unseen using other techniques. Near the pseudogap temperature T*, the CDW persists, but the associated excitations significantly weaken and the CDW wavevector shifts, becoming nearly commensurate with a periodicity of four lattice constants. The dispersive CDW excitations, phonon anomaly, and temperature dependent commensuration provide a comprehensive momentum space picture of complex CDW behavior and point to a closer relationship with the pseudogap state.

Remarkable Stability of Charge Density Wave Order in La_{1.875}Ba_{0.125}CuO_{4}.

The occurrence of charge-density-wave (CDW) order in underdoped cuprates is now well established, although the precise nature of the CDW and its relationship with superconductivity is not. Theoretical proposals include contrasting ideas such as that pairing may be driven by CDW fluctuations or that static CDWs may intertwine with a spatially modulated superconducting wave function. We test the dynamics of CDW order in La_{1.825}Ba_{0.125}CuO_{4} by using x-ray photon correlation spectroscopy at the CDW wave vector, detected resonantly at the Cu L_{3} edge. We find that the CDW domains are strikingly static, with no evidence of significant fluctuations up to 2 ¾ h. We discuss the implications of these results for some of the competing theories.

Influence of Ti doping on the incommensurate charge density wave in1T−TaS2

We report temperature-dependent transport and x-ray diffraction measurements of the influence of Ti hole doping on the charge density wave (CDW) in $1T\text{\ensuremath{-}}{\mathrm{Ta}}_{1\ensuremath{-}x}{\mathrm{Ti}}_{x}{\mathrm{S}}_{2}$. Confirming past studies, we find that even trace impurities eliminate the low-temperature commensurate (C) phase in this system. Surprisingly, the magnitude of the in-plane component of the CDW wave vector in the nearly commensurate (NC) phase does not change significantly with Ti concentration, as might be expected from a changing Fermi surface volume. Instead, the angle of the CDW in the basal plane rotates, from $11.9{}^{\ensuremath{\circ}}$ at $x=0$ to $16.4{}^{\ensuremath{\circ}}$ at $x=0.12$. Ti substitution also leads to an extended region of coexistence between incommensurate (IC) and NC phases, indicating heterogeneous nucleation near the transition. Finally, we explain a resistive anomaly originally observed by Di Salvo [F. J. Di Salvo et al., Phys. Rev. B 12, 2220 (1975)] as arising from pinning of the CDW on the crystal lattice. Our study highlights the importance of commensuration effects in the NC phase, particularly at $x\ensuremath{\sim}0.08$.