Short-range Charge Density Wave Research Articles

Annealing-Tunable Charge Density Wave in the Magnetic Kagome Material FeGe.

The unprecedented phenomenon that a charge density wave (CDW) emerges inside the antiferromagnetic (AFM) phase indicates an unusual CDW mechanism associated with magnetism in FeGe. Here, we demonstrate that both the CDW and magnetism of FeGe can be effectively tuned through postgrowth annealing treatments. Instead of the short-range CDW reported earlier, a long-range CDW order is realized below 110K in single crystals annealed at 320 °C for over 48h. The CDW and AFM transition temperatures appear to be inversely correlated with each other. The onset of the CDW phase significantly reduces the critical field of the spin-flop transition, whereas the CDW transition remains stable against minor variations in magnetic orders such as annealing-induced magnetic clusters and spin-canting transitions. Single-crystal x-ray diffraction measurements reveal substantial disorder on the Ge1 site, which is characterized by displacement of the Ge1 atom from the Fe_{3}Ge layer along the c axis and can be reversibly modified by the annealing process. The observed annealing-tunable CDW and magnetic orders can be well understood in terms of disorder on the Ge1 site. Our study provides a vital starting point for the exploration of the unconventional CDW mechanism in FeGe and of kagome materials in general.

Periodic Atomic Displacements and Visualization of the Electron-Lattice Interaction in the Cuprate

Traditionally, X-ray scattering techniques have been used to detect the breaking of the structural symmetry of the lattice, which accompanies a periodic displacement of the atoms associated with charge density wave (CDW) formation in the cuprate pseudogap states. Similarly, the Spectroscopic Imaging Scanning Tunneling Microscopy (SI-STM) has visualized the short-range CDW. However, local coupling of electrons to the lattice in the form of a short-range CDW has been a challenge to visualize, thus a link between these measurements has been missing. Here, we introduce a novel STM-based technique to visualize the local bond length variations obtained from topographic imaging with picometer precision. Application of this technique to the high-Tc cuprate superconductor Bi2Sr2CaCu2O8+{\delta} revealed a high-fidelity local lattice distortion of the BiO lattice as large as 2%. In addition, analysis of local breaking of rotational symmetry associated with the bond lengths reveals modulations around four-unit-cell periodicity in both B1 and E representations in the C4v group of the lattice, which coincides with the uni-directional d-symmetry CDW (dCDW) previously identified within the CuO2 planes, thus providing direct evidence of electron-lattice coupling in the pseudogap state and a link between the X-ray scattering and STM measurements. Overall, our results suggest that the periodic lattice displacements in E representations correspond to a locally-frozen version of the soft phonons identified by the X-ray scattering measurements, and a fluctuation of the bond length is reflected by the fluctuation of the dCDW formation near the quantum critical point.

Enhanced charge density wave with mobile superconducting vortices in La1.885Sr0.115CuO4

Superconductivity in the cuprates is found to be intertwined with charge and spin density waves. Determining the interactions between the different types of order is crucial for understanding these important materials. Here, we elucidate the role of the charge density wave (CDW) in the prototypical cuprate La1.885Sr0.115CuO4, by studying the effects of large magnetic fields (H) up to 24 Tesla. At low temperatures (T), the observed CDW peaks reveal two distinct regions in the material: a majority phase with short-range CDW coexisting with superconductivity, and a minority phase with longer-range CDW coexisting with static spin density wave (SDW). With increasing magnetic field, the CDW first grows smoothly in a manner similar to the SDW. However, at high fields we discover a sudden increase in the CDW amplitude upon entering the vortex-liquid state. Our results signify strong coupling of the CDW to mobile superconducting vortices and link enhanced CDW amplitude with local superconducting pairing across the H − T phase diagram.

Possible Manifestation of Q-Ball Mechanism of High-Tc Superconductivity in X-ray Diffraction

It is demonstrated, that recently proposed by the author Q-ball mechanism of the pseudogap state and high-Tc superconductivity in cuprates may be detected in micro X-ray diffraction, since it imposes inverse correlations between the size and scattering intensities of the Q-ball charge-density-wave (CDW) fluctuations in these compounds. The Q-ball charge Q gives the number of condensed elementary bosonic excitations in a CDW fluctuation of finite amplitude. The attraction between these excitations inside Euclidean Q-balls is self-consistently triggered by the simultaneous condensation of Cooper/local pairs. Euclidean Q-ball solutions, analogous to the famous Q-balls of squarks in the supersymmetric standard model, arise due to the global invariance of the effective theory under the U(1) phase rotation of the Fourier amplitudes of the short-range CDW fluctuations. A conserved ‘Noether charge’ Q along the Matsubara time axis equals Q∝TM2V, where the temperature T, Q-ball’s volume V, and fluctuation amplitude M enter. Several predictions are derived in an analytic form that follow from this picture. The conservation of the charge Q leads to an inverse proportionality between the volume V and X-ray scattering intensity ∼M2 of the CDW puddles found in micro X-ray scattering experiments. The theoretical temperature dependences of the most probable Q value of superconducting Q-balls and their size and scattering amplitudes fit well the recent X-ray diffraction data in the pseudogap phase of high-Tc cuprates.

Short-Range Charge Density Wave and Bandgap Modulation by Au-Implanted Defects in TiSe2

Short-Range Charge Density Wave and Bandgap Modulation by Au-Implanted Defects in TiSe₂

Short-range charge-density wave order in La1.88Sr0.12CuO4 under uniaxial pressure

Short-range charge-density wave order in La_1.88Sr_0.12CuO₄ under uniaxial pressure

Microscopic evidence for the intra-unit-cell electronic nematicity inside the pseudogap phase in YBa2Cu4O8

Understanding the nature of the mysterious pseudogap phenomenon is one of the most important issues associated with cuprate high-Tc superconductors. Here, we report 17O nuclear magnetic resonance (NMR) studies on two planar oxygen sites in stoichiometric cuprate YBa2Cu4O8 to investigate the symmetry breaking inside the pseudogap phase. We observe that the Knight shifts of the two oxygen sites are identical at high temperatures but different below Tnem ∼ 185 K, which is close to the pseudogap temperature T*. Our result provides a microscopic evidence for intra-unit-cell electronic nematicity. The difference in quadrupole resonance frequency between the two oxygen sites is unchanged below Tnem, which suggests that the observed nematicity does not directly stem from the local charge density modulation. Furthermore, a short-range charge density wave (CDW) order is observed below T ≃ 150 K. The additional broadening in the 17O-NMR spectra because of this CDW order is determined to be inequivalent for the two oxygen sites, which is similar to that observed in case of nematicity. These results suggest a possible connection between nematicity, CDW order, and pseudogap.

Robust superconductivity intertwined with charge density wave and disorder in Pd-intercalated ErTe3

Pd-intercalated ErTe$_3$ is studied as a model system to explore the effect of "intertwined" superconducting and charge density wave (CDW) orders. Despite the common wisdom that superconductivity emerges only when CDW is suppressed, we present data from STM and AC susceptibility measurements that show no direct competition between CDW order and superconductivity. Both coexist over most of the intercalation range, with uniform superconductivity over length scales that exceed the superconducting coherence length. This is despite persisting short-range CDW order and increased scattering from the Pd intercalation. While superconductivity is insensitive to local defects in either of the bi-directional CDWs, vestiges of the Fermi-level distortions are observed in the properties of the superconducting state.

Visualizing the Anomalous Charge Density Wave States in Graphene/NbSe2 Heterostructures.

Metallic layered transition metal dichalcogenides (TMDs) host collective many-body interactions, including the competing superconducting and charge density wave (CDW) states. Graphene is widely employed as a heteroepitaxial substrate for the growth of TMD layers and as an ohmic contact, where the graphene/TMD heterostructure is naturally formed. The presence of graphene can unpredictably influence the CDW order in 2D CDW conductors. This work reports the CDW transitions of 2H-NbSe2 layers in graphene/NbSe2 heterostructures. The evolution of Raman spectra demonstrates that the CDW phase transition temperatures (TCDW ) of NbSe2 are dramatically decreased when capped by graphene. The induced anomalous short-range CDW state is confirmed by scanning tunneling microscopy measurements. The findings propose a new criterion to determine the TCDW through monitoring the line shape of the A1g mode. Meanwhile, the 2D band is also discovered as an indicator to observe the CDW transitions. First-principles calculations imply that interfacial electron doping suppresses the CDW states by impeding the lattice distortion of 2H-NbSe2 . The extraordinary random CDW lattice suggests deep insight into the formation mechanism of many collective electronic states and possesses great potential in modulating multifunctional devices.

Charge density wave modulation in superconducting BaPbO3/BaBiO3 superlattices

The isotropic, non-magnetic doped BaBiO$_3$ superconductors maintain some similarities to high-Tc cuprates, while also providing a cleaner system for isolating charge density wave (CDW) physics that commonly competes with superconductivity. Artificial layered superlattices offer the possibility of engineering the interaction between superconductivity and CDW. Here we stabilize a low temperature, fluctuating short range CDW order by using artificially layered epitaxial (BaPbO$_3$)$_{3m}$/(BaBiO$_3$)$_m$ (m = 1-10 unit cells) superlattices that is not present in the optimally doped BaPb$_{0.75}$Bi$_{0.25}$O$_3$ alloy with the same overall chemical formula. Charge transfer from BaBiO$_3$ to BaPbO$_3$ effectively dopes the former and suppresses the long range CDW, however as the short range CDW fluctuations strengthens at low temperatures charge appears to localize and superconductivity is weakened. The monolayer structural control demonstrated here provides compelling implications to access controllable, local density-wave orders absent in bulk alloys and manipulate phase competition in unconventional superconductors.

Short-range charge density wave order in 2H−TaS2

$2H\text{\ensuremath{-}}\mathrm{Ta}{\mathrm{S}}_{2}$ undergoes a charge density wave (CDW) transition at ${T}_{\mathrm{CDW}}\ensuremath{\sim}75$ K, however key questions regarding the onset of CDW order remain under debate. In this study, we explore the CDW transition through a combination of temperature and excitation-dependent Raman spectroscopy, angle resolved photoemission spectroscopy (ARPES), and density functional theory (DFT). Below ${T}_{\mathrm{CDW}}$ we identify two CDW amplitude modes that redshift and broaden with increasing temperature and one zone-folded mode that disappears above ${T}_{\mathrm{CDW}}$. Above ${T}_{\mathrm{CDW}}$, we observe a strong two-phonon mode that softens substantially upon cooling, which suggests the presence of substantial lattice distortions at temperatures as high as 250 K. This correlates with the ARPES observation of the persistence of a CDW energy gap above ${T}_{\mathrm{CDW}}$ and finite-temperature DFT calculations of the phonon band structure that indicate an instability occurring well above the CDW transition temperature. DFT also provides the atomic displacements of the CDW amplitude modes and reproduces their temperature dependence. From these observations we suggest that short range CDW order exists well above ${T}_{\mathrm{CDW}}$, which poses new questions regarding the interplay between electronic structure and vibrational modes in layered CDW materials.

Using controlled disorder to probe the interplay between charge order and superconductivity in NbSe2

The interplay between superconductivity and charge-density wave (CDW) in 2H-NbSe2 is not fully understood despite decades of study. Artificially introduced disorder can tip the delicate balance between two competing long-range orders, and reveal the underlying interactions that give rise to them. Here we introduce disorder by electron irradiation and measure in-plane resistivity, Hall resistivity, X-ray scattering, and London penetration depth. With increasing disorder, the superconducting transition temperature, Tc, varies non-monotonically, whereas the CDW transition temperature, TCDW, monotonically decreases and becomes unresolvable above a critical irradiation dose where Tc drops sharply. Our results imply that the CDW order initially competes with superconductivity, but eventually assists it. We argue that at the transition where the long-range CDW order disappears, the cooperation with superconductivity is dramatically suppressed. X-ray scattering and Hall resistivity measurements reveal that the short-range CDW survives above the transition. Superconductivity persists to much higher dose levels, consistent with fully gapped superconductivity and moderate interband pairing.

Spin susceptibility of charge-ordered YBa2Cu3Oy across the upper critical field

The value of the upper critical field Hc2, a fundamental characteristic of the superconducting state, has been subject to strong controversy in high-Tc copper oxides. Since the issue has been tackled almost exclusively by macroscopic techniques so far, there is a clear need for local-probe measurements. Here, we use 17O NMR to measure the spin susceptibility [Formula: see text] of the CuO2 planes at low temperature in charge-ordered YBa2Cu3O y We find that [Formula: see text] increases (most likely linearly) with magnetic field H and saturates above field values ranging from 20 T to 40 T. This result is consistent with the lowest Hc2 values claimed previously and with the interpretation that the charge density wave (CDW) reduces Hc2 in underdoped YBa2Cu3O y Furthermore, the absence of marked deviation in [Formula: see text] at the onset of long-range CDW order indicates that this [Formula: see text] reduction and the Fermi-surface reconstruction are primarily rooted in the short-range CDW order already present in zero field, not in the field-induced long-range CDW order. Above [Formula: see text], the relatively low values of [Formula: see text] at [Formula: see text] K show that the pseudogap is a ground-state property, independent of the superconducting gap.

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.

Anomalous relaxation kinetics and charge-density-wave correlations in underdoped BaPb1−xBixO3

Superconductivity often emerges in proximity of other symmetry-breaking ground states, such as antiferromagnetism or charge-density-wave (CDW) order. However, the subtle interrelation of these phases remains poorly understood, and in some cases even the existence of short-range correlations for superconducting compositions is uncertain. In such circumstances, ultrafast experiments can provide new insights by tracking the relaxation kinetics following excitation at frequencies related to the broken-symmetry state. Here, we investigate the transient terahertz conductivity of BaPb1-x Bi x O3--a material for which superconductivity is "adjacent" to a competing CDW phase--after optical excitation tuned to the CDW absorption band. In insulating BaBiO3 we observed an increase in conductivity and a subsequent relaxation, which are consistent with quasiparticles injection across a rigid semiconducting gap. In the doped compound BaPb0.72Bi0.28O3 (superconducting below TC = 7 K), a similar response was also found immediately above TC This observation evidences the presence of a robust gap up to T [Formula: see text] 40 K, which is presumably associated with short-range CDW correlations. A qualitatively different behavior was observed in the same material for [Formula: see text] 40 K. Here, the photoconductivity was dominated by an enhancement in carrier mobility at constant density, suggestive of melting of the CDW correlations rather than excitation across an optical gap. The relaxation displayed a temperature-dependent, Arrhenius-like kinetics, suggestive of the crossing of a free-energy barrier between two phases. These results support the existence of short-range CDW correlations above TC in underdoped BaPb1-x Bi x O3, and provide information on the dynamical interplay between superconductivity and charge order.

Fe–As Bond Fluctuations in a Double-Well Potential in LaFeAsO

While for a long time iron based superconductors have been investigated looking at the average crystalline structure there is now growing interest on the divergence of local from the average structure. Here we use advanced data analysis of EXAFS, a fast and local probe, which has key advantages compared to crystallographic measurements, in unveiling the dynamics of the local structure. The results show that the Fe-As pair oscillates in the double-well potential both in undoped and in cobalt doped LaFeAsO crystals. The parameters and the characteristics of the double-well potential are determined by curve fits of the polarized EXAFS data. Temperature dependent Fe-As pair distribution and tunneling frequency are derived from selected model of two potential wells. We observe the softening of the Fe-As oscillations at the tetragonal to orthorhombic structural phase transition at 150 K in LaFeAsO. A weak broad softening is observed while decreasing the temperature from 70 to 40 K in superconducting LaFe0.89Co0.11AsO which could be correlated with the onset of short range charge density wave order.

Emergent loop current order from pair density wave superconductivity

There is evidence that the pseudogap phase in the cuprates breaks time-reversal symmetry. Here we show that pair density wave (PDW) states give rise to a translational invariant nonsuperconducting order parameter that breaks time-reversal and parity symmetries, but preserves their product. This secondary order parameter has a different origin, but shares the same symmetry properties as a magnetoelectric loop current order that has been proposed earlier in the context of the cuprates to explain the appearance of intracell magnetic order. We further show that, due to fluctuations, this secondary loop current order, which breaks only discrete symmetries, can preempt PDW order, which breaks both continuous and discrete symmetries. In such a phase, the emergent loop current order coexists with spatial short-range superconducting order and possibly short-range charge density wave (CDW) order. Finally, we propose a PDW phase that accounts for intracell magnetic order and the Kerr effect, has CDW order consistent with x-ray scattering and nuclear magnetic resonance observations, and quasi-particle properties consistent with angle-resolved photoemission scattering.

CDW and Similarity of the Mott Insulator-to-Metal Transition in Cuprates with the Gas-to-Liquid-Liquid Transition in Supercooled Water

New advances in X-ray diffraction, extended X-ray absorption fine structure (EXAFS), and X-ray absorption near edge structure (XANES) using synchrotron radiation have now provided compelling evidence for a short-range charge density wave phase (CDW) called striped phase in the CuO2 plane of all cuprate high-temperature superconductors. The CDW is associated with a bond order wave (BOW) and an orbital density wave (ODW) forming nanoscale puddles which coexist with superconducting puddles below T c . The electronic CDW crystalline phase occurs around the hole doping 0.125 between the Mott charge transfer insulator and the 2D metal. The Van der Waals (VdW) theoretical model for a liquid of anisotropic extended objects proposed for supercooled water is used to describe the following: (a) the underdoped regime as a first spinodal regime of a “slightly doped charge transfer Mott insulator puddles coexisting with the striped polaronic CDW puddles;nd (b) the optimum doping regime as a second spinodal regime where striped polaronic CDW puddles coexist with the normal 2D metal puddles. This complex phase separation with three competing phases depends on the strength of the anisotropic electron-phonon interaction that favours the formation striped polaronic CDW phase.

Charge order and its connection with Fermi-liquid charge transport in a pristine high-T(c) cuprate.

Electronic inhomogeneity appears to be an inherent characteristic of the enigmatic cuprate superconductors. Here we report the observation of charge-density-wave correlations in the model cuprate superconductor HgBa2CuO(4+δ) (T(c)=72 K) via bulk Cu L3-edge-resonant X-ray scattering. At the measured hole-doping level, both the short-range charge modulations and Fermi-liquid transport appear below the same temperature of about 200 K. Our result points to a unifying picture in which these two phenomena are preceded at the higher pseudogap temperature by q=0 magnetic order and the build-up of significant dynamic antiferromagnetic correlations. The magnitude of the charge modulation wave vector is consistent with the size of the electron pocket implied by quantum oscillation and Hall effect measurements for HgBa2CuO(4+δ) and with corresponding results for YBa2Cu3O(6+δ), which indicates that charge-density-wave correlations are universally responsible for the low-temperature quantum oscillation phenomenon.

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.