Charge Density Wave Fluctuations Research Articles

Pressure Induced Nonmonotonic Evolution of Superconductivity in 6R-TaS_{2} with a Natural Bulk Van der Waals Heterostructure.

The natural bulk Van der Waals heterostructure compound 6R-TaS_{2} consists of alternate stacking 1T- and 1H-TaS_{2} monolayers, creating a unique system that incorporates charge-density-wave (CDW) order and superconductivity (SC) in distinct monolayers. Here, after confirming that the 2D nature of the lattice is preserved up to 8GPa in 6R-TaS_{2}, we documented an unusual evolution of CDW and SC by conducting high-pressure electronic transport measurements. Upon compression, we observe a gradual suppression of CDW within the 1T layers, while the SC exhibits a dome-shaped behavior that terminates at a critical pressure P_{c} around 2.9GPa. By taking account of the fact that the substantial suppression of SC is concomitant with the complete collapse of CDW order at P_{c}, we argue that the 6R-TaS_{2} behaves like a stack of Josephson junctions and thus the suppressed superconductivity can be attributed to the weakening of Josephson coupling associated with the presence of CDW fluctuations in the 1T layers. Furthermore, the SC reversely enhances above P_{c}, implying the development of emergent superconductivity in the 1T layers after the melting of T-layer CDW orders. These results show that the 6R-TaS_{2} not only provides a promising platform to explore emergent phenomena but also serves as a model system to study the complex interactions between competing electronic states.

Ultrafast generation of hidden phases via energy-tuned electronic photoexcitation in magnetite

Phase transitions occurring in nonequilibrium conditions can evolve through high-energy intermediate states inaccessible via equilibrium adiabatic conditions. Because of the subtle nature of such hidden phases, their direct observation is extremely challenging and requires simultaneous visualization of matter at subpicoseconds and subpicometer scales. Here, we show that a magnetite crystal in the vicinity of its metal-to-insulator transition evolves through different hidden states when controlled via energy-tuned ultrashort laser pulses. By directly monitoring magnetite's crystal structure with ultrafast electron diffraction, we found that upon near-infrared (800 nm) excitation, the trimeron charge/orbital ordering pattern is destroyed in favor of a phase-separated state made of cubic-metallic and monoclinic-insulating regions. On the contrary, visible light (400 nm) activates a photodoping charge transfer process that further promotes the long-range order of the trimerons by stabilizing the charge density wave fluctuations, leading to the reinforcement of the monoclinic insulating phase. Our results demonstrate that magnetite's structure can evolve through completely different metastable hidden phases that can be reached long after the initial excitation has relaxed, breaking ground for a protocol to control emergent properties of matter.

Pseudogap behavior in charge density wave kagome material ScV6Sn6 revealed by magnetotransport measurements

Over the last few years, significant attention has been devoted to studying the kagome materials A V3Sb5 (A = K, Rb, Cs) due to their unconventional superconductivity and charge density wave (CDW) ordering. Recently {{{{rm{ScV}}}}}_{6}{{{{rm{Sn}}}}}_{6} was found to host a CDW below ≈ 90 K, and, like A V3Sb5, it contains a kagome lattice comprised only of V ions. Here we present a comprehensive magnetotransport study on {{{{rm{ScV}}}}}_{6}{{{{rm{Sn}}}}}_{6}. We discovered several anomalous transport phenomena above the CDW ordering temperature, including insulating behavior in interlayer resistivity, a strongly temperature-dependent Hall coefficient, and a violation of Kohler’s rule. All these anomalies can be consistently explained by a progressive decrease in carrier densities with decreasing temperature, suggesting the formation of a pseudogap. Our findings suggest that high-temperature CDW fluctuations play a significant role in determining the normal state electronic properties of {{{{rm{ScV}}}}}_{6}{{{{rm{Sn}}}}}_{6}.

Strong electron-phonon coupling driven pseudogap modulation and density-wave fluctuations in a correlated polar metal

There is tremendous interest in employing collective excitations of the lattice, spin, charge, and orbitals to tune strongly correlated electronic phenomena. We report such an effect in a ruthenate, Ca3Ru2O7, where two phonons with strong electron-phonon coupling modulate the electronic pseudogap as well as mediate charge and spin density wave fluctuations. Combining temperature-dependent Raman spectroscopy with density functional theory reveals two phonons, B2P and B2M, that are strongly coupled to electrons and whose scattering intensities respectively dominate in the pseudogap versus the metallic phases. The B2P squeezes the octahedra along the out of plane c-axis, while the B2M elongates it, thus modulating the Ru 4d orbital splitting and the bandwidth of the in-plane electron hopping; Thus, B2P opens the pseudogap, while B2M closes it. Moreover, the B2 phonons mediate incoherent charge and spin density wave fluctuations, as evidenced by changes in the background electronic Raman scattering that exhibit unique symmetry signatures. The polar order breaks inversion symmetry, enabling infrared activity of these phonons, paving the way for coherent light-driven control of electronic transport.

Charge density wave fluctuation driven composite order in layered kagome metals

Charge density wave fluctuation driven composite order in layered kagome metals

Ultrafast melting of charge-density wave fluctuations at room temperature in 1T-TiSe2 monitored under non-equilibrium conditions

We investigate the ultrafast lattice dynamics in 1T-TiSe2 using femtosecond reflection pump–probe and pump–pump–probe techniques at room temperature. The time-domain signals and Fourier-transformed spectra show the A1g phonon mode at 5.9 THz. Moreover, we observe an additional mode at ≈ 3 THz, corresponding to the charge-density wave (CDW) amplitude mode (AM), which is generally visible below Tc≈200 K. We argue that the emergence of the CDW amplitude mode at room temperature can be a consequence of fluctuations of order parameters based on the additional experiment using the pump–pump–probe technique, which exhibited suppression of the AM signal within the ultrafast timescale of ∼0.5 ps.

Fano interference between collective modes in cuprate high-Tc superconductors

Cuprate high-Tc superconductors are known for their intertwined interactions and the coexistence of competing orders. Uncovering experimental signatures of these interactions is often the first step in understanding their complex relations. A typical spectroscopic signature of the interaction between a discrete mode and a continuum of excitations is the Fano resonance/interference, characterized by the asymmetric light-scattering amplitude of the discrete mode as a function of the electromagnetic driving frequency. In this study, we report a new type of Fano resonance manifested by the nonlinear terahertz response of cuprate high-Tc superconductors, where we resolve both the amplitude and phase signatures of the Fano resonance. Our extensive hole-doping and magnetic field dependent investigation suggests that the Fano resonance may arise from an interplay between the superconducting fluctuations and the charge density wave fluctuations, prompting future studies to look more closely into their dynamical interactions.

Phonon softening and slowing-down of charge density wave fluctuations in BaNi2As2

BaNi$_2$As$_2$ is a nonmagnetic analogue of the iron pnictide superconductors, and in its tetragonal state exhibits an incommensurate charge-density-wave (IC-CDW) and a sizable elastoresistance. In this work, phonons in BaNi$_2$As$_2$ associated with the IC-CDW and uniform in-plane lattice distortions are investigated using high-resolution inelastic X-ray scattering. The in-plane transverse acoustic phonons reveal no softening at temperatures where the elastoresistance increases strongly, indicating the latter to be electronically driven. Systematic phonon measurements reveal the IC-CDW occurs in two stages upon cooling: underdamped phonons first soften to zero energy well above the IC-CDW ordering temperature, then the resulting quasielastic IC-CDW fluctuations gradually slow down and coalesce into the static IC-CDW order. A possible origin for our observations is the IC-CDW in tetragonal BaNi$_2$As$_2$ being uniaxial, which provides an additional Ising degree of freedom favorable for disordered IC-CDW modulations, and accounts for the elastoresistance through a weak coupling to the lattice.

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.

Functional renormalization group study of the two-dimensional Su-Schrieffer-Heeger-Hubbard model

We study the Hubbard model on the square lattice coupled in addition to the optical Su-Schrieffer-Heeger (SSH) phonons, using the singular-mode functional renormalization group method. At half-filling and in the absence of the Hubbard interaction $U$, we find the degenerate spin-density-wave (SDW)/charge-density-wave (CDW)/s-wave superconductivity (sSC) state at smaller electron-phonon coupling strength $\lambda$ and higher phonon frequency $\omega$, and the valence bond solid (VBS) state at larger $\lambda$ and lower $\omega$. After switching on a positive $U$, the VBS state is suppressed, while the SDW state is enhanced. At finite doping, the SSH phonon is found to favor sSC at $U=0$. With increasing positive $U$, we find d-wave superconductivity (dSC) and incommensurate SDW states. In a narrow window of moderate $U$ and $\lambda$, we also find the incommensurate VBS state. The sSC and dSC here can be naturally related to the CDW and SDW fluctuations, both of which can be triggered by the SSH phonons. In contrast, the repulsive interaction $U$ enhances SDW but suppresses CDW fluctuations. Our results at half filling are consistent with quantum Monte Carlo (QMC), and provide insights at finite doping where QMC may suffer from the minus sign problem.

Linear nonsaturating magnetoresistance in kagome superconductor CsV3Sb5 thin flakes

Linear nonsaturating magnetoresistance (LMR) represents a class of anomalous resistivity response to external magnetic field that has been observed in a variety of materials including but not limited to topological semi-metals, high-T c superconductors and materials with charge density wave (CDW)/spin density wave orders. Here we report the observation of LMR in layered kagome superconductor and CDW material CsV3Sb5 thin flakes, as well as the dimensional crossover and temperature (T) crossover of such LMR. Specifically, in ultrathin CsV3Sb5 crystals, the magnetoresistance (MR) exhibits a crossover from LMR at low T to quadratic B dependence above the CDW transition temperature; the MR also exhibits a crossover from LMR to sublinear MR for sample thickness at around ∼20 nm at low T. We discuss several possible origins of the LMR and attribute the effect to two-dimensional CDW fluctuations. Our results may provide a new perspective for understanding the interactions between competing orders in kagome superconductors.

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

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

Interplay of charge density waves, disorder, and superconductivity in 2H-TaSe2 elucidated by NMR

Single crystals of pristine and 6% Pd-intercalated 2H‐TaSe2 have been studied by means of 77Se nuclear magnetic resonance. The temperature dependence of the 77Se spectrum, with an unexpected line narrowing upon Pd intercalation, unravels the presence of correlated local lattice distortions far above the transition temperature of the charge density wave (CDW) order, thereby supporting a strong-coupling CDW mechanism in 2H‐TaSe2. While, the Knight shift data suggest that the incommensurate CDW transition involves a partial Fermi surface gap opening. As for spin dynamics, the 77Se spin-lattice relaxation rate as a function of temperature shows that a pseudogap behavior dominates the low-energy spin excitations even within the CDW phase, and gets stronger along with superconductivity in the Pd-6% sample. We discuss that CDW fluctuations may be responsible for the pseudogap as well as superconductivity, although the two phenomena are unlikely to be directly linked each other.

Out-of-Plane Sulfur Distortions in the Bi4O4S3 Superconductor

The local atomic structure of the non-magnetic layered superconductor Bi4O4S3 was investigated using neutron diffraction and pair density function (PDF) analysis. Although on average, the crystal structure is well ordered, evidence for local, out–of–plane sulfur distortions is provided, which may act as a conduit for charge transfer from the SO4 blocks into the superconducting BiS2 planes. In contrast with LaO1−xFxBiS2, no sulfur distortions were detected in the planes, which indicates that charge density wave fluctuations are not supported in Bi4O4S3.

Role of Equilibrium Fluctuations in Light-Induced Order.

Engineering novel states of matter with light is at the forefront of materials research. An intensely studied direction is to realize broken-symmetry phases that are "hidden" under equilibrium conditions but can be unleashed by an ultrashort laser pulse. Despite a plethora of experimental discoveries, the nature of these orders and how they transiently appear remain unclear. To this end, we investigate a nonequilibrium charge density wave (CDW) in rare-earth tritellurides, which is suppressed in equilibrium but emerges after photoexcitation. Using a pump-pump-probe protocol implemented in ultrafast electron diffraction, we demonstrate that the light-induced CDW consists solely of order parameter fluctuations, which bear striking similarities to critical fluctuations in equilibrium despite differences in the length scale. By calculating the dynamics of CDW fluctuations in a nonperturbative model, we further show that the strength of the light-induced order is governed by the amplitude of equilibrium fluctuations. These findings highlight photoinduced fluctuations as an important ingredient for the emergence of transient orders out of equilibrium. Our results further suggest that materials with strong fluctuations in equilibrium are promising platforms to host hidden orders after laser excitation.

In-plane Isotropy of the Low Energy Phonon Anomalies in YBa2Cu3O6+x

We study the temperature dependence of the low energy phonons in the $(H, 0, L)$ reciprocal plane of the highly ordered ortho-II YBa$_2$Cu$_3$O$_{6.55}$ cuprate high temperature superconductor by means of high-resolution inelastic x-ray scattering. Anomalies associated with the emergence of long-range charge density wave (CDW) fluctuations are observed, and are qualitatively similar to those previously observed in the $(0, K, L)$ plane. This confirms the unconventional nature of this bi-dimensional CDW, which is not soft-phonon driven. With the support of first principles calculations, the symmetry of the anomalous phonon is identified and is found to match that of the charge modulation. This suggests in turn that these anomalies originate from a direct coupling between the phonons and the collective CDW excitations.

Broadening and sharpening of the Drude peak through antiferromagnetic fluctuations

Antiferromagnetic or charge density wave fluctuations couple with light through the recently discovered {\pi}-ton contribution to the optical conductivity, and quite generically constitute the dominant vertex corrections in low-dimensional correlated electron systems. Here we study the arguably simplest version of these $\pi$-tons based on the semi-analytical random phase approximation (RPA) ladder in the transversal particle-hole channel. The vertex corrections to the optical conductivity are calculated directly for real frequencies. We validate that the RPA qualitatively reproduces the {\pi}-ton vertex corrections to the Drude peak in the Hubbard model. Depending on the temperature we find vertex corrections to broaden or sharpen the Drude peak.

Effects of disorder and hydrostatic pressure on charge density wave and superconductivity in 2H−TaS2

We report the comparative effects of disorder and hydrostatic pressure on charge density wave (CDW) and superconductivity (SC) in $2H\text{\ensuremath{-}}{\mathrm{TaS}}_{2}$ by measuring electrical resistivity and ac magnetic susceptibility. For the crystals in the clean limit (low disorder level), CDW ground state is suppressed completely at a critical pressure ${P}_{\mathrm{c}}\ensuremath{\sim}6.24(5)\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$ where a dome-shaped pressure dependence of superconducting transition temperature ${T}_{\mathrm{c}}$(P) appears with a maximum value of ${{T}_{\mathrm{c}}}^{\mathrm{max}}\ensuremath{\sim}9.15\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, indicating strong competitions between CDW and SC. The temperature exponent $n$ of low-temperature resistivity data decreases from \ensuremath{\sim}3.36 at ambient pressure (AP) to \ensuremath{\sim}1.29(2) at ${P}_{\mathrm{c}}$ and then retains a saturated value \ensuremath{\sim}2.10(4) when the pressure is higher than 7.5 GPa; accordingly, the quadratic temperature coefficient of normal-state resistivity A peaks out just at ${P}_{\mathrm{c}}$ with an enhancement by nearly one order in magnitude. These features strongly manifest that the enhanced critical CDW fluctuations near ${P}_{\mathrm{c}}$ are possible important glues for superconducting pairings. High-pressure magnetic susceptibility indicates that superconducting shielding volume increases with pressure and retains a nearly constant value above ${P}_{\mathrm{c}}$, which evidences that the enhancement of ${T}_{\mathrm{c}}$(P) is accompanied by the expense of CDW. For those crystals in dirty limit (high disorder level), there is no clear CDW phase transition in resistivity; the pressure dependence of ${T}_{\mathrm{c}}$(P) and $n$ broadens up and becomes less apparent in comparison with the clean crystals. Our results suggest that disorder scattering and the melting of CDW are two factors affecting SC, and the melting of CDW dominates the change of ${T}_{\mathrm{c}}$ below ${P}_{\mathrm{c}}$; the enhancement of ${T}_{\mathrm{c}}$(P) is associated with the suppression of CDW by pressure and the increase in the density of states at Fermi level; however, after the CDW collapse, superconducting pairing strength is strongly weakened by impurity scattering above ${P}_{\mathrm{c}}$ according to Anderson's theorem.

Momentum-dependent electron-phonon coupling in charge density wave systems

Many charge density wave (CDW) systems exhibit $q(T)$ electron-hole modulations continuously varying with $T$ and saturating upon cooling at an incommensurate value even if the maximum occurring in the electron-hole Lindhard response does not exhibit such a thermal shift. Using a simple RPA argument we show that the experimental $q(T)$ can be understood if the electron-phonon coupling (EPC) $g(q)$, necessary to set coupled electronic and structural modulations, is momentum dependent. In this analysis, the sense of variation of $q(T)$ depends upon the sign of $\frac{\ensuremath{\partial}g(q)}{\ensuremath{\partial}q}$ and its amplitude of thermal variation is controlled by the electron-hole coherence length (or CDW rigidity) in the modulation direction. This model quantitatively accounts for the thermal dependence of $q(T)$ in the one-dimensional (1D) CDW system ${\mathrm{K}}_{0.3}\mathrm{Mo}{\mathrm{O}}_{3}$ (blue bronze) both in its CDW ground state and in its pretransitional CDW fluctuation regime. We suggest that such a general analysis can be extended to account for the $q(T)$ dependence observed in other 1D and 2D CDW systems such as the transition metal di- and trichalcogenides as well as the lanthanide and rare-earth tritellurides. Using a detailed analysis of the low frequency phonon spectrum of the blue bronze, we then propose a new scenario for the $q$ dependent EPC, where $g(q)$ is due to a momentum-dependent hybridization between the critical phonon branch bearing the Kohn anomaly and other low-lying phonon branches. This allows obtaining a sign of $\frac{\ensuremath{\partial}g(q)}{\ensuremath{\partial}q}$ in agreement with that deduced from the analysis of $q(T)$. Finally, we propose that similar hybridization effects could also be relevant for other 1D and 2D CDW systems exhibiting a thermally dependent modulation.

Diagrammatic study of optical excitations in correlated systems

The optical conductivity contains relevant information on the properties of correlated electron systems. In infinite dimensions, where dynamical mean field theory becomes exact, vertex corrections can be neglected and the conductivity computed from particle-hole bubbles. An interesting question concerns the nature and effect of the most relevant vertex corrections in finite-dimensional systems. A recent numerical study showed that the dominant vertex correction near an ordering instability with wave vector {\pi} comes from a vertical ladder, analogous to the Maki-Thompson diagram. Since the RPA version of this ladder diagram, dubbed {\pi}-ton, can be easily evaluated, this suggests a simple procedure for incorporating antiferromagnetic or charge density wave fluctuations into dynamical mean field estimates of the optical conductivity and related susceptibilities. We implement this procedure for the half-filled Hubbard model, considering the {\pi}-ton and a double-ladder extension of the {\pi}-ton, and reveal the spectral signatures of these vertex corrections.