Charge Density Wave Condensate Research Articles

The noise of the charge density waves in quasi-1D NbSe3 nanowires — contributions of electrons and quantum condensate

Low-frequency electronic noise in charge-density-wave van der Waals materials has been an important characteristic, providing information about the material quality, phase transitions, and collective current transport. However, the noise sources and mechanisms have not been completely understood, particularly for the materials with a non-fully gapped Fermi surface where the electrical current includes components from individual electrons and the sliding charge-density wave. We investigated noise in nanowires of quasi-one-dimensional NbSe3, focusing on a temperature range near the Pearls transition TP1 ∼ 145 K. The data analysis allowed us to separate the noise produced by the individual conduction electrons and the quantum condensate of the charge density waves before and after the onset of sliding. The noise as a function of temperature and electric bias reveals several intriguing peaks. We explained the observed features by the depinning threshold field, the creep and sliding of the charge density waves, and the possible existence of the hidden phases. It was found that the charge density wave condensate is particularly noisy at the moment of depinning. The noise of the collective current reduces with the increasing bias voltage in contrast to the noise of the individual electrons. Our results shed light on the behavior of the charge density wave quantum condensate and demonstrate the potential of noise spectroscopy for investigating the properties of low-dimensional quantum materials.

Non-Maxwell–Boltzmann dependence of channel carrier concentration in a quasi one dimensional charge density wave channel in the ballistic transport regime

With the aid of a coherent transport model utilizing the non-equilibrium Green function approach, a three terminal device with metallic gate, source and drain and a quasi one dimensional charge density wave (CDW) channel is simulated focussing on the transistor behaviour brought about by a sweep of the channel potential or equivalently the chemical potential in the channel. The channel is strongly insulating only at half-filling and moving to lower and higher carrier concentrations both incur a mean field phase transition to a conducting state. With the aid of conductance calculations for a pinned CDW condensate, we present calculations for the sub-threshold slope in terms of the hopping parameter or equivalently the width of the tight-binding chain. The effects of source to drain bias and length are examined. The conductance profiles are analyed in relation to transmission profiles. The observed CDW profiles are explained in terms of filling and Fermi surface nesting. Boundary conditions, gap equations and response functions are shown to reveal the commensurability conditions and size of the transport gap. The channel carrier concentration is modulated in an athermal (non-Maxwellian–Boltzmann) fashion, thereby making it an interesting prospect for steep transistors.

Coherent, time-correlated tunneling of density wave electrons

A growing body of evidence reveals that charge density wave (CDW) transport is a high-temperature cooperative quantum phenomenon. According to the time-correlated soliton tunneling (ST) model, quantum solitons, or electron-phonon correlates within the CDW condensate, act much like electrons tunneling through a Coulomb-blockade tunnel junction. Pair creation of charged fluidic soliton droplets is prevented by their electrostatic energy below a Coulomb-blockade threshold electric field. Above threshold, the quantum fluid flows in a periodic fashion, via a hybrid between Zener-like and coherent Josephson-like tunneling. We summarize the time-correlated ST model and compare model simulations with experiment. The ST model shows excellent agreement with coherent voltage oscillations, and with CDW current-voltage characteristics. Finally, we discuss implications for physics and potential applications.

Impact of the charge density wave state in the electrodynamic response of ZrTe3−xSex : Optical evidence for a pseudogap phase

The emergence of superconductivity upon progressively suppressing the long-range, charge-density-wave (CDW) order characterizes the phase diagram of several materials of interest in the on-going solid-state physics research. Se-doped ${\mathrm{ZrTe}}_{3}$ compounds provide the most recent, suitable arena in order to investigate the interplay of otherwise competing orders in layeredlike two-dimensional systems. We present an optical study of the CDW state in ${\mathrm{ZrTe}}_{3\ensuremath{-}x}{\mathrm{Se}}_{x}$ at selected Se dopings, based on the measurement of the reflectivity from the far-infrared up to the ultraviolet, as a function of temperature. We particularly focus our attention to the redistribution of the spectral weight, which images the impact of the CDW state within the optical conductivity across the phase diagram of the title compounds. The electrodynamic response is consistent with a scenario based on a long-range CDW condensate at low Se doping. Upon increasing the Se content, this then gives way to local, short-range order CDW segments. Our spectral weight analysis reveals the presence of a pseudogap phase, as fingerprint of the CDW precursor effects and thus shaping the charge dynamics of the title compounds in their normal state, preceding the onset of superconductivity.

Time-Dependent Ginzburg–Landau Equation and Boltzmann Transport Equation for Charge-Density-Wave Conductors

The time-dependent Ginzburg-Landau equation and the Boltzmann transport equation for one-dimensional charge-density-wave (CDW) conductors are derived from a microscopic model by applying the Keldysh Green's function approach under a quasiclassical approximation. The effects of external electric field and impurity pinning of the CDW are fully taken into account without relying on a phenomenological argument. These equations simultaneously describe spatiotemporal dynamics of both the CDW and quasiparticles, so they serve as a powerful tool to analyze various nonequilibrium phenomena, such as the current conversion between the CDW condensate and quasiparticles mediated by phase slips. It is shown that, in typical situations, the equations correctly describe the nonlinear behavior of electric conductivity in a simpler manner.

Impurity Effect on the Inter-Chain Dielectric Response of the CDW Condensate in K0.3MoO3

We study the effect of impurity on the charge-density-wave (CDW) state via low-frequency dielectric measurements, especially for the inter-chain direction. The extremely high dielectric constant seen in non-doped K0.3MoO3 is strongly reduced by W- or V-doping, demonstrating that the three-dimensional (3D) phase rigidity is an innate characteristic of CDW condensate. In the impurity-doped K0.3MoO3, the 3D rigidity has been lost and the CDW state exhibits a different nature in which the dielectric response of CDW cannot be explained in terms of the screened phason model.

Field-Dependent Dielectric Response of the Three-Dimensional Charge-Density Wave in K0.3MoO3

The dielectric response of K0.3MoO3 was investigated both in the charge-density-wave (CDW) chain axis and in the inter-chain direction. At sufficiently low frequencies, the anomalous rise in the dielectric constant e(T) was observed isotropically, indicating three-dimensionality of the CDW condensate. On the other hand, e(T) curves are highly sensitive to ac field in the chain direction. The anomaly was inferred to be caused by hopping of the charged phase defects, which is apparently inconsistent with the glassy CDW picture.

Charge-density wave condensate in charge-ordered manganites: impact of ferromagnetic order and spin-glass disorder

The behavior of charge-density wave (CDW) condensates with the systematic introduction of ferromagnetic (FM) and spin-glass phases in the charge-ordered (CO) lattice of Nd0.5Sr0.5MnO3 (NSMO) and Eu0.5Sr0.5MnO3 (ESMO) epitaxial thin films was investigated by terahertz time-domain spectroscopy. The optical conductivity of (100)-oriented NSMO film, in which the CO lattice has an insignificant volume of the FM phase, exhibits a peak with attributes of CDW collective excitation at ∼3.2 meV. This peak becomes completely submerged in the Drude continuum as the volume of the epitaxial strain-induced FM phase increases in the CO state of (110)- and (111)-oriented NSMO films. In contrast, the ESMO (100) film, having a short-range CO phase amid a spin-glass-like state, displays a subtle CDW peak in conductivity. Modeling the optical terahertz conductivity with the phenomenological Lorentz–Drude relation and extracting the optical weight due to both contributions (Lorentz and Drude), it was found that the manifestation of CDW condensates is associated with the generic strength of charge ordering and that the condensate suffers a more pronounced suppression when FM order dilutes the CO lattice than when spin-glass disorder weakens the CO state.

Infrared and Raman investigation of the charge–density-wave state in rare-earth tri-telluride compounds

We summarize our recent efforts in investigating the charge–density-wave (CDW) state of the rare-earth tri-tellurides RTe3 by means of infrared and Raman techniques. We identify the CDW gap, as order parameter of the broken-symmetry ground state, as well as the collective mode of the CDW condensate.

Pressure dependence of the single particle excitation in the charge-density-waveCeTe3system

We present new data on the pressure dependence at 300 K of the optical reflectivity of CeTe$_3$, which undergoes a charge-density-wave (CDW) phase transition well above room temperature. The collected data cover an unprecedented broad spectral range from the infrared up to the ultraviolet, which allows a robust determination of the gap as well as of the fraction of the Fermi surface affected by the formation of the CDW condensate. Upon compressing the lattice there is a progressive closing of the gap inducing a transfer of spectral weight from the gap feature into the Drude component. At frequencies above the CDW gap we also identify a power-law behavior, consistent with findings along the $R$Te$_3$ series (i.e., chemical pressure) and suggestive of a Tomonaga-Luttinger liquid scenario at high energy scales. This newest set of data is placed in the context of our previous investigations of this class of materials and allows us to revisit important concepts for the physics of CDW state in layered-like two-dimensional systems.

Evidence for coupling between charge density waves and phonons in two-dimensional rare-earth tritellurides

We report on a Raman-scattering investigation of the charge density wave (CDW), quasi-two-dimensional rare-earth tritellurides $R{\text{Te}}_{3}$ ($R=\text{La}$, Ce, Pr, Nd, Sm, Gd, and Dy) at ambient pressure, and of ${\text{LaTe}}_{3}$ and ${\text{CeTe}}_{3}$ under externally applied pressure. The observed phonon peaks can be ascribed to the Raman-active modes for both the undistorted and the distorted lattices in the CDW state by means of a first-principles calculation. The latter also predicts the Kohn anomaly in the phonon dispersion, driving the CDW transition. The integrated intensity of the two most prominent modes scales as a characteristic power of the CDW-gap amplitude upon compressing the lattice, which provides clear evidence for the tight coupling between the CDW condensate and the vibrational modes.

Optical properties of the charge-density-wave polychalcogenide compounds R 2Te 5 (R=Nd, Sm and Gd)

We investigate the rare-earth polychalcogenide $R_2$Te$_5$ ($R$=Nd, Sm and Gd) charge-density-wave (CDW) compounds by optical methods. From the absorption spectrum we extract the excitation energy of the CDW gap and estimate the fraction of the Fermi surface which is gapped by the formation of the CDW condensate. In analogy to previous findings on the related $R$Te$_n$ (n=2 and 3) families, we establish the progressive closing of the CDW gap and the moderate enhancement of the metallic component upon chemically compressing the lattice.

Pressure dependence of the optical properties of the charge-density-wave compoundLaTe2

We report the pressure dependence of the optical response of $\mathrm{La}{\mathrm{Te}}_{2}$, which is deep in the charge-density-wave (CDW) ground state even at $300\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. The reflectivity spectrum is collected in the midinfrared spectral range at room temperature and at pressures between 0 and $7\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$. We extract the energy scale due to the single-particle excitation across the CDW gap and the Drude weight. We establish that the gap decreases upon compressing the lattice while the Drude weight increases. This signals a reduction in the quality of nesting upon applying pressure, therefore inducing a lesser impact of the CDW condensate on the electronic properties of $\mathrm{La}{\mathrm{Te}}_{2}$. The consequent suppression of the CDW gap leads to a release of additional charge carriers, manifested by the shift of weight from the gap feature into the metallic component of the optical response. On the contrary, the power-law behavior, seen in the optical conductivity at energies above the gap excitation and indicating a weakly interacting limit within the Tomonaga-Luttinger liquid scenario, seems to be only moderately dependent on pressure.

Peierls transition in two-dimensional metallic monophosphate tungsten bronzes

Abstract The two-dimensional metallic bronzes made of ReO3-type layers of MoO6 or WO6 octahedra present quasi-one-dimensional (1D) electronic structures along three directions of preferential overlap of the t2g transition metal orbitals. They exhibit a Peierls instability towards the formation of charge density waves (CDW) at the 2kF critical wave vector allowing to nest simultaneously the Fermi surfaces associated to two quasi-1D band structures out of three. The Peierls transition is achieved through a periodic lattice distortion (PLD), that we analyse, in the present work, for the monophosphate tungsten bronzes. The Peierls critical temperature decreases in presence of disorder, which breaks the electron–hole pairs forming the CDW condensate, and in presence of misfit between the PLD wave vector and the 2kF nesting wave vector. The pair breaking effect accounts for the drop of the Peierls transition in the NaxP4W12O44 (x

Nonlinear conduction of charge-density wave in the quantum Hall regime of η-Mo 4O 11

Nonlinear pulsed electric field response of charge-density wave (CDW) in η-Mo 4O 11 has been measured in magnetic fields where the quantum Hall effect (QHE) is observable. We have found that the relaxation time characterizing the sliding motion of CDW condensates shows pronounced peaks at magnetic fields corresponding to the Hall plateaus, which strongly suggests that a charge transfer from the CDW condensate system to the quantized carrier (QHE) system occurs.

Nonlinear response to pulsed electric field in η-Mo 4O 11 crystal under magnetic field

Pulsed electric field response for a charge-density-wave (CDW) material η-Mo 4O 11 crystal along the b-axis (nesting direction) has been measured at 4.2 Kin magnetic field up to 3 T, Above a threshold electric field E T, we have observed a nonlinear response to the pulsed electric field, which is due to a deformation of CDW condensates, followed by a sliding motion. The former decay curve can be expressed by a simple exponential form a relaxation time τ D, while the latter obeys an extended exponential form with τ S. These characteristic relaxation times are dependent on both electric and magnetic field intensities, for which qualitative discussion is given.

Temperature dependence of the anisotropic electrodynamics in the ladder compounds

The optical reflectivity as a function of temperature of the title compound for x =0 ; 5a nd 12 has been measured over a broad spectral range from 4 meV up to 12 eV. Our ndings suggest a very anisotropic dynamics of the charge excitation spectrum when measuring along or perpendicular to the ladders. Moreover, a metal-insulator transition develops at low temperatures, leading to a suppression of Drude spectral weight in the far and mid-infrared spectral range. We identify this behaviour as a consequence of the localization eects for small Ca substitution, and of the possible formation of a charge density wave condensate for large Ca substitution.

Theory of Aharonov–Bohm oscillations resulting from a charge density wave condensate flowing across an array of columnar defects in a magnetic field

We propose a microscopic theory for the Aharonov–Bohm oscillations, observed by Latyshev et al. in the magnetotransport experiment in NbSe3 with a charge density wave (CDW). The CDW slides across an array of columnar defects in a high magnetic field. For the charge carrying quanta of CDW these defects are elementary solenoids carrying a magnetic flux. The quantum CDW current acquires a component oscillating with the flux, with the period hc/2e. Its magnitude is proportional to the concentration of columnar defects. The lower limit to the phase breaking length for these oscillations is set by the minimal Lee–Rice coherence length.

Vibrational properties of the CDW condensate in the quasi-one-dimensional conductor (TaSe 4) 2I: Numerical and experimental study

We report on the numerical and experimental study of the vibrational spectrum of the charge-density-wave (CDW) conductor (TaSe 4) 2I. The microscopic mechanism accounting for the giant IR peak at frequencies about ∼ 40 cm −1 in the (TaSe 4) 2I is proposed. The mechanism is based on an assumption about dynamical charge transfer between adjacent CDW periods accompanying their vibration in corresponding normal mode with wave vector equal to that of superstructure. The mechanism is consistent also with the increase in the IR intensity of the peak observed experimentally when heating the (TaSe 4) 2I crystal above the Peierls transition temperature T p = 261 K. Critical index of the Peierls transition order parameter determined from the temperature dependence of the phase phonons intensity is found to be about 0.17, consistent with the results of X-ray experiments.

On the Fröhlich charge density wave and Peierls transition

The exact solution of the system of nonlinear equations for Frohlich charge density wave (CDW) in the continuum approximation is discussed, and the temperature behaviour of the CDW condensate is investigated in a framework of the mean-field approximation. It is shown that the CDW representation in the form of a conventional harmonic wave is only correct under certain conditions, namely, not too strong an electron-phonon interaction or not too low an electron density. According to the exact solution, the CDW is essentially a nonlinear wave represented by a harmonic series. This is confirmed by the experimental data on the CDW current oscillation spectra in which the overtones are present together with the principal harmonic (the so called “narrow band noise”). At strong enough electron-phonon coupling or at low enough electron density the CDW wave vector is temperature dependent, and the BCS relation between Peierls transition temperature and energetic gap in the electron spectra at zero temperature is violated.