Pinned Charge Density Waves Research Articles

An exactly solvable model of randomly pinned charge density waves in two dimensions

The nature of the interplay between fluctuations and quenched random disorder is a long-standing open problem, particularly in systems with a continuous order parameter. This lack of a full theoretical treatment has been underscored by recent advances in experiments on charge density wave materials. To address this problem, we formulate an exactly solvable model of a two-dimensional randomly pinned incommensurate charge density wave, and use the large-N technique to map out the phase diagram and order parameter correlations. Our approach captures the physics of the Berezinskii–Kosterlitz–Thouless phase transition in the clean limit at large N. We pay particular attention to the roles of thermal fluctuations and quenched random field disorder in destroying long-range order, finding a novel crossover between weakly- and strongly-disordered regimes.

Thermoelectric transport properties of gapless pinned charge density waves

Quantum strongly correlated matter exhibits properties which are not easily explainable in the conventional framework of Fermi liquids. Universal effective field theory tools are applicable in these cases regardless of the microscopic details of the quantum system, since they are based on symmetries. It is necessary, however, to construct these effective tools in full generality, avoiding restrictions coming from particular microscopic descriptions which may inadequately constrain the coefficients that enter in the effective theory. In this work we demonstrate with explicit examples how the hydrodynamic coefficients, which have been recently reinstated in the effective theory of pinned charge density waves (CDWs), can affect the phenomenology of the thermoelectric transport in strongly correlated quantum matter. Our examples, based on two classes of holographic models with pinned CDW, have microscopics which are conceptually different from Fermi liquids. Therefore, the above transport coefficients are nonzero, contrary to the conventional approach. We show how these coefficients allow one to take into account the change of sign of the Seebeck coefficient and the low resistivity of the CDW phase of the cuprate high temperature superconductors, without referring to the effects of Fermi surface reconstruction.

Phase relaxation and pattern formation in holographic gapless charge density waves

We study the dynamics of spontaneous translation symmetry breaking in holographic models in presence of weak explicit sources. We show that, unlike conventional gapped quantum charge density wave systems, this dynamics is well characterized by the effective time dependent Ginzburg-Landau equation, both above and below the critical temperature, which leads to a “gapless” algebraic pattern of metal-insulator phase transition. In this framework we elucidate the nature of the damped Goldstone mode (the phason), which has earlier been identified in the effective hydrodynamic theory of pinned charge density wave and observed in holographic homogeneous lattice models. We follow the motion of the quasinormal modes across the dynamical phase transition in models with either periodic inhomogeneous or helical homogeneous spatial structures, showing that the phase relaxation rate is continuous at the critical temperature. Moreover, we find that the qualitative low-energy dynamics of the broken phase is universal, insensitive to the precise pattern of translation symmetry breaking, and therefore applies to homogeneous models as well.

A New Type of Charge-Density-Wave Pinning in Orthorhombic TaS3 Crystals with Quenching Defects

Diminishing in the concentration of quenching defects during thermocycling of orthorhombic TaS$_3$ samples in the temperature range below the Peierls transition temperature $T <T_P$ is observed. It makes it possible to study the character of pinning of the charge density wave (CDW) by these defects. A number of fundamental differences from pinning by ordinary local pinning centers - impurities and point defects - have been found. We conclude that quenching defects are extended (non-local) objects (presumably, dislocations) that can diffuse from the crystal during low-temperature termocycling due to their strong interaction with the CDW, which is intrinsic for the Peierls conductors. The presence of these defects leads to a previously unknown non-local type of CDW pinning that acts on $T_P$ and the threshold field for the onset of the CDW sliding, $E_T$, differently in comparison with the local pinning centers.

Microwave Spectroscopy of a Weakly Pinned Charge Density Wave in a Superinductor.

A chain of small Josephson junctions (a.k.a. superinductor) emerged recently as a high-inductance, low-loss element of superconducting quantum devices. We notice that the intrinsic parameters of a typical superinductor in fact place it into the Bose glass universality class for which the propagation of waves in a sufficiently long chain is hindered by pinning. Its weakness provides for a broad crossover from the spectrum of well-resolved plasmon standing waves at high frequencies to the low-frequency excitation spectrum of a pinned charge density wave. We relate the scattering amplitude of microwave photons reflected off a superinductor to the dynamics of a Bose glass. The dynamics at long and short scales compared to the Larkin pinning length determines the low- and high-frequency asymptotes of the reflection amplitude.

Effect of Cu doping on superconductivity in TaSe3: Relationship between superconductivity and induced charge density wave

By measuring the temperature dependence of the resistance, we investigated the effect of Cu doping on superconductivity (SC) in Cu-doped TaSe3 in which the charge density wave (CDW) transition is induced by Cu doping. We observed an emergence of a region where the SC transition temperature (TC) decreased in samples with higher Cu concentrations and found that the region tended to expand with increasing Cu concentration. In addition, the temperature dependence of the upper critical field (HC2) of Cu-doped TaSe3 was found to differ from that of pure TaSe3. Based on these experimental results and the fact that the SC of TaSe3 is filamentary, we conclude that SC is suppressed locally by Cu doping and competes with the CDW in Cu-doped TaSe3. The resistance anomaly due to the CDW transition was extremely small and the size of the anomaly was enhanced with increasing Cu concentration but the temperature at which the anomaly appeared hardly changed. These results of the anomaly and the local suppression of SC suggest that the induced CDWs have short-range order in the vicinity of Cu atoms. We also discuss the effect of the pinning of CDWs on the relationship between SC and short-range order CDWs.

Low-Frequency Current Fluctuations and Sliding of the Charge Density Waves in Two-Dimensional Materials.

We investigated low-frequency noise in two-dimensional (2D) charge density wave (CDW) systems, 1 T-TaS2 thin films, as they were driven from the nearly commensurate (NC) to incommensurate (IC) CDW phases by voltage and temperature stimuli. This study revealed that noise in 1 T-TaS2 has two pronounced maxima at the bias voltages, which correspond to the onset of CDW sliding and the NC-to-IC phase transition. We observed unusual Lorentzian features and exceptionally strong noise dependence on electric bias and temperature, leading to the conclusion that electronic noise in 2D CDW systems has a unique physical origin different from known fundamental noise types. We argue that noise spectroscopy can serve as a useful tool for understanding electronic transport phenomena in 2D CDW materials characterized by coexistence of different phases and strong pinning.

Phase coexistence and pinning of charge density waves by interfaces in chromium

We study the temperature dependence of the charge density wave (CDW) in a chromium thin film using x-ray diffraction. We exploit the interference between the CDW satellite peaks and Laue oscillations to determine the amplitude, the phase, and the period of the CDW. We find discrete half-integer periods of CDW in the film and switching of the number of periods by one upon cooling/heating with a thermal hysteresis of 20 K. The transition between different CDW periods occurs over a temperature range of 30 K, slightly larger than the width of the thermal hysteresis. A comparison with simulations shows that the phase transition occurs as a variation of the volume fraction of two distinct phases with well-defined periodicities. The phase of the CDW is constant for all temperatures, and we attribute it to strong pinning of the CDW by the mismatch-induced strain at the film-substrate interface.

The Peierls instability and charge density wave in one-dimensional electronic conductors

Abstract We review salient structural and electronic features associated with the concomitant Peierls–charge density wave (CDW) instabilities observed in most one-dimensional (1D) inorganic and organic electronic conductors. First of all, the genesis of these concepts is placed in an historical perspective. We then present basic experimental facts supporting the general description of these 1D electron–phonon coupled systems developed in the 1970s. In this framework we shall consider in particular the role of 1D fluctuations on both lattice and electronic degrees of freedom, and of the inter-chain Coulomb coupling between CDWs in stabilizing in 3D the Peierls transition at finite temperature. We also clarify, in relation with experimental findings, the various conditions of adiabaticity of the electron–phonon coupling. Finally we illustrate by recent structural measurements the pioneering work of Jacques Friedel on CDW elasticity and plasticity and CDW pinning to defects through the appearance of Friedel oscillations.

Long-range order and pinning of charge-density waves in competition with superconductivity

Recent experiments show that charge-density-wave correlations are prevalent in underdoped cuprate superconductors. The correlations are short ranged at weak magnetic fields but their intensity and spatial extent increase rapidly at low temperatures beyond a crossover field. Here we consider the possibility of long-range charge-density-wave order in a model of a layered system where such order competes with superconductivity.We show that in the clean limit, low-temperature long-range order is stabilized by arbitrarily weak magnetic fields. This apparent discrepancy with the experiments is resolved by the presence of disorder. Like the field, disorder nucleates halos of charge-density wave, but unlike the former it also disrupts interhalo coherence, leading to a correlation length that is always finite. Our results are compatible with various experimental trends, including the onset of longer range correlations induced by interlayer coupling above a characteristic field scale.

Effect of a dilute random field on a continuous-symmetry order parameter

XY and Heisenberg spins, subjected to strong random fields acting at few points in space with concentration $c_r \ll 1$, are studied numerically on 3d lattices containing over four million sites. Glassy behavior with strong dependence on initial conditions is found. Beginning with a random initial orientation of spins, the system evolves into ferromagnetic domains inversely proportional to $c_r$ in size. The area of the hysteresis loop, $m(H)$, scales as $c_r^2$. These findings are explained by mapping the effect of strong dilute random field onto the effect of weak continuous random field. Our theory applies directly to ferromagnets with magnetic impurities, and is conceptually relevant to strongly pinned vortex lattices in superconductors and pinned charge density waves.

전하밀도파 이론으로 결정질 태양전지의 입사각에 따른 단락전류밀도 변화 연구

광 입사각에 따른 태양전지의 양자효율을 전류의 출력으로 변환시켜 측정하였다. 기존의 태양전지의 원리는 태양전지가 태양광을 받았을 때 전자와 전공으로 분리되어 전류가 흐르게 된다는 것이었다. 그렇지만 저자들 중에 일부가 얼마 전에 태양전지원리를 새롭게 주장한 바 있다. 그 이론은 전하밀도파(charge density wave)들이 고정(pinning) 되었을 때, 이 고정 전위벽(pinning potential barrier)을 태양 광에 의해 넘을 수 있어서 전자 덩어리에 의한 전류 즉 단락전류(<TEX>$I_{SC}$</TEX>)가 가능하다는 것이었다. 본 실험에서는 태양광의 입사각에 따른 태양전지의 단락전류밀도 (<TEX>$J_{SC}$</TEX>)를 측정하여 비교해본 결과 측정값들과 전하밀도파 이론과 매우 일치함을 보인다. We measure solar currents transformed from quantum efficiency as a function of incident angles of solar lights. According to conventional models for solar cells, solar currents can be induced when electrons are separated into electrons and holes in the presence of incident solar lights. On the contrary, solar currents can be possible at the time when pinned charge density waves go beyond the pinning potential barrier under the influence of incident solar beams suggested by some authors. In this experiment, measured solar currents and our theory are in good correspondence to confirm the angle dependence of solar lights.

ChemInform Abstract: Synthesis and Characterization of the Pseudo-1-D Mixed-Valence (Et4- nMenN)Cu2X4 Salts: Pinned Charge Density Wave Systems Exhibiting Intervalence Charge Transfer.

ChemInform is a weekly Abstracting Service, delivering concise information at a glance that was extracted from about 100 leading journals. To access a ChemInform Abstract of an article which was published elsewhere, please select a “Full Text” option. The original article is trackable via the “References” option.

Currents of solar cell explained by pinned charge density waves

We present a mechanism that explains currents in solar cells using charge density wave (CDW) concepts. We treated pinned CDWs as being equivalent to moving CDWs that have been confined within a typical quantum well, using the many different examples where pinning occurs at the barrier. The currents in the solar cells are not described in terms of the unique semiconductor difference between electrons and holes, but are instead explained by making use of pinned CDWs in terms of the electrons contained therein, with a potential barrier that is lower than the energy gap in the solar cell material. The mechanism of the function of the solar cell is thus herein ascribed to the transport of pinned CDWs. The functions of solar cells are indispensable with impurities in the case of our CDW model different from conventional explanation.

Transportation of pinned charge density waves

We investigated the transport of pinned charge density waves (CDWs) that is observed in low dimensional materials. We treated pinned CDWs as moving CDWs that were confined within a typical quantum well amongst the many different types where pinning occurs at the barrier. We calculated the current flowing out of the quantum well by confined CDWs. The calculated conductivity is in good correspondence with experimental data in TTF–TCNQ, where the measured Fröhlich–Peierls temperature is 60 K much higher than the theoretical value of 20 K. The voltage dependence of the conductivity was calculated, where this is easily transformed into the dependence of electric field. The magnetic susceptibility was also calculated with a similar trend of experimental data. The susceptibility is a diamagnetic contribution by CDWs in addition to the constant background Pauli paramagnetic part.

Low-energy collective dynamics of charge stripes in the doped nickelateLa2−xSrxNiO4+δobserved with optical conductivity measurements

We have investigated charge dynamics in the static stripe ordered phase of ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}\mathrm{Ni}{\mathrm{O}}_{4+\ensuremath{\delta}}$ at lattice temperatures below the charge ordering transition, via optical conductivity measurements at low energies $(1--10\phantom{\rule{0.3em}{0ex}}\mathrm{meV})$. The thermally activated dynamic response of the charge stripes is found to be characteristic of a collective mode such as a pinned charge density wave. At incommensurate doping levels, the pinning energy is reduced, owing to the presence of real-space defects in the stripe order, and a pronounced increase in the oscillator strength is seen. The results provide compelling evidence for the existence of low-energy collective modes of the charge stripes.

Atomic structure and charge-density waves of blue bronzeK0.3MoO3(201¯)by variable-temperature scanning tunneling microscopy

Blue bronze $({\mathrm{K}}_{0.3}\mathrm{Mo}{\mathrm{O}}_{3})$ has been the focus of a number of scattering, transport, scanning tunneling microscopy (STM), and theoretical studies that have provided insight into the relation between atomic structure and charge-density wave (CDW) formation. However, the full extent of a relation of the CDWs to the atomic lattice and the microscopic origin of CDW pinning are still not completely resolved. In this study STM is used to distinguish the atomic structure and CDWs at the $(20\overline{1})$ surface. Within the STM's spatial resolution, the CDWs are incommensurate with the lattice at midrange temperatures and approach commensurability at low temperatures. Incommensurate CDWs are present on the surface and the degree of the incommensurability between blue bronze lattice and CDW lattice agree well with those determined from bulk scattering techniques.

Disorder effects on the charge-density waves structure in V- and W-doped blue bronzes: Friedel oscillations and charge-density wave pinning

We present an x-ray diffuse scattering study of the charge-density wave (CDW) structure in the doped blue bronzes ${\mathrm{K}}_{0.3}({\mathrm{Mo}}_{1\ensuremath{-}x}{\mathrm{V}}_{x}){\mathrm{O}}_{3}$ $(x=2.8%)$, ${\mathrm{Rb}}_{0.3}({\mathrm{Mo}}_{1\ensuremath{-}x}{\mathrm{V}}_{x}){\mathrm{O}}_{3}$ ($x=1.44%$ and 0.28%), and ${\mathrm{K}}_{0.3}({\mathrm{Mo}}_{1\ensuremath{-}x}{\mathrm{W}}_{x}){\mathrm{O}}_{3}$ $(x=2%)$. At low temperature, the $\ifmmode\pm\else\textpm\fi{}2{k}_{F}$ satellite reflections are broadened in all four compounds, and shifted in V-doped compounds. Moreover, we have observed an intensity asymmetry of the $\ifmmode\pm\else\textpm\fi{}2{k}_{F}$ satellite reflections relative to the pure compound, and a profile asymmetry of each satellite reflections. We show that both effects, intensity and profile asymmetry, give access to the local properties of CDW in disordered systems, including the pinning and the phase shifts around impurities. This leads us to propose a complete scenario of the pinning in doped blue bronzes. In the V-doped compounds, we show that the profile asymmetry is due to Friedel oscillations around the charged V substituent and that the intensity asymmetry is related to the strong pinning of the CDW. In the W-doped crystal, the CDW is weakly pinned in regions containing a few tens of neutral W substituents and the CDW phase is slightly distorted around the W impurities. Exact calculations are presented to sustain these ideas.

Simulation of transient current through PMMA thin films based on a random walk model

A piecewise continuous, time dependent diffusive coupling in a classical one-dimensional randomly pinned charge density wave model has been used for the analysis of experimentally observed transient current data for polymethyl methacrylate. Satisfactory agreement has confirmed that this can be a dynamical model for the behavior of the transient current. The analysis also suggests the presence of three different regimes in the decay of the transient current.

Case studies of molecular disorder

Abstract In this review we present three representative examples of molecular disorder: substitution disorder for carbon nanotubes in zeolite, coupling between substitution disorder and displacements through the pinning of charge-density waves in one-dimensional molecular conductors, and the combination of random packing with orientational disorder in the C60—C60 dimers systems.