Local Charge Density Wave Research Articles

Nonmetallic power-law behavior of conductance in Ni-doped NbSe3 nanowires

We report on diverse transport properties observed in NbSe3 nanowires of dilute Ni concentrations, where the resistance of some nanowires retains metallic behavior with regions of negative absolute resistance and switching transition showing up in current-voltage curve at sufficiently low temperatures, while others demonstrate metal-insulator transitions below the first charge density wave (CDW) transition. The temperature and voltage dependence of the resistance for the nonmetallic samples are governed by power laws; however, the anomalous features of the CDW transitions still retain. The observed transport behaviors are apparently due to the variation of potential along the conducting channel caused by different kinds of nonuniformities. A phenomenological model with one-dimensional phase slippage occurring in the certain segment of the nanowire, where Friedel oscillations-enhanced local CDW domains cluster altogether over the whole cross section, is presented as the possible mechanism for the nonmetallic power-law behavior. Our work sheds new light on the possible origin of nonmetallic power-law behavior in NbSe3, which has been under debate for a long time.

Emergent superconductivity upon disordering a charge density wave ground state

We explore the interplay of a charge density wave (CDW) order and s-wave superconductivity (sSC) in a disordered system. Recent experiments on 1T-TiSe_2, where the pristine sample has a commensurate CDW order and the superconductivity appears upon copper intercalation, motivates our study. Starting with an extended Hubbard model, with parameters which yield a CDW ground state within Hartree-Fock-Bogoliubov formalism in pure systems, we show that the addition of disorder quickly wipes out the global charge order by disrupting periodic modulation of density at some (low) strength of disorder. Along with this, the subdominant superconducting order emerges in regions that spatially anti-correlates with islands of strong local CDW order. The short-range density modulations, however, continue to persist and show discernible effects up to a larger disorder strength. The local CDW puddles reduce in size with increasing disorder and they finally lose their relevance in effecting the properties of the system. Our results have strong implications for the experimental phase diagram of transition metal dichalcogenides.

Superconductivity and Charge Density Wave in ZrTe3-xSex.

Charge density wave (CDW), the periodic modulation of the electronic charge density, will open a gap on the Fermi surface that commonly leads to decreased or vanishing conductivity. On the other hand superconductivity, a commonly believed competing order, features a Fermi surface gap that results in infinite conductivity. Here we report that superconductivity emerges upon Se doping in CDW conductor ZrTe3 when the long range CDW order is gradually suppressed. Superconducting critical temperature Tc(x) in ZrTe3−xSex (0 ≤ x ≤ 0.1) increases up to 4 K plateau for 0.04 ≤ x ≤ 0.07. Further increase in Se content results in diminishing Tc and filametary superconductivity. The CDW modes from Raman spectra are observed in x = 0.04 and 0.1 crystals, where signature of ZrTe3 CDW order in resistivity vanishes. The electronic-scattering for high Tc crystals is dominated by local CDW fluctuations at high temperatures, the resistivity is linear up to highest measured T = 300 K and contributes to substantial in-plane anisotropy.

Dynamic correlations in sliding charge-density waves probed by spatially resolved measurements of voltage oscillations

In sliding charge-density wave (CDW) conductors such as ${\text{NbSe}}_{3}$, voltage oscillations at a frequency proportional to the local CDW velocity accompany CDW motion and can furnish many insights into the dynamics of these systems. We have used high-performance cryogenic differential amplifiers to make position-dependent measurements of voltage oscillations in the quasisteady state. These measurements yield voltage-voltage and velocity-velocity correlations and the temperature dependence of the CDW's longitudinal and transverse velocity coherence.

Deformation of a charge density wave in the vicinity of a point contact with a normal metal

The current-voltage characteristics of Cu-K0.3MoO3 point contacts between a metal and a semiconductor with a charge density wave (CDW) are studied for various diameters of the contacts in a wide range of temperatures T and voltages V. In the interval 80 K ≲ T ≲ 150 K, the current-voltage characteristics are correctly described in the framework of a semiconductor model: screening of an external electric field causes CDW deformation, shifts the chemical potential of quasiparticles, and changes the point contact resistance. It is shown that the chemical potential is above the middle of the Peierls gap in equilibrium and approaches the middle upon an increase in temperature. The current-voltage characteristics of point contacts with a diameter d ≳ 100 A exhibit a sharp decrease in resistance for |V| > V t , which is associated with the beginning of local CDW sliding within the contact region. The V t (d, T) dependence can be explained by the size effect in the CDW phase slip.

Is the Roton in Superfluid4He the Ghost of a Bragg Spot?

It has always been assumed that the roton in 4He had to do with local vorticity—hence the name! We present here an alternate view: the roton is viewed as a “soft mode”, precursor of a crystallization instability. In such a picture the liquid is “nearly solid”, and the long observed similarities of heat propagation in liquid and solid phases are naturally explained. In this qualitative paper we consider three models successively. A lattice gas with one atom per site displays a Mott localization transition, as shown by the Bangalore group. The important result is the vanishing of the superfluid order parameter (condensate fraction N o) at the transition. There is no breakdown of translational symmetry and consequently no soft mode. Another lattice model with half filling, with an added nearest neighbour repulsion, was studied by Matsubara and Matsuda in the early 1950s it displays a first order transition between a superfluid and a localized charge density wave state. The excitation spectrum has a soft mode at zone edge near the transition, signalling the proximity of the CDW instability. Finally, we consider the realistic situation of a continuous system with no preexisting lattice. We approach the problem from the limit N o = 0 instead of the ideal gas N o = N. When N o = 0 the quasiparticle spectrum and the charge density spectrum are decoupled. The latter should have a soft mode ω=ωm if crystallization is close. That soft mode is a normal state property that has nothing to do with superfluidity. A small N o acts to hybridize quasiparticles and density fluctuations: the resulting anticrossing lowers ωm 2 as well as the ground state energy. We show that N o is bounded for two reasons: (i) if ω m 2 turns negative, the liquid is unstable towards freezing (ii) depletion due to quantum fluctuation exceeds N o if the latter is too large. The resulting upper bound noindent for N/N o is ≪ 1, a consequence of the deep roton minimum. The whole paper is qualitative, based on outrageous simplifications in order to make algebra tractable.

Micro-contact spectroscopy features of quasi-one-dimensional materials with a charge-density wave

We have applied the method of point-contact (PC) spectroscopy to conductors with a charge-density-wave (CDW) ground state. Recent experimental results of the investigation of characteristics of PC formed between a normal metal (N) and different CDW conductors are reported. For a uniform N–CDW boundary, we show that the interaction of carriers injected from the normal metal with the CDW results in their reflection without changes in the sign of the charge but with a momentum transfer 2pF to the condensate of electron–hole pairs carried away from the N–CDW interface. In the case of a non-uniform N–CDW boundary (direct point contact), a strong local CDW deformation, due to a band bending effect, was observed in materials with a semiconducting ground state. The chemical potential can be strongly modified, changing the conductivity type in the vicinity of the PC. It was shown that, in the case of a CDW conductor with a metal or semimetal ground state, the band bending effect is negligible (because of the screening of the electric field by remaining normal carriers) and the spectroscopy of the Peierls energy gap is possible.

Study of C–I–C CDW phase transition in TTF–TCNQ with STM

TTF–TCNQ is a one-dimensional charge transfer compound. Charge density wave (CDW) transition occurs at 54 K in TTF–TCNQ, and CDW presents three phases: high temperature commensurate phase ( T>49 K; 2 a ×3.39 b ); inter-mediated incommensurate phase ( T=38–49 K; μ a × 3.39 b ) and low temperature commensurate phase ( T<38 K; 4 a ×3.39 b ). In this report, we present our experimental result on cleaved (0 0 1) surfaces of TTF–TCNQ with UHV–LT–STM (Omicron LTSTM). For a broad temperature range (33–100 K), molecular resolution of TTF–TCNQ has been obtained. Below 54 K an additional two-dimensional superstructure of CDW appears in our images. The ordering of CDW modulation both along a and b direction are first revealed by our STM measurement. Our result shows that, on (0 0 1) surface of TTF–TCNQ, C–I–C CDW phase transition persists in nanometer scale and C–I–C transition is homogeneous. The determination of local CDW phase shift will be presented in this report too. At high temperature (60–280 K), we observed a v-shape pseudo-gap. The pseudo-gap and Peierls-gap co-exist at low temperature.

Effects of long-range electronic interactions on a one-dimensional electron system

The effects of a long-range electronic potential on a one-dimensional chain of spinless fermions are investigated by numerical techniques (exact diagonalization of rings with up to 30 sites complemented by finite size analysis) and analytic calculations. Due to a competition between the ${2k}_{F}$ oscillations in the density and the (very slow) log divergence of the long wavelength part of the Coulomb potential, the metallic character of the system is enhanced at intermediate (and up to quite large) length scales. Despite some similarities, we found that this quasimetallic regime is not of the Luttinger liquid type, as evidenced by strong deviations from predictions of conformal field theory and in agreement with the picture of a (very weakly pinned) Wigner crystal. When the strength of the Coulomb interaction is substantially increased, we observe a smooth crossover to a strongly localized charge density wave.

Effects of long range electronic interactions on a one-dimensional electron system

The effects of a long range electronic potential on a one dimensional chain of spinless fermions are investigated by numerical techniques and analytic calculations. Due to a competition between the 2k F oscillations in the density and the log divergence of the long wavelength part of the Coulomb potential, the metallic character of the system is enhanced at intermediate (and up to quite large) lengthscales. We found that this quasi-metallic regime is not of the Luttinger Liquid type, as evidenced by strong deviations from predictions of conformal field theory and in agreement with the picture of a (very weakly pinned) Wigner crystal. When the strength of the Coulomb interaction is substantially increased, we observe a smooth cross-over to a strongly localized charge density wave.

Effect of non-magnetic impurity in superconducting states of t–J model

Abstract The effect of non-magnetic impurities in the superconducting state of the t – J model is studied. The Bogoliubov de Gennes equation is derived via a slave-boson mean-field approximation, and we solve it numerically at T =0. The d x 2 − y 2 -wave order parameter is suppressed near an impurity and the extended s-wave component is induced. The local charge density wave (CDW)-like feature due to the Friedel oscillations is found, which leads to the splitting of the expected zero-energy Andreev bound state. Therefore, an instability towards a state breaking locally time reversal symmetry or exhibiting antiferromagnetic order is unlikely to occur.

Four-step scenario for doping-induced phase changes in a three-dimensional charge-density-wave system

A four-step scenario for the phase changes in ${\mathrm{Ba}}_{(1\ensuremath{-}x)}{\mathrm{K}}_{x}{\mathrm{BiO}}_{3}$ is proposed. This aims at giving a global view of the whole evolution process induced by hole doping. For this purpose, we utilize simple but standard methods such as the Hartree-Fock approximation and the adiabatic approximation. The parent material is ${\mathrm{BaBiO}}_{3}$, whose ground state is well established as a three-dimensional charge-density wave (CDW). While hole doping on this material is very light, we observe in the simulation that the hole bipolaron (BP) state is a local minimum with a higher energy than a pair of extended holes. We call this stage of doping the first step. Beyond a rather low critical concentration of holes, however, the second step emerges, where the BP state is stabilized as the lowest one. Moreover, upon continuing the doping, the system loses the initial long-range order of CDW and becomes disordered only with local CDW domains. The absorption spectrum in this third step shows a main band that moves to lower energies in accordance with the hole concentration. Lastly, at the final stage of doping, the pseudogap in the electronic density of states (DOS) collapses and the system becomes metallic. The aforementioned local CDW, however, still remains with reduced but finite fraction. Thus, this fourth step is characterized by a rather anomalous state of the metal. This scenario is qualitatively consistent with the experimental facts and gives a reasonable description of the evolution of this material from very lightly doped states to heavily doped ones.

Effect of randomness on the Mott state.

Competition between Mott and Anderson metal-insulator transitions is studied in a one dimensional spinless fermion system of 200 sites. Although the long range charge density wave (CDW) order and gap of the Mott phase are destroyed by weak randomness, the elementary excitations are still solitons based on the local CDW order. The solitons are easily localized in the random potential. Thus for weak randomness and large interaction, a disordered Mott phase exists in which the localization is determined by the local CDW order in contrast to the conventional Anderson localization picture in the weak interaction limit.

Localized excitations in competing bond-order-wave, charge-density-wave, and spin-density-wave systems

The characteristics of localized excitations in quasi-one-dimensional systems are rather sensitive to the interplay between the electron-phonon (e-ph) and electron-electron (e-e) interactions giving rise to competition and possible coexistence of various symmetry-broken ground states such as the bond-order wave (BOW), the charge-density wave (CDW), and the spin-density wave (SDW). Such effects are observable in halogen-bridged mixed-valence transition-metal complexes, and can be elucidated within the Bogoliubov--de Gennes formalism using an extended Peierls-Hubbard model. The coexistence of local BOW, CDW, and SDW distortions is demonstrated in this paper for polarons and self-trapped excitons (STE) in different symmetry-broken ground states. An extensive study of localized excitations over a wide range of the on-site e-ph coupling ${\ensuremath{\lambda}}_{2}$ and the Hubbard interaction U leads to the following observations. (a) As ${\ensuremath{\lambda}}_{2}$ increases at fixed U, the number of bound states inside the gap changes from two to four for the STE case and from two to three for the polaron case. (b) Upon its further increase, one type of STE with a certain pattern of SDW distortion and charge transfer is transforming into another type of STE with a different pattern. (c) A nonmonotonic dependence of the lattice relaxation energy on ${\ensuremath{\lambda}}_{2}$ is predicted within the lattice relaxation approach developed by Su and Yu earlier, and is attributed to a crossover from the weak-coupling to strong-coupling behavior showing up as the emergence of new bound states inside the gap. Moreover, the nonradiative transition rate of STE is also calculated and is used to tentatively interpret the very short lifetime of STE in PtCl complexes. Such nonmonotonic dependence of the relaxation rate on the coupling constant may also be observed in other quasi-one-dimensional systems as well.

The current conversion kinetics in charge density waves

We derive and study the two-fluid dissipative hydrodynamics equations for the Charge Density Wave (CDW) plastic flow in the presence of a homogeneous distribution of defects: solitons and dislocations. For a one-dimensional development of the injection current impulse we find that the first electric field E ∞ ∋ j ∞ and the nominal CDW current j ∞ are established along the sample length in a very short time. Later on the diffusion front passes along with a constant velocity bE ∞, where b is a mobility of solitons. It is followed by growth of the soliton concentration ϱ, and by decrease of local coherent CDW current j ∋ E. At largest time t they develop as j ∋ ϱ −1 s ∋ t −1 3 or as ∋ («/t) 1 3 . The total electric current is nearly additive J ≈ j + 2 j s being almost constant. Also a stationary distribution is found at the presence of a constant CDW current passing by the injective terminal. It is characterized by a step-like profile of the defects concentration. The pseudostationary time-limited regime is found for the minority carriers injection.

Various regimes of charge-density waves in layered compounds.

In this paper we have subjected different layered transition-metal dichalcogenides to scanning tunneling microscopy to reveal the electronic charge distribution associated with the charge-density-wave (CDW) part of the superstructure, in addition to the atomic corrugation. The observations presented display three regimes ranging from a localized CDW centered around defects or impurities in the case of 1T-TiS2, via an intermediate regime governed by overlapping envelope functions in 2H-NbSe2, to a fully developed CDW in 1T-TaSe2 (as well as in a large number of other compounds). We have obtained strong indication from both direct-space observations and comparison to calculated images based upon the Ginzburg-Landau theory that localized charge-density waves do exist in conjunction with associated lattice distortions. The fact that these observations have been made in solids ranging from (dirty) semi-conductor (1T-TiS2) to semimetal (1T-TaSe2) to metallic (2H-NbSe2) points to the general applicability of the phenomenological Ginzburg-Landau theory, employed to describe the various regimes in which the formation of charge-density waves and the accompanying periodic lattice distortions appear to act.

Scanning Tunneling Microscopy on Charge Density Waves in Layered Compounds

AbstractDifferent layered transition metal dichalcogenides were subjected to scanning tunneling microscopy to reveal the electronic charge distribution associated with the charge density wave (CDW) part of the superstructure, in addition to the atomic corrugation. The observations presented display three regimes ranging from localized CDW centred around defects/impurities in the case of lT-TiS2, via an intermediate regime governed by overlapping envelope functions in 2H-NbSe2, to a fully developed CDW system in 1T-TaSe2 (as well in a large number of other compounds). The fact that these observations have been made in solids ranging from (dirty) semiconductor (1T-TiS2) to semimetal (1T-TaSe2) to metallic (2H-NbSe2) points at the general applicability of the phenomenological Ginzburg-Landau theory, employed to describe the various regimes in which the formation of charge density waves and the accompanying periodic lattice distortions appear to act.

Local charge density wave and metal-insulator transition in Ba(K)Bi(Pb)O3

We have obtained a coherent interpretation of the basic electronic structure and the metal-semiconductor transition for both representative compounds Ba 1−xK xBiO 3 and BaBi 1−xPb xO 3. A self-consistent calculation with respect to the short range order of metallic (Bi,Pb) sites and to the charge transfer in our model show that the local nature of C.D.W. caused essentially by attractive electron interaction on the Bi sites provides a good comparison with structural, optical and transport experiments. We also discuss the role of the metal-oxygen bonding on the electronic structure of these compounds.

Diverging strains in the phase-deformation model of sliding charge-density waves.

We show that when a spatially uniform, time-independent electric field is applied to a charge-density wave (CDW), the time-averaged local CDW velocity is spatially inhomogeneous, with nonzero spatial average, because models that do not allow for the coexistence of regions with different time-averaged mean velocities have places with infinite energy density. To establish this result we present a heuristic scaling argument, rigorous results on a simplified lattice model, and a study of the continuum phase equation of motion for the CDW. Flux-line motion in type-II superconductors is also considered; similarities and differences between flux-line motion and CDW motion are discussed.

Effects of high magnetic fields on charge-density waves in NbSe3.

The magnetotransport properties of ${\mathrm{NbSe}}_{3}$ in the temperature range below the second charge-density-wave (CDW) onset of 59 K have been studied in magnetic fields up to 230 kG. At liquid-helium temperatures giant magnetoquantum oscillations caused by magnetic breakdown (MB) between the normal Fermi surface (FS) and open orbits on the nested sheets of the FS dominate the magnetotransport and are extremely sensitive to the pinned CDW configuration. Spatial variations in the phase of the pinned CDW change the local Fermi level and CDW gap, giving rise to a distribution of FS cross-sectional areas. These variations in FS cross section and CDW gap produce frequency shifts, amplitude modulations, and beat structures in the quantum oscillations observed in both the magnetoresistance and Hall effect. A model conductivity tensor has been developed describing the open-orbit network and MB interference as well as the closed-orbit contribution. The adjustable parameters of the model are the frequency of oscillation, the frequency-distribution spread \ensuremath{\Delta}F, and critical MB parameter ${\ensuremath{\omega}}_{0}$\ensuremath{\tau}.The model has been used to study the detailed configurations of the pinned CDW in nominally pure ${\mathrm{NbSe}}_{3}$ crystals and in ${\mathrm{NbSe}}_{3}$ crystals doped with Fe, Ni, and Co. Unique fits to the data can be generated, and the resulting FS distributions provide direct information on the local CDW domain structure produced by pinning and repinning the CDW or by deliberately introducing impurities. At temperatures in the range 10--59 K, the oscillation amplitude decreases rapidly as the scattering time decreases, and a new magnetoresistance enhancement is observed. The dc resistance anomaly associated with the CDW is enhanced by up to a factor of 4 in a magnetic field of 226 kG and, if assigned exclusively to FS obliteration, it would require an increase from 60% obliteration at H=0 to 92% at H=227 kG. Accurate measurements also indicate a small increase in the transition temperature of \ensuremath{\sim}0.5 K in a magnetic field of 226 kG. These results have been analyzed in terms of a theory proposed by Balseiro and Falicov in which a transverse magnetic field induces a more perfect nesting of the FS.Magnetic-field modifications of the electronic spectrum at the Fermi level can become large when the cyclotron energy \ensuremath{\Elzxh}${\ensuremath{\omega}}_{c}$ is on the order of the CDW gap \ensuremath{\Delta}. Both the enhancement of the magnetoresistance and the sign change in the Hall effect can be related to this mechanism. In addition to the magnetic-field-induced changes in the static CDW state, studies of the dynamics of CDW motion have also been carried out in magnetic fields up to 230 kG. The magnetoresistance response to the CDW motion can be modeled with equations similar to those of the Bardeen tunneling model. At high electric fields the enhanced magnetoresistance in the range 10--59 K is quenched; in the quantum-oscillation regime the enhanced dc magnetoresistance is quenched while the oscillation amplitude saturates. The large magnetoresistance in the static CDW state allows measurement of the threshold electric field down to low temperatures. For the nominally pure crystals the temperature dependence of ${E}_{T}$ in high magnetic fields follows a thermal-fluctuation model similar to that observed at H=0, and the magnitude of ${E}_{T}$ is not significantly changed from the values observed at H=0. At very low temperatures a departure from the dynamics of the tunneling model can give rise to a large region of zero dynamic resistance. This behavior is observed in the highest-purity crystals and is rapidly modified by impurities. The magnetic field facilitates the study of a large range of both static and dynamic CDW effects at low temperature: A systematic classification has been accomplished. Adequate theoretical models have been developed for several of the effects, although further refinement of the models and additional experimental confirmation are needed.