Charge Density Wave Amplitude Research Articles

Evidence for topological defects in a photoinduced phase transition

Upon excitation with an intense ultrafast laser pulse, a symmetry-broken ground state can undergo a non-equilibrium phase transition through pathways dissimilar from those in thermal equilibrium. Determining the mechanism underlying these photo-induced phase transitions (PIPTs) has been a long-standing issue in the study of condensed matter systems. To this end, we investigate the light-induced melting of a unidirectional charge density wave (CDW) material, LaTe$_3$. Using a suite of time-resolved probes, we independently track the amplitude and phase dynamics of the CDW. We find that a quick ($\sim\,$1$\,$ps) recovery of the CDW amplitude is followed by a slower reestablishment of phase coherence. This longer timescale is dictated by the presence of topological defects: long-range order (LRO) is inhibited and is only restored when the defects annihilate. Our results provide a framework for understanding other PIPTs by identifying the generation of defects as a governing mechanism.

Enhanced superconductivity upon weakening of charge density wave transport in 2H-TaS2 in the two-dimensional limit

As superconductors are thinned down to the 2D limit, their critical temperature $T_c$ typically decreases. Here we report the opposite behavior, a substantial enhancement of $T_c$ with decreasing thickness, in 2D crystalline superconductor 2H-TaS$_2$. Remarkably, in the monolayer limit, $T_c$ increases to 3.4 K compared to 0.8 K in the bulk. Accompanying this trend in superconductivity, we observe suppression of the charge-density wave (CDW) transition with decreasing thickness. To explain these trends, we perform electronic structure calculations showing that a reduction of the CDW amplitude results in a substantial increase of the density of states at the Fermi energy, which contributes to the enhancement of $T_c$. Our results establish ultra-thin 2H-TaS$_2$ as an ideal platform to study the competition between CDW order and superconductivity.

Hall voltage drives pulsing counter-currents of the sliding charge density wave and of quantized normal carriers at self-filled Landau levels

Remnant pockets of carriers left over after formation of a charge density wave (CDW) were brought, by virtue of transverse electric and magnetic fields, to a current-carrying state at quantized Landau Levels. The generated Hall voltage polarizes and puts to sliding the flexible CDW background. The screening from the CDW allows for a so strong redistribution of normal electrons density under the action of the Lorentz force alone, that an integer filling of the lowest Landau level might be reached at one edge at the expense of the full depletion at another edge of the Hall bar. With the Hall field exceeding the sliding threshold, the regime of exactly compensated collective and normal counter-currents develops in the open-circuit direction across the bar. The annihilation of the two currents proceeds via a regular sequence of phase slips which are the space-time vortices of the CDW phase around the enforced amplitude nodes. The resulting spontaneous generation of coherent high (~GHz) frequency signals was detected by observations of multiple Shapiro steps. This picture results from studies of micron-sized Hall bars in crystals of NbSe3 prepared by means of focused ion beams. The interpretation is confirmed and illustrated by a numerical solution of the derived equations. The depinning pulse propagates from edges to the bulk and the sliding sets in, accompanied by the generation of periodic phase slips near the Hall bar edge where the CDW phase is advanced in steps of 2π at expense of the CDW amplitude passing through zero.

Raman spectroscopy of optical phonon and charge density wave modes in 1T-TiSe2 exfoliated flakes

1T-TiSe2 is a model transition metal dichalcogenide material that develops charge density waves (CDWs). Here we present variable-temperature Raman spectroscopy study on both CDW and optical phonon modes of 1T-TiSe2 thin layers exfoliated onto SiO2 substrate. Raman scattering intensities of all modes reach a maximum when the sample thickness is about 12nm. This phenomenon can be explained by optical interference effect between the sample and the substrate. The CDW amplitude modes experience redshift and broadening as temperature increases. We extract CDW transition temperature (TCDW) from temperature dependence of the frequency of A1gCDW mode. We find that TCDW decreases in thinner flakes, which could be due to extrinsic effects.

Revealing the role of electrons and phonons in the ultrafast recovery of charge density wave correlations in 1T−TiSe2

Using time- and angle-resolved photoemission spectroscopy with selective near- and mid-infrared photon excitations, we investigate the femtosecond dynamics of the charge density wave (CDW) phase in 1$T$-TiSe$_2$, as well as the dynamics of CDW fluctuations at 240 K. In the CDW phase, we observe the coherent oscillation of the CDW amplitude mode. At 240 K, we single out an ultrafast component in the recovery of the CDW correlations, which we explain as the manifestation of electron-hole correlations. Our momentum-resolved study of femtosecond electron dynamics supports a mechanism for the CDW phase resulting from the cooperation between the interband Coulomb interaction, the mechanism of excitonic insulator phase formation, and electron-phonon coupling.

Photoinduced Enhancement of the Charge Density Wave Amplitude.

Symmetry breaking and the emergence of order is one of the most fascinating phenomena in condensed matter physics. It leads to a plethora of intriguing ground states found in antiferromagnets, Mott insulators, superconductors, and density-wave systems. Exploiting states of matter far from equilibrium can provide even more striking routes to symmetry-lowered, ordered states. Here, we demonstrate for the case of elemental chromium that moderate ultrafast photoexcitation can transiently enhance the charge-density-wave (CDW) amplitude by up to 30% above its equilibrium value, while strong excitations lead to an oscillating, large-amplitude CDW state that persists above the equilibrium transition temperature. Both effects result from dynamic electron-phonon interactions, providing an efficient mechanism to selectively transform a broad excitation of the electronic order into a well-defined, long-lived coherent lattice vibration. This mechanism may be exploited to transiently enhance order parameters in other systems with coupled degrees of freedom.

Femtosecond dynamics of decoupled superlattice zones in 4Hb–TaSe2 single crystals

Strongly correlated electronic crystal systems marked by temperature-dependent phase transitions often feature an emergence of new structural periodicities, arising from an interplay between modulated electron density and periodic lattice distortion. We investigate the structural evolution of superlattice clusters in 4Hb–TaSe2 single crystals on a subpicosecond and atomic resolution via femtosecond electron diffraction (FED). The superlattice clusters comprise of two six-member rings each, related by a rotational symmetry and held in position by Coulombic mode repulsion. The two six-member rings are decoupled into two possible zones, which are further decoupled into respective site-specific satellite reflections in the reciprocal space. Governed by the interlayer interactions and the electron diffraction simulation analysis, FED measurements are used to demonstrate the suppression and dynamics of the decoupled superlattice zones. The simultaneous temporal evolution of the two CDW reflection orders are assigned to the decoupled Raman-active Ag and soft phonon modes previously reported on an isomorphic crystal structure (4Hb–TaS2). It is found that the charge density wave amplitude mode dominates over the corresponding phase mode.

Ultrafast resonant soft x-ray diffraction dynamics of the charge density wave inTbTe3

Understanding the emergence of collective behavior in correlated electron systems remains at the forefront of modern condensed matter physics. Disentangling the degrees of freedom responsible for collective behavior can lead to insights into the microscopic origins of emergent properties and phase transitions. Utilizing an optical pump, resonant soft x-ray diffraction probe we are able to track, in real time, the dynamics of the charge density wave (CDW) in ${\mathrm{TbTe}}_{3}$, a model system that violates traditional views of a Fermi surface nested CDW. We observe coherent oscillations corresponding to the CDW amplitude mode at $2.4$ THz and a coherent optical phonon mode at $\ensuremath{\sim}1.7\phantom{\rule{0.16em}{0ex}}\mathrm{THz}$. We show how such observations reveal the anisotropic energy optimization between in-plane Te charge density modulations and the three-dimensional lattice coupling.

Direct observation of single-electron solitons and Friedel oscillations in a quasi-one dimensional material with incommensurate charge-density waves

We have performed scanning tunneling microscopy experiments in the quasi-one dimensional charge density wave (CDW) system NbSe3, where we could image and study in detail individual solitons corresponding to the self-trapping of a single electron. Our analysis shows that the type of soliton we observed is an “Amplitude Soliton”, characterized by a vanishing CDW amplitude at the soliton center and by a π-shift of its phase along the chain direction. Pairs of solitons or multiple solitons were also observed. Such observations could be made only in the high-temperature CDW phase. Additionally, one-dimensional Friedel oscillations around charged defects could also be imaged and are found to be superimposed to the CDW. The distinction between amplitude solitons and Friedel oscillations can be made without any ambiguity.

Modeling of dislocations in a CDW junction: Interference of the CDW and normal carriers

We derive and study equations for dissipative transient processes in a constraint incommensurate charge density wave (CDW) with remnant pockets or a thermal population of normal carriers. The attention was paid to give the correct conservation of condensed and normal electrons, which was problematic at presence of moving dislocation cores if working within an intuitive Ginzburg–Landau like model. We performed a numeric modeling for stationary and transient states in a rectangular geometry when the voltage V or the normal current are applied across the conducting chains. We observe creation of an array of electronic vortices, the dislocations, at or close to the junction surface; their number increases stepwise with increasing V. The dislocation core strongly concentrates the normal carriers but the CDW phase distortions almost neutralize the total charge. At other regimes, the lines of the zero CDW amplitude flash across the sample working as phase slips. The studies were inspired by, and can be applied to experiments on mesa-junctions in NbSe3 and TaS3.

Electric field gradient wave (EFGW) in iron-based superconductor Ba0.6K0.4Fe2As2 studied by Mössbauer spectroscopy

The optimally doped ‘122’ iron-based superconductor Ba0.6K0.4Fe2As2 has been studied by 57Fe Mössbauer spectroscopy versus temperature ranging from 4.2K till 300K with particular attention paid to the superconducting transition around 38K. The spectra do not contain magnetic components and they exhibit quasi-continuous distribution of quadrupole split doublets. A distribution follows the electric field gradient (EFG) spatial modulation (wave) – EFGW. The EFGW is accompanied by some charge density wave (CDW) having about an order of magnitude lesser influence on the spectrum. The EFGW could be modeled as widely separated narrow sheets with the EFG increasing from small till maximum value almost linearly and subsequently dropping back to the original value in a similar fashion – across the sheet. One encounters very small and almost constant EFG between sheets. The EFGW shape and amplitude as well as the amplitude of CDW are strongly affected by a superconducting transition. All modulations are damped significantly at transition (38K) and recover at a temperature being about 14K lower. The maximum quadrupole splitting at 4.2K amounts to about 2.1mm/s, while the dispersion of CDW seen on the iron nuclei could be estimated far away from the superconducting gap opening and at low temperature as 0.5el./a.u.3. It drops to about 0.3el./a.u.3 just below transition to the superconducting state.

Interplay of Charge-Density Wave and Magnetic Order in Ternary Rare-Earth Nickel Carbides, RNiC2 (R=Pr and Nd)

The electrical and structural properties of NdNiC2 and PrNiC2 are examined in single-crystalline samples in order to investigate the interplay of charge-density wave (CDW) and magnetic order in ternary rare-earth nickel carbides, RNiC2, where R is a rare-earth element. PrNiC2 (no magnetic order down to 1.5 K) and NdNiC2 [antiferromagnetic (AF) transition at 17.2 K] show resistance anomalies at 89 and 121 K, respectively, which are revealed to be CDW transitions by observing X-ray satellite reflections. NdNiC2 also shows a gradual decrease in both resistivity and CDW amplitude below the Neel temperature. In the AF phase, the magnetoresistance sharply decreases where a ferromagnetic (FM) order occurs, which is realized above the spin-flop magnetic field. These results clearly suggest that the relationships between CDW and magnetic order in RNiC2 depend on whether the magnetic order is AF or FM.

Momentum-Dependent Charge Correlations inYBa2Cu3O6+δSuperconductors Probed by Resonant X-Ray Scattering: Evidence for Three Competing Phases

We use resonant x-ray scattering to determine the momentum-dependent charge correlations in YBa(2)Cu(3) O(6.55) samples with highly ordered chain arrays of oxygen acceptors (ortho-II structure). The results reveal nearly critical, biaxial charge density wave (CDW) correlations at in-plane wave vectors (0.315, 0) and (0, 0.325). The corresponding scattering intensity exhibits a strong uniaxial anisotropy. The CDW amplitude and correlation length are enhanced as superconductivity is weakened by an external magnetic field. Analogous experiments are carried out on a YBa(2)Cu(3)O(6.6) crystal with a dilute concentration of spinless (Zn) impurities, which had earlier been shown to nucleate incommensurate magnetic order. Compared to pristine crystals with the same doping level, the CDW amplitude and correlation length are found to be strongly reduced. These results indicate a three-phase competition between spin-modulated, charge-modulated, and superconducting states in underdoped YBa(2)Cu(3)O(6+δ).

Scanning-Tunneling Microscope Imaging of Single-Electron Solitons in a Material with Incommensurate Charge-Density Waves

We report on scanning-tunneling microscopy experiments in a charge-density wave (CDW) system allowing visually capturing and studying in detail the individual solitons corresponding to the self-trapping of just one electron. This "Amplitude Soliton" is marked by vanishing of the CDW amplitude and by the π shift of its phase. It might be the realization of the spinon--the long-sought particle (along with the holon) in the study of science of strongly correlated electronic systems. As a distinct feature we also observe one-dimensional Friedel oscillations superimposed on the CDW which develop independently of solitons.

Finite-length charge-density waves on terminated atomic wires

Finite-size effects in charge-density waves (CDWs) were unveiled using scanning tunneling microscopy for metallic atomic wires on the Au/Si(553) surface, as terminated by adsorbate impurities. We found that CDW formed at low temperature adopts the finite-length boundary condition in two distinct ways, depending on the length scale. For longer wires than $\ensuremath{\sim}$10 nm, the CDW correlation length, the decay length of the CDW amplitude from the terminating ends, scales continuously with the wire length as predicted in a recent hyperscaling theory [Phys. Rev. B 75, 205428 (2007)]. For shorter wires, the boundary condition becomes discrete with respect to the CDW wavelength of 3${a}_{0}$. For incommensurate wire lengths with 3${a}_{0}$, fluctuating CDW states were observed, which are due to the motion of solitonlike antiphase boundaries.

Femtosecond core-level photoemision spectroscopy on1T-TaS2using a 60-eV laser source

Time-resolved photoelectron spectroscopy (trPES) can directly detect transient electronic structure, thus bringing out its promising potential to clarify nonequilibrium processes arising in condensed matters. Here we report the result of core-level (CL) trPES on 1T-TaS2, realized by developing a high-intensity 60 eV laser obtained by high-order harmonic (HH) generation. Ta4f CL-trPES offers the transient amplitude of the charge-density-wave (CDW), via the site-selective and real-time observation of Ta electrons. The present result indicates an ultrafast photoinduced melting and recovery of CDW amplitude, followed by a peculiar long-life oscillation (i.e. collective amplitudon excitation) accompanying the transfer of 0.01 electrons among adjacent Ta atoms. CL-trPES offers a broad range of opportunities for investigating the ultrafast atom-specific electron dynamics in photo-related phenomena of interest.

A charge density wave in the hidden order state ofURu2Si2

We argue that the hidden order (HO) state inURu2Si2 will induce a charge density wave. The modulation vector of thecharge density wave will be twice that of the hidden order state,QCDW = 2QHO.To illustrate how the charge density wave arises we use a Ginzburg–Landau theory that containsa coupling of the charge density wave amplitude to the square of the HO order parameterΔHO. This simple analysis allows us to predict the intensity and temperature dependence of thecharge density wave order parameter in terms of the susceptibilities and coupling constantsused in the Ginzburg–Landau analysis.

Disentanglement of the Electronic and Lattice Parts of the Order Parameter in a 1D Charge Density Wave System Probed by Femtosecond Spectroscopy

We report on the high resolution studies of the temperature (T) dependence of the q=0 phonon spectrum in the quasi-one-dimensional charge density wave (CDW) compound K(0.3)MoO(3) utilizing time-resolved optical spectroscopy. Numerous modes that appear below T(c) show pronounced T dependences of their amplitudes, frequencies, and dampings. Utilizing the time-dependent Ginzburg-Landau theory we show that these modes result from linear coupling of the electronic part of the order parameter to the 2k(F) phonons, while the (electronic) CDW amplitude mode is overdamped.

Raman scattering evidence for a cascade evolution of the charge-density-wave collective amplitude mode

The two-dimensional rare-earth tritellurides undergo a unidirectional charge-density-wave (CDW) transition at high temperature and, for the heaviest members of the series, a bidirectional one at low temperature. Raman scattering experiments as a function of temperature on ${\text{DyTe}}_{3}$ and on ${\text{LaTe}}_{3}$ at 6 GPa provide a clear-cut evidence for the emergence of the respective collective CDW amplitude excitations. In the unidirectional CDW phase, we discover that the amplitude mode develops as a succession of two mean-field BCS-like transitions with different critical temperatures, which we associate with the presence of two adjacent Te planes in the structure.

Mott Phase at the Surface of1T−TaSe2Observed by Scanning Tunneling Microscopy

In this Letter we report the observation, by scanning tunneling microscopy, of a Mott metal to insulator transition at the surface of 1T-TaSe2. Our spectroscopic data compare considerably well with previous angle-resolved photoemission spectroscopy measurements and confirm the presence of a large hysteresis related to a first order process. The local character of the tunneling spectroscopy technique allows a direct visualization of the surface symmetry and provides spectroscopic measurements on the defect-free region of the sample. It follows that the electronic localization is driven purely by the enhancement of the charge density wave amplitude which drives a bandwidth controlled metal-insulator transition.