Incommensurate Charge Density Wave State Research Articles

Nonreciprocal nonlinear responses in moving charge density waves

The incommensurate charge density wave states (CDWs) can exhibit steady motion in the flow limit after depinning, behaving as a nonequilibrium system with time-dependent states. Since the moving CDW, like an electric current, breaks both time-reversal and inversion symmetries, one may speculate the emergence of nonreciprocal nonlinear responses from such motion. However, the moving CDW order parameter is intrinsically time-dependent in the lab frame, and it is known to be challenging to evaluate the responses of such a time-varying system. In this work, following the principle of Galilean relativity, we resolve this time-dependent hard problem in the lab frame by mapping the system to the comoving frame with static CDW states through the Galilean transformation. We explicitly show that the nonreciprocal nonlinear responses would be generated by the movement of CDW states through violating Galilean relativity.

Ultrafast excitation and topological soliton formation in incommensurate charge density wave states

Topological soliton is a nonperturbative excitation in commensurate density wave states and connects degenerate ground states. In incommensurate density wave states, ground states are continuously degenerate and topological soliton is reckoned to be smoothly connected to the perturbative phason excitation. We study the ultrafast nonequilibrium dynamics due to photoexcited electron-hole pair in a one-dimensional chain with an incommensurate charge density wave ground state. Time-resolved evolution reveals both perturbative excitation of collective modes and nonperturbative topological phase transition due to creating novel topological solitons, where the continuous complex order parameter with amplitude and phase is essential. We identify the nontrivial phase-winding solitons in the complex plane unique to this nonequilibrium state and capture it by a low-energy effective model. The perturbative temporal gap oscillation and the solitonic in-gap states enter the optical conductivity absorption edge and the spectral density related to spectroscopic measurement, providing concrete connections to real experiments.

Modulated crystal structure of the atypical charge density wave state of single-crystal Lu2Ir3Si5

The three-dimensional charge density wave (CDW) compound ${\mathrm{Lu}}_{2}{\mathrm{Ir}}_{3}{\mathrm{Si}}_{5}$ undergoes a first-order CDW phase transition at around 200 K. An atypical CDW state is found, that is characterized by an incommensurate CDW with $\mathbf{q}=[0.2499(3),0.4843(4),0.2386(2)]$ at 60 K, and a large orthorhombic-to-triclinic lattice distortion with $\ensuremath{\beta}=91.945{(2)}^{\ensuremath{\circ}}$. We present the modulated crystal structure of the incommensurate CDW state. Structural analysis shows that the CDW resides on the zigzag chains of iridium atoms along $\mathbf{c}$. The structural distortions are completely similar between nonmagnetic ${\mathrm{Lu}}_{2}{\mathrm{Ir}}_{3}{\mathrm{Si}}_{5}$ and previously studied isostructural magnetic ${\mathrm{Er}}_{2}{\mathrm{Ir}}_{3}{\mathrm{Si}}_{5}$ with the small differences explained by the different values of the atomic radii of Lu and Er. Such a similarity is unique to ${R}_{2}{\mathrm{Ir}}_{3}{\mathrm{Si}}_{5}$ $(R=\mathrm{rare}\phantom{\rule{0.28em}{0ex}}\mathrm{earth})$. It differs from, for example, the rare-earth CDW compounds ${R}_{5}{\mathrm{Ir}}_{4}{\mathrm{Si}}_{10}$ for which ${\mathrm{Lu}}_{5}{\mathrm{Ir}}_{4}{\mathrm{Si}}_{10}$ and ${\mathrm{Er}}_{5}{\mathrm{Ir}}_{4}{\mathrm{Si}}_{10}$ possess entirely different CDW states. We argue that the mechanism of CDW formation, thus, is different for ${R}_{2}{\mathrm{Ir}}_{3}{\mathrm{Si}}_{5}$ and ${R}_{5}{\mathrm{Ir}}_{4}{\mathrm{Si}}_{10}$.

Transistor-Less Logic Circuits Implemented With 2-D Charge Density Wave Devices

We propose logic gates and circuits implemented with 2-D charge density wave (CDW) devices, which operate at room temperature. The 1T-TaS2 charge density wave devices exhibit a voltage triggered phase transition between the nearly commensurate and incommensurate CDW states, which is accompanied by an abrupt change of the resistance and hysteresis. The unique output characteristics of such devices allow for building logic gates and circuits without any transistors. Using the experimentally measured current–voltage characteristics, we model and numerically simulate the performance of the inverter and the OR logic gates consisting of CDW devices and regular resistors. Owing to the radiation-hard nature of the CDW devices and absence of transistors, the proposed circuits can be utilized in various harsh environments on earth or outer space.

Total-Ionizing-Dose Effects on Threshold Switching in $1{T}$ -TaS2 Charge Density Wave Devices

The 1T polytype of TaS2 exhibits voltage-triggered threshold switching as a result of a phase transition from nearly commensurate to incommensurate charge density wave states. Threshold switching, persistent above room temperature, can be utilized in a variety of electronic devices, e.g., voltage controlled oscillators. We evaluated the total-ionizing-dose response of thin film 1T-TaS2 at doses up to 1 Mrad(SiO2). The threshold voltage changed by less than 2% after irradiation, with persistent self-sustained oscillations observed through the full irradiation sequence. The radiation hardness is attributed to the high intrinsic carrier concentration of 1T-TaS2 in both of the phases that lead to threshold switching. These results suggest that charge density wave devices, implemented with thin films of 1T-TaS2, are promising for applications in high radiation environments.

Theory of hydrodynamic transport in fluctuating electronic charge density wave states

We describe the collective hydrodynamic motion of an incommensurate charge density wave state in a clean electronic system. Our description simultaneously incorporates the effects of both pinning due to weak disorder and also phase relaxation due to proliferating dislocations. We show that the interplay between these two phenomena has important consequences for charge and momentum transport. For instance, it can lead to metal-insulator transitions. We furthermore identify signatures of fluctuating density waves in frequency and spatially resolved conductivities. Phase disordering is well known to lead to a large viscosity. We derive a precise formula for the phase relaxation rate in terms of the viscosity in the dislocation cores. We thereby determine the viscosity of the superconducting state of BSCCO from the observed melting dynamics of Abrikosov lattices and show that the result is consistent with dissipation into Bogoliubov quasiparticles.

Charge Density Wave States and Structural Transition in Layered Chalcogenide TaSe2−xTex**Supported by the National Basic Research Program of China under Grant Nos 2015CB921300 and 2012CB821404, the National Key Research and Development Program of China under Grant Nos 2016YFA0300300 and 2016YFA0300404, the National Natural Science Foundation of China under Grant Nos 11474323, 11604372, 11274368, 91221102, 11190022, 11674326 and 91422303, and the

The structural features and three-dimensional nature of the charge density wave (CDW) state of the layered chalcogenide 1T-TaSe2−xTex () are characterized by Cs-corrected transmission electron microscopy measurements. Notable changes of both average structure and the CDW state arising from Te substitution for Se are clearly demonstrated in samples with . The commensurate CDW state characterized by the known star-of-David clustering in the 1T-TaSe2 crystal becomes visibly unstable with Te substitution and vanishes when x = 0.3. The 1T-TaSe2−xTex () samples generally adopt a remarkable incommensurate CDW state with monoclinic distortion, which could be fundamentally in correlation with the strong q-dependent electron–phonon coupling-induced period-lattice-distortion as identified in TaTe2. Systematic analysis demonstrates that the occurrence of superconductivity is related to the suppression of the commensurate CDW phase and the presence of discommensuration is an evident structural feature observed in the superconducting samples.

Controlling many-body states by the electric-field effect in a two-dimensional material

To understand the complex physics of a system with strong electron-electron interactions, the ideal is to control and monitor its properties while tuning an external electric field applied to the system (the electric-field effect). Indeed, complete electric-field control of many-body states in strongly correlated electron systems is fundamental to the next generation of condensed matter research and devices. However, the material must be thin enough to avoid shielding of the electric field in the bulk material. Two-dimensional materials do not experience electrical screening, and their charge-carrier density can be controlled by gating. Octahedral titanium diselenide (1T-TiSe2) is a prototypical two-dimensional material that reveals a charge-density wave (CDW) and superconductivity in its phase diagram, presenting several similarities with other layered systems such as copper oxides, iron pnictides, and crystals of rare-earth elements and actinide atoms. By studying 1T-TiSe2 single crystals with thicknesses of 10 nanometres or less, encapsulated in two-dimensional layers of hexagonal boron nitride, we achieve unprecedented control over the CDW transition temperature (tuned from 170 kelvin to 40 kelvin), and over the superconductivity transition temperature (tuned from a quantum critical point at 0 kelvin up to 3 kelvin). Electrically driving TiSe2 over different ordered electronic phases allows us to study the details of the phase transitions between many-body states. Observations of periodic oscillations of magnetoresistance induced by the Little-Parks effect show that the appearance of superconductivity is directly correlated with the spatial texturing of the amplitude and phase of the superconductivity order parameter, corresponding to a two-dimensional matrix of superconductivity. We infer that this superconductivity matrix is supported by a matrix of incommensurate CDW states embedded in the commensurate CDW states. Our results show that spatially modulated electronic states are fundamental to the appearance of two-dimensional superconductivity.

Studies of 27Al NMR in SrAl4

A charge density wave (CDW) transition at TCDW = 243K and a structural phase (SP) transition at approximately 100K occur in SrAl4 with the BaAl4-type body center tetragonal structure, which is the divalent and non-4f electron reference compound of EuAl4. To understand the behaviors of the CDW and SP transitions, the 27Al NMR measurements using a single crystal and a powder sample of SrAl4 have been carried out. The line width below TCDW is modulated by an electrical quadruple interaction between 27Al nucleus and CDW charge modulation. The incommensurate CDW state below TCDW changes into a different structure below TSP. The temperature dependences of Knight shifts of 27Al(I) and 27Al(II) show the different behaviors. The temperature variation of 27Al(I) Knight shift shows anomalies at the CDW and SP transition temperatures, revealing the shift to negative side below TCDW, which is attributable to the core polarization of the d-electrons. However, 27Al(II) Knight shift keeps almost constant except for the small shift due to the SP transition. The 1/T1T of 27Al(I) indicates the obvious changes due to the CDW and SP transitions, while that of 27Al(II) takes a constant value. The density of state at the Fermi level at Al(I) site below 60K would be about 0.9 times less than that above TCDW.

Lattice dynamical signature of charge density wave formation in underdopedYBa2Cu3O6+x

We report a detailed Raman scattering study of the lattice dynamics in detwinned single crystals of the underdoped high temperature superconductor YBa2Cu3O6+x (x=0.75, 0.6, 0.55 and 0.45). Whereas at room temperature the phonon spectra of these compounds are similar to that of optimally doped YBa2Cu3O6.99, additional Raman-active modes appear upon cooling below ~170-200 K in underdoped crystals. The temperature dependence of these new features indicates that they are associated with the incommensurate charge density wave state recently discovered using synchrotron x-ray scattering techniques on the same single crystals. Raman scattering has thus the potential to explore the evolution of this state under extreme conditions.

Commensurate charge-density wave with frustrated interchain coupling inSmNiC2

Temperature-dependent x-ray diffraction on ${\text{SmNiC}}_{2}$ has shown that the orthorhombic lattice symmetry of this compound persist down to a temperature of at least 9 K, i.e., into the charge-density-wave (CDW) state below ${T}_{\text{CDW}}=148\text{ }\text{K}$ and in the ferromagnetically ordered state below ${T}_{C}=17.7\text{ }\text{K}$. The modulated crystal structure has been determined for the incommensurate CDW state with ${\mathbf{q}}_{\text{CDW}}=(0.5,0.516,0)$ at $T=60\text{ }\text{K}$. The observed atomic modulation displacements indicate that the CDW should be considered as a commensurate CDW centered on chains of Ni atoms along $\mathbf{a}$. Frustrated interchain coupling is responsible for the incommensurability of the three-dimensionally ordered CDW state.

Charge-density waves arising from two electron bands

A theory for a quasi-one-dimensional incommensurate charge-density wave state arising from electron–phonon (el–phon) interaction connecting electron states in two different bands is presented. An expression for the fundamental component of the energy gap as a function of the effective el–phon coupling, valid for all coupling strengths, has been found. For a single band, the expression simplifies to a reciprocal hyperbolic-sine dependence on the reciprocal effective coupling. The effective coupling, although simply related to the n assumed phonon-band frequencies, is not generally expressible as a sum of independent functions of these frequencies. The theory is applied to tetrathiofulvalinium–tetracyanoquinodimethane and to potassium blue bronze.

93Nb NMR study of the charge density wave state inNbSe2

93Nb NMR studies were carried out for a single crystal ofNbSe2 at 73.328 MHz in the temperature range 9–300 K to investigate the normaland charge density wave (CDW) states. Detailed analysis of the NMR lineshape of the central transition using a classical incommensurate modelreveals the change in the conduction electron spin dynamics from aboveTCDW. An increase of theKnight shift below TCDW reflects modification to the uniform part of the conduction electron density of states. As suggestedtheoretically, the Knight shift distribution is found to be directly proportional to the square ofthe amplitude of the CDW. The results further indicate an incommensurate CDW state in2H-NbSe2. Analysis of the NMR spectra using the McMillan incommensuratemodel suggests a large value of the discommensuration parameter(γ) whichis almost temperature independent, in contrast to the much smaller value previously reported in the caseof 2H-TaSe2.

Fermi surface studies of the charge-density-wave state of the quasi-two-dimensional monophosphate tungsten bronzeP4W12O44

The monophosphate tungsten bronze ${\mathrm{P}}_{4}{\mathrm{W}}_{12}{\mathrm{O}}_{44}$ is a quasi-two-dimensional conductor which shows successive Peierls instabilities towards incommensurate charge density wave states. Previous Shubnikov--de Haas and de Haas--van Alphen studies performed in the lowest temperature charge density wave state had established that the Fermi surface includes several small quasi cylindrical pockets. We now report angle dependent magnetoresistance oscillations which provide the shape and orientation of one warped Fermi surface pocket. We suggest a possible location of this pocket on the basis of the Fermi surface calculated for the high temperature phase and of the charge density wave nesting vectors.

Finite temperature spectral function of Mott insulators and charge density wave states.

We calculate the low-temperature spectral function of one-dimensional incommensurate charge density wave states and half filled Mott insulators. At T=0 there are two dispersing features associated with the spin and charge degrees of freedom, respectively. We show that already at very low temperatures (compared to the gap) one of these features gets severely damped. We comment on implications of this result for photoemission experiments.

Giant striction and thermal expansion anomalies in actinide systems with structural instabilities

A fluctuation theory is presented to discuss the phenomenon of giant striction, associated with a displacive phase transition, which takes account of both phonon and overdamped soft mode excitations - paraphonons. The expansion anomalies in uranium and plutonium below 50 K are attributed to the effects of giant striction and soft mode behaviour accompanying the transition to the incommensurate charge density wave state observed in neutron scattering experiments.

The 2D-electric-field gradient profile in the incommensurate charge density wave state of 1T-TaS2

Using time differential perturbed angular correlation we probed the incommensurate 2D-plane wave charge density wave in 1T-TaS2 via the181Ta nuclear quadrupole interaction. For the interpretation of the observed line profiles a non-local treatment of the ICDW-perturbation is required. Taking the tensorial character of the electric field gradient into account the wavelength of the CDW-modulation can be derived from the line profiles within an accuracy of better than 5%.

The Effect of Giant Striction and Thermal Expansion Anomalies in Systems with Structural Instabilities

AbstractA simple fluctuation theory analogous to the spin‐fluctuation theory of the magneto‐volume effect is presented to discuss the phenomenon of giant striction, associated with displacive phase transitions, and thermal expansion anomalies. It is argued that the giant striction accompanying the phase transition to the incommensurate charge density wave state is responsible for the low temperature anomalous expansion of α‐uranium and α‐plutonium. The spontaneous striction values in these materials are estimated to be 4.57 × 10−3 and 1.82 × 10−2 comparable with those known for systems with giant magnetostriction.

Mössbauer studies of the charge-density-wave state of 57FeK0.30MoO3

Mössbauer studies have been performed between 6 K and 300 K on single crystals of 57 Fe-doped K 0.30 MoO 3 , which show a Peierls transition at 180 K towards on incommensurate charge density wave state. The spectra show three doublets. A strong line broadening below 120 K indicates that the Fe impurities are strong pinning centers for the charge density wave above ∼ 120 K and become progressively weak pinning ones below, in agreement with theoretical models.

Kink lattice structure and midgap band in incommensurate Charge Density Waves

By diagonalizing the one-dimensional Fröhlich model numerically, we investigate the incommensurate charge density wave states within a mean field approximation. It is found that the midgap band inside the main Peierls energy gap always appears in nearly commensurate states, which is attributed to the formation of the kink (or soliton) lattice of the electron- and ion-density modulations. The overall band structure against band filling is shown to be self-similar and recursive. Experimental relevance of our finding is discussed.