Charge Density Wave State Research Articles

Interplay between pair density waves and random field disorders in the pseudogap regime of cuprate superconductors

To capture various experimental results in the pseudogap regime of the underdoped cuprate superconductors for temperature $T<T^{*}$, we propose a four-component pair density wave (PDW) state, in which all components compete with each other. Without random field disorders (RFD), only one of the PDW components survives. If the RFD is included, this state could become phase separated and consist of short range PDW stripes, in which two PDW components coexist but differ in magnitudes, resulting in charge density waves (CDW) and a time-reversal symmetry breaking order, in the form of loop current, as secondary composite orders. We call this phase-separated pair nematic (PSPN) state, which could be responsible for the pseudogap. Using a phenomenological Ginzburg-Landau approach and Monte Carlo simulations, we found that in this state, RFD induces short range static CDW with phase-separated patterns in the directional components and the static CDW is destroyed by thermal phase fluctuations at a crossover temperature $T_{CO}<T^{*}$, above which the CDW becomes dynamically fluctuating. The experimentally found CDW with predominantly d-wave form factor constrains the PDW components to have $s^{\prime}\pm id$ pairing symmetries. We also construct a lattice model and compute the spectral functions for the PSPN state and find good agreement with ARPES results.

Spin-valley locking in the normal state of a transition-metal dichalcogenide superconductor.

Metallic transition-metal dichalcogenides (TMDCs) are benchmark systems for studying and controlling intertwined electronic orders in solids, with superconductivity developing from a charge-density wave state. The interplay between such phases is thought to play a critical role in the unconventional superconductivity of cuprates, Fe-based and heavy-fermion systems, yet even for the more moderately-correlated TMDCs, their nature and origins have proved controversial. Here, we study a prototypical example, 2H-NbSe2, by spin- and angle-resolved photoemission and first-principles theory. We find that the normal state, from which its hallmark collective phases emerge, is characterized by quasiparticles whose spin is locked to their valley pseudospin. This results from a combination of strong spin–orbit interactions and local inversion symmetry breaking, while interlayer coupling further drives a rich three-dimensional momentum dependence of the underlying Fermi-surface spin texture. These findings necessitate a re-investigation of the nature of charge order and superconducting pairing in NbSe2 and related TMDCs.

Fast electronic resistance switching involving hidden charge density wave states.

The functionality of computer memory elements is currently based on multi-stability, driven either by locally manipulating the density of electrons in transistors or by switching magnetic or ferroelectric order. Another possibility is switching between metallic and insulating phases by the motion of ions, but their speed is limited by slow nucleation and inhomogeneous percolative growth. Here we demonstrate fast resistance switching in a charge density wave system caused by pulsed current injection. As a charge pulse travels through the material, it converts a commensurately ordered polaronic Mott insulating state in 1T–TaS2 to a metastable electronic state with textured domain walls, accompanied with a conversion of polarons to band states, and concurrent rapid switching from an insulator to a metal. The large resistance change, high switching speed (30 ps) and ultralow energy per bit opens the way to new concepts in non-volatile memory devices manipulating all-electronic states.

Interplay of charge density wave and multiband superconductivity in 2H-PdxTaSe2.

2H-TaSe2 has been one of unique transition metal dichalcogenides exhibiting several phase transitions due to a delicate balance among competing electronic ground states. An unusual metallic state at high-T is sequentially followed by an incommensurate charge density wave (ICDW) state at ≈122 K and a commensurate charge density wave (CCDW) state at ≈90 K, and superconductivity at TC ~ 0.14 K. Upon systematic intercalation of Pd ions into TaSe2, we find that CCDW order is destabilized more rapidly than ICDW to indicate a hidden quantum phase transition point at x ~ 0.09–0.10. Moreover, TC shows a dramatic enhancement up to 3.3 K at x = 0.08, ~24 times of TC in 2H-TaSe2, in proportional to the density of states N(EF). Investigations of upper critical fields Hc2 in single crystals reveal evidences of multiband superconductivity as temperature-dependent anisotropy factor γH = , quasi-linear increase of , and an upward, positive-curvature in near TC. Furthermore, analysis of temperature-dependent electronic specific heat corroborates the presence of multiple superconducting gaps. Based on above findings and electronic phase diagram vs x, we propose that the increase of N(EF) and effective electron-phonon coupling in the vicinity of CDW quantum phase transition should be a key to the large enhancement of TC in PdxTaSe2.

(Invited) Temperature, Magnetic Field, and Dimensionality Effects on the Raman Spectra of TaSe2

In bulk form, TaSe2 exhibits transitions between commensurate and incommensurate charge-density wave (CDW) phases, and is attracting interest for advanced device applications. In order to explore the evolution of the groundstate CDW phase with layer number, mechanical exfoliation of bulk crystals provides few- to single-layer flakes. In the present work, we extend our opto-thermal Raman measurements1 on MoS2 to include other TMDs, specifically TaSe2 in both 1T and 2H crystallographic phases. A novel, magneto-Raman microscope system affords measurement of low-frequency (down to 10 cm-1) vibrational modes as a function of: temperature (100 K to 400 K), magnetic field (0 T to 9T) and laser excitation. The dependence of the observed Raman-active phonons on temperature and magnetic field will be discussed and compared with earlier results on MoS2. Specifically, we observe the appearance of low-frequency, zone-folded modes in the CDW state, which soften with temperature similar to the higher frequency, in-plane E2g mode. Additionally, we compare the measured magneto-Raman results to calculations using ab initio, density functional theory. 1ACS Nano 2014 8, 986

Electronic structure of SnF3: An example of valence skipper which forms charge density wave

In the present study we calculated the electronic structure of the valence skipping compound SnF3 and BaBiO3 from first-principles. We confirmed that the charge-density-wave (CDW) is formed in SnF3, and the Sn atoms in two crystallographic different sites take the valence Sn2+ and Sn4+. Structure optimization study reveals that this CDW is stable, though the atomic position is slightly different from the experimental data. This behavior is in contrast with the case of BaBiO3, where the structure optimization leads to the uniform state, which means that two Bi sites are equivalent. The CDW state is hard in SnF3, which means that the CDW gap is large enough and it is difficult to melt this CDW order.

Dynamics of pattern-loaded fermions in bichromatic optical lattices

Motivated by experiments in Munich (M. Schreiber et. al. Science \textbf{349}, 842), we study the dynamics of interacting fermions initially prepared in charge density wave states in one-dimensional bichromatic optical lattices. The experiment sees a marked lack of thermalization, which has been taken as evidence for an interacting generalization of Anderson localization, dubbed "many-body localization". We model the experiments using an interacting Aubry-Andre model and develop a computationally efficient low-density cluster expansion to calculate the even-odd density imbalance as a function of interaction strength and potential strength. Our calculations agree with the experimental results and shed light on the phenomena. We also explore a two-dimensional generalization. The cluster expansion method we develop should have broad applicability to similar problems in non-equilibrium quantum physics.

Spin Dynamics in the Bi-Directional Charge Density Wave State of High-T c Superconductors

In this paper, we investigate the dynamical spin susceptibility in the bi-directional charge density wave (BCDW) state by adopting a random-phase approximation. In the BCDW state, we find that no spin resonance exists and only a broad commensurate peak appears for the frequency dependence of the dynamical spin susceptibility at Q = (π,π), though a low-energy spin gap feature can also be found as in the superconducting state. While the “hourglass” type of the dispersion for the BCDW state bears some similarities with that in the superconducting state, the momentum distribution of Im χ+−(Q,ω) is just the opposite with the incommensurate peaks lying along the diagonal direction for the energy below ωc and along the axial direction above ωc. In the coexistence of SC and BCDW, the frequency dependence of the dynamical spin susceptibility at Q = (π,π) generally shows the two-peak structure, reflecting two energy scales of the spin excitations. These unique features may serve as signatures to verify whether or not the BCDW state is responsible for the formation of the Fermi arcs.

Strong charge density wave fluctuation and sliding state in PdTeI with quasi-one-dimensional PdTe chains

In quasi-one-dimensional (quasi-1D) system, the charge density wave (CDW) transition temperature TCDW is usually lower than the mean-field-theory predicted TMF and a CDW fluctuation region exists between them. Here, we investigate the physical properties of PdTeI single crystal containing quasi-1D PdTe chains. Surprisingly, we find that the carrier concentration decreases gradually before the long-range CDW ordering state occurring at T1 ~ 110 K, reflecting the existence of strong CDW fluctuation with possible pseudogap state at T >> T1 because of dynamic charge separation of Pd ions (Pd3+ -> Pd2+ + Pd4+). Moreover, the sliding CDW state appears below T2 ~ 6 K. Combined such low T2 with the feature of multiple quasi-1D bands, PdTeI exhibits exotic crossover behavior from negative to huge positive magnetoresistance under magnetic field and field-induced localization. Thus, PdTeI provides a novel platform for studying the CDW fluctuation and the interplay between magnetic field and CDW state.

Electronic structure of the titanium-based oxypnictide superconductorBa0.95Na0.05Ti2Sb2Oand direct observation of its charge density wave order

${\mathrm{Ba}}_{0.95}{\mathrm{Na}}_{0.05}{\mathrm{Ti}}_{2}{\mathrm{Sb}}_{2}\mathrm{O}$ is a titanium-based oxypnictide superconductor with possible density wave order. We have performed high-resolution angle-resolved photoemission spectroscopy and scanning tunneling microscopy (STM) studies on ${\mathrm{Ba}}_{0.95}{\mathrm{Na}}_{0.05}{\mathrm{Ti}}_{2}{\mathrm{Sb}}_{2}\mathrm{O}$. Our STM studies find a charge density wave (CDW) order with the wave vector of ($\ensuremath{\pi}, \ensuremath{\pi}$). The electronic structure shows both multiorbital and three-dimensional nature, consistent with the theoretical calculations. The observed Fermi surfaces are well nested along the ($\ensuremath{\pi}, \ensuremath{\pi}$) direction, which might drive the CDW transition. Likely due to the weak strength of the CDW order, we do not observe a leading-edge gap. Instead, we observe an overall spectral weight enhancement with decreasing temperature, but the rate of this enhancement is abruptly reduced or diminished in the CDW state, suggesting the suppression of spectral weight or opening of a partial CDW gap. Our results give a comprehensive picture of the electronic structure and direct observation of the CDW order in ${\mathrm{Ba}}_{0.95}{\mathrm{Na}}_{0.05}{\mathrm{Ti}}_{2}{\mathrm{Sb}}_{2}\mathrm{O}$.

Strain tuning of the charge density wave in monolayer and bilayer 1T-TaS2.

Using first-principles calculations, we investigate the strain effects on the charge density wave states of monolayer and bilayer 1T-TaS2. The modified stability of the charge density wave in the monolayer is understood in terms of the strain dependent electron localization, which determines the distortion amplitude. On the other hand, in the bilayer, the effect of strain on the interlayer interaction is also crucial. The rich phase diagram under strain opens new venues for applications of 1T-TaS2. We interpret the experimentally observed insulating state of bulk 1T-TaS2 as inherited from the monolayer by effective interlayer decoupling.

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.

Quantum Lattice Fluctuations in the Charge Density Wave State beyond the Adiabatic Approximation

We have developed a tractable numerical method in which large-amplitude quantum lattice fluctuations can be described beyond the adiabatic approximation using the coherent state representation of phonons. A many-body wave function is constructed by the superposition of direct products of non-orthogonal Slater determinants for electrons and coherent states of phonons. Both orbitals in all the Slater determinants and the amplitudes of all the coherent states are simultaneously optimized. We apply the method to the one-dimensional Su–Schrieffer–Heeger model with the on-site and nearest-neighbor-site Coulomb interactions. It is shown the lattice fluctuations in doped charge density wave (CDW) systems are described by the translational and vibrational motion of lattice solitons. Such lattice solitons induce bond alternation in the doped CDW system while the lattice becomes equidistant in the half-filled CDW system.

Quasiparticle spectra of2H−NbSe2: Two-band superconductivity and the role of tunneling selectivity

We have studied the superconducting state of 2H−NbSe2 by scanning tunneling spectroscopy along two different crystal orientations, the c and the a/b axes. Along the c axis a large gap is dominant in the spectra, while a smaller gap is measured along the a/b axis. We show that these spectra are accurately described by the McMillan model where the small gap is induced through the coupling to the band associated with the large gap. In order to assign the small and large gaps to specific parts of the 2H−NbSe2 Fermi surface, the electronic structure was studied using first-principles calculations. While we cannot exclude the possibility of intrinsic anisotropy of the gaps, we propose that the large gap opens in the Fermi surface cylinders located around the corner K points while the sheets located around Γ are associated with the small gap. An additional component of the Fermi surface, a selenium based pocket, plays an essential role in the tunneling process. The role of the charge density wave occurring in this material is also discussed. Finally, we are able to give a coherent description of the observed characteristics of the tunneling spectra of 2H−NbSe2 as well as the differences with 2H−NbS2 where no charge density wave state is present. Further experimental work, such as high-resolution ARPES, would be very useful to confirm our interpretation. The approach and modeling developed here could also be relevant for other compounds of the dichalcogenide family.

Finite-temperature coupled-cluster, many-body perturbation, and restricted and unrestricted Hartree-Fock study on one-dimensional solids: Luttinger liquids, Peierls transitions, and spin- and charge-density waves.

One-dimensional (1D) solids exhibit a number of striking electronic structures including charge-density wave (CDW) and spin-density wave (SDW). Also, the Peierls theorem states that at zero temperature, a 1D system predicted by simple band theory to be a metal will spontaneously dimerize and open a finite fundamental bandgap, while at higher temperatures, it will assume the equidistant geometry with zero bandgap (a Peierls transition). We computationally study these unique electronic structures and transition in polyyne and all-trans polyacetylene using finite-temperature generalizations of ab initio spin-unrestricted Hartree-Fock (UHF) and spin-restricted coupled-cluster doubles (CCD) theories, extending upon previous work [He et al., J. Chem. Phys. 140, 024702 (2014)] that is based on spin-restricted Hartree-Fock (RHF) and second-order many-body perturbation (MP2) theories. Unlike RHF, UHF can predict SDW as well as CDW and metallic states, and unlike MP2, CCD does not diverge even if the underlying RHF reference wave function is metallic. UHF predicts a gapped SDW state with no dimerization at low temperatures, which gradually becomes metallic as the temperature is raised. CCD, meanwhile, confirms that electron correlation lowers the Peierls transition temperature. Furthermore, we show that the results from all theories for both polymers are subject to a unified interpretation in terms of the UHF solutions to the Hubbard-Peierls model using different values of the electron-electron interaction strength, U/t, in its Hamiltonian. The CCD wave function is shown to encompass the form of the exact solution of the Tomonaga-Luttinger model and is thus expected to describe accurately the electronic structure of Luttinger liquids.

Competition between excitonic charge and spin density waves: Influence of electron-phonon and Hund's rule couplings

We analyze the stability of excitonic ground states in the two-band Hubbard model with additional electron-phonon and Hund's rule couplings using a combination of mean-field and variational cluster approaches. We show that both the interband Coulomb interaction and the electron-phonon interaction will cooperatively stabilize a charge density wave (CDW) state which typifies an "excitonic" CDW if predominantly triggered by the effective interorbital electron-hole attraction or a "phononic" CDW if mostly caused by the coupling to the lattice degrees of freedom. By contrast, the Hund's rule coupling promotes an excitonic spin density wave. We determine the transition between excitonic charge and spin density waves and comment on a fixation of the phase of the excitonic order parameter that would prevent the formation of a superfluid condensate of excitons. The implications for exciton condensation in several material classes with strongly correlated electrons are discussed.

Ferromagnetic-nematic order and strongly correlated phases of fermions in optical flux lattices

We study a model of a 2D ultracold atomic gas subject to an "optical flux lattice": a laser configuration where Raman-dressed atoms experience a strong artificial magnetic field. This leads to a bandstructure of narrow energy bands with non-zero Chern numbers. We consider the case of two-level (spin-$1/2$) fermionic atoms in this lattice, interacting via a repulsive $s$-wave contact interaction. Atoms restricted to the lowest band are described by an effective model of spinless fermions with interactions that couple states in a momentum-dependent manner across the Brillouin zone; a consequence of the Raman dressing of the two spin states. We present the results of detailed exact diagonalization studies of the many-body states for a range of filling factors, $\nu$. First, we present evidence for the existence of a phase with coupled ferromagnetic--nematic ordering, which was previously suggested by a mean-field analysis. Second, we present evidence indicating the presence of a Laughlin-like fractional quantum Hall state occurring at filling factor $\nu = 1/3$. Finally, we observe a charge density wave state at $\nu=1/2$, which we are able to cleanly distinguish from the Laughlin-like state by its translational symmetry breaking and relatively small participation ratio.

Direct Observations of Photoexcitation Induced Dynamics of Charge Density Wave and Charge-Orbital Ordered State Using 2.8 MeV Ultrafast Electron Diffraction

Direct Observations of Photoexcitation Induced Dynamics of Charge Density Wave and Charge-Orbital Ordered State Using 2.8 MeV Ultrafast Electron Diffraction

Controlling the metal-to-insulator relaxation of the metastable hidden quantum state in 1T-TaS2.

Controllable switching between metastable macroscopic quantum states under nonequilibrium conditions induced either by light or with an external electric field is rapidly becoming of great fundamental interest. We investigate the relaxation properties of a "hidden" (H) charge density wave (CDW) state in thin single crystals of the layered dichalcogenide 1T-TaS2, which can be reached by either a single 35-fs optical laser pulse or an ~30-ps electrical pulse. From measurements of the temperature dependence of the resistivity under different excitation conditions, we find that the metallic H state relaxes to the insulating Mott ground state through a sequence of intermediate metastable states via discrete jumps over a "Devil's staircase." In between the discrete steps, an underlying glassy relaxation process is observed, which arises because of reciprocal-space commensurability frustration between the CDW and the underlying lattice. We show that the metastable state relaxation rate may be externally stabilized by substrate strain, thus opening the way to the design of nonvolatile ultrafast high-temperature memory devices based on switching between CDW states with large intrinsic differences in electrical resistance.

ChemInform Abstract: Charge‐Bistable Pd(III)/Pd(II,IV) Coordination Polymers: Phase Transitions and Their Applications to Optical Properties

AbstractReview: 60 refs.