CDW Phase Research Articles

Endotaxial stabilization of 2D charge density waves with long-range order

Charge density waves are emergent quantum states that spontaneously reduce crystal symmetry, drive metal-insulator transitions, and precede superconductivity. In low-dimensions, distinct quantum states arise, however, thermal fluctuations and external disorder destroy long-range order. Here we stabilize ordered two-dimensional (2D) charge density waves through endotaxial synthesis of confined monolayers of 1T-TaS2. Specifically, an ordered incommensurate charge density wave (oIC-CDW) is realized in 2D with dramatically enhanced amplitude and resistivity. By enhancing CDW order, the hexatic nature of charge density waves becomes observable. Upon heating via in-situ TEM, the CDW continuously melts in a reversible hexatic process wherein topological defects form in the charge density wave. From these results, new regimes of the CDW phase diagram for 1T-TaS2 are derived and consistent with the predicted emergence of vestigial quantum order.

π Phase Interlayer Shift and Stacking Fault in the Kagome Superconductor CsV_{3}Sb_{5}.

The stacking degree of freedom is a crucial factor in tuning material properties and has been extensively investigated in layered materials. The kagome superconductor CsV_{3}Sb_{5} was recently discovered to exhibit a three-dimensional CDW phase below T_{CDW}∼94 K. Despite the thorough investigation of in-plane modulation, the out-of-plane modulation has remained ambiguous. Here, our polarization- and temperature-dependent Raman measurements reveal the breaking of C_{6} rotational symmetry and the presence of three distinct domains oriented at approximately 120° to each other. The observations demonstrate that the CDW phase can be naturally explained as a 2c staggered order phase with adjacent layers exhibiting a relative π phase shift. Further, we discover a first-order structural phase transition at approximately 65K and suggest that it is a stacking order-disorder phase transition due to stacking fault, supported by the thermal hysteresis behavior of a Cs-related phonon mode. Our findings highlight the significance of the stacking degree of freedom in CsV_{3}Sb_{5} and offer structural insights to comprehend the entanglement between superconductivity and CDW.

Origin of the Anomalous Electrical Transports in Quasi-One-Dimensional Ta2NiSe7.

Exploration of exotic transport behavior is of great interest and importance for revealing the properties of the CDW phase of quasi-one-dimensional Ta2NiSe7. We report the anisotropic electrical transport properties of Ta2NiSe7 single crystals in the CDW phase. The anisotropic constant (γ = ρb/ρc) increased rapidly at TCDW = 60 K upon cooling. The results of the Hall resistivity show that both the concentrations and mobilities of carriers change abruptly at TCDW. The out-of-plane AMR exhibits C2 and C4 symmetry components while the in-plane AMR exhibits C2, C4, and C6 at the CDW state. The planar Hall effect is observed in Ta2NiSe7 at low temperature, which is suggested to originate from the anisotropic orbital magnetoresistance. The calculated results show that the Fermi surface of Ta2NiSe7 was slightly reconstructed due to the CDW transition. This work highlights the enhancement of Fermi surface anisotropy during CDW formation and provides a novel approach to study the CDW materials.

Detection of Nontrivial Topology Driven by Charge Density Wave in a Semi‐Dirac Metal

AbstractThe presence of electron correlations in a system with topological order can lead to exotic ground states. Considering single crystals of LaAgSb2 which has a square net crystal structure, one finds multiple charge density wave transitions (CDW) as the temperature is lowered. Large planar Hall (PHE) signals are found in the CDW phase, which are still finite in the high‐temperature phase though they change sign. Optimizing the structure within first‐principles calculations, one finds an unusual chiral metallic phase. This is because as the temperature is lowered, the separation between the Ag/Sb atoms on different layers decreases, leading to stronger repulsions between electrons associated with atoms on different layers. This leads to successive layers sliding with respect to each other, thereby stabilizing a chiral structure in which inversion symmetry is also broken. The large Berry curvature associated with the low‐temperature structure explains the low‐temperature PHE. At high temperature, the PHE arises from the changes induced in the anisotropic Dirac cone in presence of a magnetic field. This work represents a route toward detecting and understanding the mechanism in a correlation‐driven topological transition through electron transport measurements, complemented by ab‐initio electronic structure calculations.

Correlation between charge density wave phase transition and hydrogen adsorption in 1T-TaS2 thin film devices

Thin films of tantalum disulfide in the 1T-polytype structural phase (1T-TaS2), a type of metallic two-dimensional (2D) transition metal dichalcogenides (TMDs), are reactive to H2. Interestingly, in the incommensurate charge-density wave (ICCDW) phase with a metallic state, the electrical resistance of the 1T-TaS2 thin film decreases when H2 is adsorbed on it and returns to its initial value upon desorption. In contrast, the electrical resistance of the film in the nearly commensurate CDW (NCCDW) phase, which has a subtle band overlap or a small bandgap, does not change upon H2 adsorption/desorption. This difference in H2 reactivity is a result of differences in the electronic structure of the two 1T-TaS2 phases, namely, the ICCDW and NCCDW phases. Compared to other semiconductor 2D-TMDs such as MoS2 and WS2, the metallic TaS2 has been theoretically proven to capture gas molecules more easily because Ta has a stronger positive charge than Mo or W. Our experimental results provide evidence of this. Notably, this study is the first example of H2 sensing using 1T-TaS2 thin films and demonstrates the possibility of controlling the reactivity of the sensors to the gas by changing the electronic structure via CDW phase transitions.

Microscopic nature of the charge-density wave in the kagome superconductorRbV3Sb5

The recently discovered vanadium-based kagome metals AV$_3$Sb$_5$ (A = K, Rb, Cs) offer the possibility to study the interplay between competing electronic orderings, such as charge density order and superconductivity. We focus on the former and provide a comprehensive set of $^{51}$V, $^{87}$Rb, and $^{121}$Sb magnetic resonance measurements on an RbV$_3$Sb$_5$ single crystal. Elucidating the symmetries and properties of the CDW phase is essential to understanding the unconventional electronic orderings occurring in this material. We establish the structure of the $2\times 2 \times 2$ superlattice that describes the system below the charge density wave transition by combining both experimental and computational methods, with a methodology that can be readily applied to the remaining compounds of the same family. Our results give compelling evidence that the CDW structure occurring below 103 K for RbV$_3$Sb$_5$ is the so-called Inverse Start of David pattern $\pi$-shifted along the c axis (also known as staggered tri-hexagonal).

Enhanced Intertwined Spin and Charge Orders in the t–J Model in a Small J Case

The one-band t–J model captures strong correlations in cuprate high-temperature superconductors. It accounts for the various intertwined spin and charge orders, and the superconductivity in the phase diagrams. To see the correlation effect on the intertwined orders, we implement the density matrix renormalization group method to simulate the t–J model in a small J case with t/J = 10, which is in a deeper Mott region than that with t/J ≃ 3 in cuprate superconducting compounds. We examine the results on a six-leg lattice with both the nearest and next-nearest-neighbor hoppings and antiferromagnetic coupling, and find the absence of superconductivity and enhanced intertwined spin and charge orders in the phase diagram. Besides the stripe phases, we find a new SDW + CDW phase in which the spin modulation is a (π, π) antiferromagnetism, while the wavelength of the charge modulation is shorter than that of the stripe phases. Our results suggest the enhanced intertwined orders and suppressed superconductivity in the deep Mott region.

Elastic properties at the charge density wave phase transitions in TbTe3, ErTe3 and HoTe3

ABSTRACT Rare earth tritelluride TbTe, ErTe and HoTe exhibit two successive charge density wave phase transitions and . The transition to the incommensurate phase at is reflected in the longitudinal elastic stiffness components and . In the incommensurate phase below the longitudinal stiffness components , are augmented by a contribution from quartic anharmonic interaction with the onset of the incommensurate ordering. The temperature dependences of the elastic constants , are shown to follow a law. The mechanism for the lower CDW phase transition is significantly different from that at the upper CDW phase transition.

Evidence for multiband superconductivity and charge density waves in Ni-doped ZrTe2

We carried out a comprehensive study of the electronic, magnetic, and thermodynamic properties of Ni-doped ZrTe$_2$. High quality Ni$_{0.04}$ZrTe$_{1.89}$ single crystals show a possible coexistence of charge density waves (CDW, T$_{CDW}\approx287$\,K) with superconductivity (T$_c\approx 4.1$\,K), which we report here for the first time. The temperature dependence of the lower (H$_{c_1}$) and upper (H$_{c_2}$) critical magnetic fields both deviate significantly from the behaviors expected in conventional single-gap s-wave superconductors. However, the behaviors of the normalized superfluid density $\rho_s(T)$ and H$_{c_2}(T)$ can be described well using a two-gap model for the Fermi surface, in a manner consistent with conventional multiband superconductivity. Electrical resistivity and specific heat measurements show clear anomalies centered near 287\,K consistent with a CDW phase transition. Additionally, electronic-structure calculations support the coexistence of electron-phonon multiband superconductivity and CDW order due to the compensated disconnected nature of the electron- and hole-pockets at the Fermi surface. Our electronic structure calculations also suggest that ZrTe$_2$ could reach a non-trivial topological type-II Dirac semimetallic state. These findings highlight that Ni-doped ZrTe2 can be uniquely important for probing the coexistence of superconducting and CDW ground states in an electronic system with non-trivial topology.

Pressure-induced suppression of charge density phases across the entire rare-earth tritellurides by optical spectroscopy

Pressure studies on the rare-earth tritellurides established the pressure-induced suppression of charge density wave phases. The hydrostatic pressure required to suppress the CDW phase is reduced for materials with larger internal chemical pressure.

Signatures of the charge density wave collective mode in the infrared optical response of VSe2

We present a detailed study of the bulk electronic structure of high quality VSe$_{2}$ single crystals using optical spectroscopy. Upon entering the charge density wave phase below the critical temperature of 112 K, the optical conductivity of VSe$_2$ undergoes a significant rearrangement. A Drude response present above the critical temperature is suppressed while a new interband transition appears around 0.07\,eV. From our analysis, we estimate that part of the spectral weight of the Drude response is transferred to a collective mode of the CDW phase. The remaining normal state charge dynamics appears to become strongly damped by interactions with the lattice as evidenced by a mass enhancement factor m$^{*}$/m$\approx$3. In addition to the changes taking place in the electronic structure, we observe the emergence of infrared active phonons below the critical temperature associated with the 4a x 4a lattice reconstruction.

Ultrafast Modulations and Detection of a Ferro-Rotational Charge Density Wave Using Time-Resolved Electric Quadrupole Second Harmonic Generation.

We show the ferro-rotational nature of the commensurate charge density wave (CCDW) in 1T-TaS_{2} and track its dynamic modulations by temperature-dependent and time-resolved electric quadrupole rotation anisotropy-second harmonic generation (EQ RA-SHG), respectively. The ultrafast modulations manifest as the breathing and the rotation of the EQ RA-SHG patterns at three frequencies around the reported single CCDW amplitude mode frequency. A sudden shift of the triplet frequencies and a dramatic increase in the breathing and rotation magnitude further reveal a photoinduced transient CDW phase across a critical pump fluence of ∼0.5 mJ/cm^{2}.

A semi exact solution for a metallic phase in a Holstein-Hubbard chain at half filling with Gaussian anharmonic phonons

The nature of phase transition from an antiferromagnetic SDW polaronic Mott insulator to the paramagnetic bipolaronic CDW Peierls insulator is studied for the half-filled Holstein-Hubbard model in one dimension in the presence of Gaussian phonon anharmonicity. A number of unitary transformations performed in succession on the Hamiltonian followed by a general many-phonon averaging leads to an effective electronic Hamiltonian which is then treated exactly by using the Bethe-Ansatz technique of Lieb and Wu to determine the energy of the ground state of the system. Next using the Mott–Hubbard metallicity condition, local spin-moment calculation, and the concept of quantum entanglement entropy and double occupancy, it is shown that in a plane spanned by the electron–phonon coupling coefficient and onsite Coulomb correlation energy, there exists a window in which the SDW and CDW phases are separated by an intermediate phase that is metallic.

Disorder-induced phase transitions in a spinful one-dimensional system

We analyse a modified set of renormalisation group equations for disordered spinful fermions described by the Luttinger liquid model. The modification is necessary to take special care of the factitious admixture of the disorder to the interaction coupling constants undergoing renormalisation. Only properly separated amplitudes of elastic and inelastic processes allow the identification of true phases and the construction of the phase diagram (a similar procedure has been earlier implemented for the spinless case). In the spinful case, these modified equations enable us to demonstrate that in some region of the bare parameters values the phase diagram contains two massive phases, charge (CDW) and spin (SDW) density waves, which are separated by an insulating phase. These gapped phases are achieved at finite critical temperatures that vanish at the phase boundaries indicating the presence of a disorder-induced quantum phase transition. The critical temperatures as a function of disorder are reasonably well fit by a stretch exponential with the universal stretching critical exponent ν=1/3. A quantum phase transition between CDW and SDW phases driven by disorder strength has not been predicted before and this observation must be taken into account when analysing recent multiple experiments on phase transitions in quasi-one-dimensional structures.

Efficient and flexible approach to simulate low-dimensional quantum lattice models with large local Hilbert spaces

Quantum lattice models with large local Hilbert spaces emerge across various fields in quantum many-body physics. Problems such as the interplay between fermions and phonons, the BCS-BEC crossover of interacting bosons, or decoherence in quantum simulators have been extensively studied both theoretically and experimentally. In recent years, tensor network methods have become one of the most successful tools to treat such lattice systems numerically. Nevertheless, systems with large local Hilbert spaces remain challenging. Here, we introduce a mapping that allows to construct artificial U(1)U(1) symmetries for any type of lattice model. Exploiting the generated symmetries, numerical expenses that are related to the local degrees of freedom decrease significantly. This allows for an efficient treatment of systems with large local dimensions. Further exploring this mapping, we reveal an intimate connection between the Schmidt values of the corresponding matrixproductstate representation and the singlesite reduced density matrix. Our findings motivate an intuitive physical picture of the truncations occurring in typical algorithms and we give bounds on the numerical complexity in comparison to standard methods that do not exploit such artificial symmetries. We demonstrate this new mapping, provide an implementation recipe for an existing code, and perform example calculations for the Holstein model at half filling. We studied systems with a very large number of lattice sites up to L=501L=501 while accounting for N_{\rm ph}=63 phonons per site with high precision in the CDW phase.

Quantum Monte Carlo study of the hardcore bosons with finite-range interactions in one-dimensional optical lattices

Using Quantum Monte Carlo algorithm, we study the quantum behaviors of the hardcore bosons with finite-range interactions in one-dimensional optical lattices, such finite-range interactions were realized in Rydberg-dressed alkali atoms loaded into optical lattices. With the choice of the hardcore boson density ρ=0.75 and finite-interaction range rc=4, the ground-state of the system is expected to be degenerate due to the cluster formation. With the increase of interaction strength V/t, we find the system switches from the superfluid phase to supersolid phase and finally to CDW phase. The finite temperature effect and the finite size effect are also carefully examined.

Phase‐Dependent Band Gap Engineering in Alloys of Metal‐Semiconductor Transition Metal Dichalcogenides

AbstractBandgap engineering plays a critical role in optimizing the electrical, optical and (photo)‐electrochemical applications of semiconductors. Alloying has been a historically successful way of tuning bandgaps by making solid solutions of two isovalent semiconductors. In this work, a novel form of bandgap engineering involving alloying non‐isovalent cations in a 2D transition metal dichalcogenide (TMDC) is presented. By alloying semiconducting MoSe2 with metallic NbSe2, two structural phases of Mo0.5Nb0.5Se2, the 1T and 2H phases, are produced each with emergent electronic structure. At room temperature, it is observed that the 1T and 2H phases are semiconducting and metallic, respectively. For the 1T structure, scanning tunneling microscopy/spectroscopy (STM/STS) is used to measure band gaps in the range of 0.42–0.58 at 77 K. Electron diffraction patterns of the 1T structure obtained at room temperature show the presence of a nearly commensurate charge density wave (NCCDW) phase with periodic lattice distortions that result in an uncommon 4 × 4 supercell, rotated approximately 4° from the lattice. Density‐functional‐theory calculations confirm that local distortions, such as those in a NCCDW, can open up a band gap in 1T‐Mo0.5Nb0.5Se2, but not in the 2H phase. This work expands the boundaries of alloy‐based bandgap engineering by introducing a novel technique that facilitates CDW phases through alloying.

First-principles study of the low-temperature charge density wave phase in the quasi-one-dimensional Weyl chiral compound (TaSe4)2I

Using {\it ab initio} density functional theory, we study the lattice phase transition of quasi-one-dimensional (TaSe$_4$)$_2$I. In the undistorted state, the strongly anisotropic semimetal band structure presents two non-equivalent Weyl points. In previous efforts, two possible Ta-tetramerization patterns were proposed to be associated with the low-temperature structure. Our phonon calculations indicate that the orthorhombic $F222$ CDW-I phase is the most likely ground state for this quasi-one-dimensional system. In addition, the monoclinic $C2$ CDW-II phase may also be stable according to the phonon dispersion spectrum. Since these two phases have very similar energies in our DFT calculations, both these Ta-tetramerization distortions likely compete or coexist at low temperatures. The semimetal to insulator transition is induced by a Fermi-surface-driven instability that supports the Peierls scenario, which affects the Weyl physics developed above $T_{\rm CDW}$. Furthermore, the spin-orbit coupling generates Rashba-like band splittings in the insulating CDW phases.

The evidence of stacking disorder from dielectric response along the c-axis in the commensurate CDW phase in bulk 1T-TaS2

The temperature dependent polarization properties along the c-axis of 1T-TaS2 single crystals are investigated. The dielectric constant in MHz region enhances with cooling from 150 K down to 12 K, whereas the spectra disperse only slightly. The dielectric loss spectra at various temperatures indicate a hopping process of localized carriers induced by the out-of-plane stacking disorder. We propose that the enhancement of the polarization with decreasing temperature can be explained by an electrostatic-shielding effect associated with carriers localized in small metallic domains.

Temperature effect on dynamic properties of the 1D CDW system in the presence of the uncondensed-carriers: A numerical study

We report results regarding the temperature effect on dynamic properties of a 1D CDW system in the presence of normal carriers. It was showed that, for a given normal carriers concentration, the CDW phase profile fluctuations are attenuated by thermal fluctuations for the reason that the free-carrier relaxation process leads to a screening of the applied electrical field to depin the CDW. Further, the behavior of both the threshold field and nonlinear excess conductivity with respect to temperature were found to be non-monotonous. These findings are explained by the damping process and by generating CDW dislocation.