Charge Density Wave Phase Research Articles

Multiple Quantum States Induced in 1T‐TaSe2 by Controlling the Stacking Order of Charge Density Waves

AbstractVan der Waals (vdW) materials afford unprecedented opportunities for control of electronic properties by utilizing the stacking degree of freedom. An intriguing frontier, largely unexplored, is the stacking of charge density wave (CDW) phases that is a broken‐symmetry state with periodically modulated charge density and the atomic lattice. Employing density functional theory, it is uncovered that the stacking order can play a significant role in the quantum phase transitions of layered 1T‐TaSe2 with a striking 2D CDW order. By controlling the vertical stacking order of CDWs, bulk 1T‐TaSe2 can host various electronic phases including quasi‐1D and 3D metals and band insulators. Particularly, the ground‐state stacking configuration shows 3D metallicity due to the enhanced intralayer and interlayer electron hopping, and the second lowest energy configuration shows band insulating behavior via interlayer dimerization, implying potential metal‐insulator transition. In ultrathin‐layer 1T‐TaSe2, not only the stacking order but also the thickness dictate the electronic properties. While the monolayer is a Mott insulator, the bilayer (trilayer) is a band insulator (metal). More interestingly, the four‐layer emerges as an insulator or a semimetal dependent on its stacking order. The wide‐tunable electronic properties of 1T‐TaSe2 CDW compound will open a new pathway for designing novel quantum devices.

Exploring interacting topological insulator in the extended Su-Schrieffer-Heeger model

Exploring topological phases in interacting systems is a challenging task. We investigate many-body topological physics of interacting fermions in an extended Su-Schrieffer-Heeger (SSH) model, which extends the two sublattices of SSH model into four sublattices and thus is dubbed SSH4 model, based on the density-matrix renormalization-group numerical method. The interaction-driven phase transition from topological insulator to charge density wave (CDW) phase can be identified by analyzing the variations of entanglement spectrum, entanglement entropies, energy gaps, CDW order parameter, and fidelity. We map the global phase diagram of the many-body ground state, which contains nontrivial topological insulator, trivial insulator and CDW phases, respectively. In contrast to interacting SSH model, in which the phase transitions to the CDW phase are argued to be first-order phase transitions, the phase transitions between the CDW phase and topologically trivial/nontrivial phases are shown to be continuous phase transitions. Finally, we {also} show the phase diagram of interacting spinful SSH4 model, where the attractive (repulsive) on-site spin interaction amplifies (suppresses) the CDW phase. The models analyzed here can be implemented with ultracold atoms on optical superlattices.

Bulk evidence of anisotropic s-wave pairing with no sign change in the kagome superconductor CsV3Sb5

The recently discovered kagome superconductors AV3Sb5 (A = K, Rb, Cs) exhibit unusual charge-density-wave (CDW) orders with time-reversal and rotational symmetry breaking. One of the most crucial unresolved issues is identifying the symmetry of the superconductivity that develops inside the CDW phase. Theory predicts a variety of unconventional superconducting symmetries with sign-changing and chiral order parameters. Experimentally, however, superconducting phase information in AV3Sb5 is still lacking. Here we report the impurity effects in CsV3Sb5 using electron irradiation as a phase-sensitive probe of superconductivity. Our magnetic penetration depth measurements reveal that with increasing impurities, an anisotropic fully-gapped state changes to an isotropic full-gap state without passing through a nodal state. Furthermore, transport measurements under pressure show that the double superconducting dome in the pressure-temperature phase diagram survives against sufficient impurities. These results support that CsV3Sb5 is a non-chiral, anisotropic s-wave superconductor with no sign change both at ambient and under pressure.

Interplay of charge ordering and superconductivity in two-dimensional 2H group V transition-metal dichalcogenides

Layered $2H\text{\ensuremath{-}}T{X}_{2}$ with $T=\mathrm{Nb}$, Ta and $X=\mathrm{S}$, Se exhibit rich dimensionality effects on charge density wave (CDW) order and superconductivity, but comprehensive understanding of these correlated quantum phases in the two-dimensional limit of $2H\text{\ensuremath{-}}T{X}_{2}$ is still lacking, hindering their practical applications. Here, I calculate from first principles the phonon linewidth and bare susceptibility to study the origin of CDW formation in ${\mathrm{NbSe}}_{2}$, ${\mathrm{TaS}}_{2}$, ${\mathrm{TaSe}}_{2}$, and ${\mathrm{NbS}}_{2}$ monolayers, analyze their relative CDW strength, and evaluate electron-phonon superconductivity within the fully anisotropic Migdal-Eliashberg theory. A peaked linewidth of the longitudinal acoustic branch and no Fermi-surface nesting around ${\mathbf{q}}_{\mathrm{CDW}}$ indicate CDW instability driven by the wave-vector-dependent electron-phonon coupling. The $3\ifmmode\times\else\texttimes\fi{}3$ CDW ground state favors a distinct hollow-centered clustering of transition-metal atoms, with larger distortion amplitude in ${\mathrm{NbSe}}_{2}$ and ${\mathrm{TaSe}}_{2}$ than in ${\mathrm{TaS}}_{2}$ and ${\mathrm{NbS}}_{2}$. Superconducting results of the monolayer CDW phase prove that strong spin-orbit coupling effects are dominant in determining the critical temperature ${T}_{\mathrm{c}}$ of each system via modifying both the strength and anisotropic extent of electron-phonon interactions. I also recapitulate measured opposite thickness dependencies of ${T}_{\mathrm{c}}$ in $\mathrm{Nb}{X}_{2}$ and $\mathrm{Ta}{X}_{2}$, and show that whether superconductivity is weakened or enhanced in monolayer limit relies on specific evolution of CDW-modulated Fermi-level density of states and electron-phonon matrix elements under reduced dimensionality. This work lays the foundation for applications of $2H$ group V transition-metal dichalcogenides in versatile nanoscale quantum devices.

Nodeless Superconductivity in Kagome Metal CsV3Sb5 with and without Time Reversal Symmetry Breaking.

The kagome metal CsV3Sb5 features an unusual competition between the charge-density-wave (CDW) order and superconductivity. Evidence for time reversal symmetry breaking (TRSB) inside the CDW phase has been accumulating. Hence, the superconductivity in CsV3Sb5 emerges from a TRSB normal state, potentially resulting in an exotic superconducting state. To reveal the pairing symmetry, we first investigate the effect of nonmagnetic impurity. Our results show that the superconducting critical temperature is insensitive to disorder, pointing to conventional s-wave superconductivity. Moreover, our measurements of the self-field critical current (Ic,sf), which is related to the London penetration depth, also confirm conventional s-wave superconductivity with strong coupling. Finally, we measure Ic,sf where the CDW order is removed by pressure and superconductivity emerges from the pristine normal state. Our results show that s-wave gap symmetry is retained, providing strong evidence for the presence of conventional s-wave superconductivity in CsV3Sb5 irrespective of the presence of the TRSB.

Emergent superconducting fluctuations in compressed kagome superconductor CsV3Sb5

The recent discovery of superconductivity (SC) and charge density wave (CDW) in kagome metals AV3Sb5 (A = K, Rb, Cs) provides an ideal playground for the study of emergent electronic orders. Application of moderate pressure leads to a two-dome-shaped SC phase regime in CsV3Sb5 accompanied by the destabilizing of CDW phase. Nonetheless, the nature of this pressure-tuned SC state and its interplay with the CDW are yet to be explored. Here, we perform soft point-contact spectroscopy (SPCS) measurements in CsV3Sb5 to investigate the evolution of superconducting order parameter with pressure. Surprisingly, we find that the superconducting gap is significantly enhanced between the two SC domes, at which the zero-resistance temperature is suppressed and the transition is remarkably broadened. Moreover, the temperature-dependence of the SC gap in this pressure range severely deviates from the conventional Bardeen-Cooper-Schrieffer (BCS) behavior, evidencing for strong Cooper pair phase fluctuations. These findings reveal the complex intertwining of the CDW with SC in the compressed CsV3Sb5, suggesting striking parallel to the cuprate superconductor La2−xBaxCuO4. Our results point to the essential role of charge degree of freedom in the development of intertwining electronic orders, and thus provide new constraints for theories.

Nanoscale Friction across the First-Order Charge Density Wave Phase Transition of 1T-TaS2.

Nanotribology using atomic force microscopy (AFM) can be considered as a unique approach to analyze phase transition materials by localized mechanical interaction. In this work, we investigate friction on the lamellar transition metal dichalcogenide 1T-TaS2, which can undergo first-order charge density wave (CDW) phase transitions. Based on temperature-dependent atomic force microscopy under ultrahigh vacuum conditions (UHV), we can characterize the general friction levels across the first-order phase transitions and for the different phases. While structural and electronic properties for different phases appear to be of minor influence on friction, a distinct peak in friction is observed during the phase transition when cooling the sample from the nearly commensurate CDW (NC-CDW) phase to the commensurate CDW (C-CDW) phase. By performing systematic measurements as a function of load, scan velocity, and scan time, a recently proposed friction mechanism can be corroborated, where the AFM tip gradually induces local transformations of the material close to the spinodal point in a thermally activated and shear-assisted process until the surface is fully "harvested". Our results demonstrate that repeated nanomechanical stress can trigger local first-order phase transitions constituting a so far little explored mechanical energy dissipation channel.

Thickness dependent charge density wave networks on thin 1T-TaS$$_2$$

We investigate mechanically exfoliated thin 1T-TaS $$_2$$ with scanning tunneling microscopy at room temperature. Sample preparation without air exposure enables access to intrinsic charge-density-wave (CDW) phases of thin 1T-TaS $$_2$$ . At room temperature, we can observe the expected nearly commensurate CDW (NCCDW) phase on thin flakes similar to bulk 1T-TaS $$_2$$ . Further analysis reveals that CDW domains in the NCCDW phase become smaller and have a more anisotropic shape with decreasing thickness in the range of 8–28 layers. Our findings demonstrate that the anisotropic CDW nature of thin 1T-TaS $$_2$$ would be crucial to understand its exotic CDW-related phenomena and demand a systematic study on its correlation between the thickness-driven CDW domain anisotropy and the intermediate CDW states in thin 1T-TaS $$_2$$ .

Evolution of static charge density wave order, amplitude mode dynamics, and suppression of Kohn anomalies at the hysteretic transition in EuTe4

Charge density wave (CDW) induces periodic spatial modulation of the charge density that is commensurate or incommensurate with the host lattice periodicity, and leads to partial or complete electronic band-gap opening at the Fermi level (${E}_{\mathrm{F}}$). The recent finding of unconventional hysteresis within the CDW phase of ${\mathrm{EuTe}}_{4}$, not observable in other rare-earth tellurides $R{\mathrm{Te}}_{n}$ ($n=2$, 3), has highlighted the role of the relative phase of CDW distortion in weakly coupled Te layers. However, detailed structural and dynamical characterization of CDW distortion on the hysteretic transition is lacking. Here we report on the static CDW order, dynamics of the amplitude mode, and their evolution on the hysteretic transition using meV resolution elastic and inelastic x-ray scattering. We discover previously unidentified multiple commensurate and incommensurate CDW wave vectors ${\mathbf{q}}_{\mathrm{CDW}}$ along all three crystallographic axes. Importantly, we find that the previously reported $b$-axis CDW peak is coupled with the interlayer CDW phase and consequently co-occurs with the doubling of the unit cell along the $c$ axis. We confirm the presence of the competing $a$-axis CDW order but found it to be four orders of magnitude weaker than the $b$-axis CDW. Furthermore, we observe multiple Kohn anomalies at ${\mathbf{q}}_{\mathrm{CDW}}$ driven by Fermi surface nesting and hidden nesting, confirming earlier reports based on electronic and lattice susceptibility simulations. The amplitude mode and Kohn anomalies are found to suppress on unconventional hysteretic transition, suggesting the presence of nondegenerate metastable states, which we identify from the x-ray scattering measurements and simulations.

Interplay of the charge density wave transition with topological and superconducting properties.

Exotic phenomena due to the interplay of different quantum orders have been observed and the study of these phenomena has emerged as a new frontier in condensed matter research, especially in the two-dimensional limit. Here, we report the coexistence of charge density waves (CDWs), superconductivity, and nontrivial topology in monolayer 1H-MSe2 (M = Nb, Ta) triggered by momentum-dependent electron-phonon coupling through electron doping. At a critical electron doping concentration, new 2 × 2 CDW phases emerge with nontrivial topology, Dirac cones, and van Hove singularities. Interestingly, these 2 × 2 CDW phases are also superconducting. Our findings not only reveal a route towards realizing nontrivial electronic characters by CDW engineering, but also provide an exciting platform to modulate different quantum states at the confluence of CDWs, superconductivity, nontrivial topology, and electron-phonon coupling.

Charge instability of topological Fermi arcs in chiral crystal CoSi

Topological boundary states emerged at the spatial boundary between topological non-trivial and trivial phases, are usually gapless, or commonly referred as metallic states. For example, the surface state of a topological insulator is a gapless Dirac state. These metallic topological boundary states are typically well described by non-interacting fermions. However, the behavior of topological boundary states with significant electron–electron interactions, which could turn the gapless boundary states into gapped ordered states, e.g., density wave states or superconducting states, is of great interest theoretically, but is still lacking evidence experimentally. Here, we report the observation of incommensurable charge density wave (CDW) formed on the topological boundary states driven by the electron–electron interactions on the (001) surface of CoSi. The wavevector of CDW varies as the temperature changes, which coincides with the evolution of topological surface Fermi arcs with temperature. The orientation of the CDW phase is determined by the chirality of the Fermi arcs, which indicates a direct association between CDW and Fermi arcs. Our finding will stimulate the search of more interactions-driven ordered states, such as superconductivity and magnetism, on the boundaries of topological materials.

Nonlocal Probing of Amplitude Mode Dynamics in Charge-Density-Wave Phase of EuTe 4

Amplitude mode is collective excitation emerging from frozen lattice distortions below the charge-density-wave (CDW) transition temperature T CDW and relates to the order parameter. Generally, the amplitude mode is non-polar (symmetry-even) and does not interact with incoming infrared photons. However, if the amplitude mode is polar (symmetry-odd), it can potentially couple with incoming photons, thus forming a coupled phonon–polariton quasiparticle that can travel with light-like speed beyond the optically excited region. Here, we present the amplitude mode dynamics far beyond the optically excited depth of ∼150 nm in the CDW phase of ∼10-μm-thick single-crystal EuTe 4 using time-resolved x-ray diffraction. The observed oscillations of the CDW peak, triggered by photoexcitation, occur at the amplitude mode frequency ω AM . However, the underdamped oscillations and their propagation beyond the optically excited depth are at odds with the observation of the overdamped nature of the amplitude mode measured using meV-resolution inelastic x-ray scattering and polarized Raman scattering. The ω AM is found to decrease with increasing fluence owing to a rise in the sample temperature, which is independently confirmed using polarized Raman scattering and ab-initio molecular dynamics simulations. We rationalize the above observations by explicitly calculating two coupled quasiparticles—phonon–polariton and exciton–polariton. Our data and simulations cannot conclusively confirm or rule out the one but point toward the likely origin from propagating phonon–polariton. The observed non-local behavior of amplitude mode thus provides an opportunity to engineer material properties at a substantially faster time scale with optical pulses.

Large kagome family candidates with topological superconductivity and charge density waves

A group of recently discovered nonmagnetic metal kagome structures ${A\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$ (A = K, Rb, Cs) has aroused widespread interest both experimentally and theoretically due to their unusual charge density wave (CDW) and intertwined superconductivity. However, they all possess weak electron-phonon coupling (EPC) and low superconducting transition temperature ${T}_{c}$. Here, we perform high-throughput first-principles calculations on such kagome candidates with ${A\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$ prototype structure, and propose 24 dynamically stable kagome metals. The calculation based on Bardeen-Cooper-Schrieffer theory shows that most of these metals are superconductors with much stronger EPC than the reported ${A\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$ materials, and their ${T}_{c}$ are between 0.3 and 5.0 K. Moreover, several compounds, such as ${\mathrm{KZr}}_{3}{\mathrm{Pb}}_{5}$ with the highest ${T}_{c}$, are identified as ${\mathbb{Z}}_{2}$ topological metals with clear Dirac cone topological surface states near the Fermi level. In addition, we take ${\mathrm{NaZr}}_{3}{\mathrm{As}}_{5}$ as an example to demonstrate the possible CDW phases. Our results provide rich platforms for exploring various physics with the kagome structure, in which the coexistence of superconductivity and the nontrivial topological nature provides promising insights for the discovery of topological superconductors.

Orbital-Hybridization-Driven Charge Density Wave Transition in CsV3 Sb5 Kagome Superconductor.

Owing to its inherent non-trivial geometry, the unique structural motif of the recently discovered kagome topological superconductor AV3 Sb5 (A = K, Rb, Cs) is an ideal host of diverse topologically non-trivial phenomena, including giant anomalous Hall conductivity, topological charge order, charge density wave (CDW), and unconventional superconductivity. Despite possessing a normal-state CDW order in the form of topological chiral charge order and diverse superconducting gaps structures, it remains unclear how fundamental atomic-level properties and many-body effects including Fermi surface nesting, electron-phonon coupling, and orbital hybridization contribute to these symmetry-breaking phenomena. Here, the direct participation of the V3d-Sb5p orbital hybridization in mediating the CDW phase transition in CsV3 Sb5 is reported. The combination of temperature-dependent X-ray absorption and first-principles studies clearly indicates the inverse Star-of-David structure as the preferred reconstruction in the low-temperature CDW phase. The results highlight the critical role that Sb orbitals play and establish orbital hybridization as the direct mediator of the CDW states and structural transition dynamics in kagome unconventional superconductors. This is a significant step toward the fundamental understanding and control of the emerging correlated phases from the kagome lattice through the orbital interactions and provides promising approaches to novel regimes in unconventional orders and topology.

Interplay of the Staggered and Three‐Body Interaction Potentials on the Quantum Phases of a Spin‐1 Ultracold Atom in an Optical Lattice

AbstractThe interplay of the staggered and the three‐body interaction potentials on the quantum phases of a spin‐1 Bose Hubbard model using a mean field approximation (MFA) is studied. In the antiferromagnetic (AF) case, a smaller value of the staggered potential (SP) results in the charge and the spin density wave ordering along with the Mott insulator (MI) and the staggered superfluid (SSF) phases. While the competition between two types of the potential leads to the stabilization of the higher order MI and charge density wave (CDW) phases with increasing three‐body interaction strength. Further, the spin eigenvalue and nematic order parameters are calculated to scrutinize the spin singlet‐nematic formation in the MI and the CDW phases and spin population fractions to analyze the nature of the SSF phase. A signature of the spin density wave (SDW) pattern is also observed in the gapped phase lobes. In case of a purely three‐body interaction, the third and higher order insulating lobes become dominant with increasing staggered potential strength. Subsequently, all MFA phase diagrams are then nicely corroborated with the analytical results obtained using a perturbative expansion corresponding to the AF and ferromagnetic cases.

Coexistence of trihexagonal and star-of-David pattern in the charge density wave of the kagome superconductor AV3Sb5

The recently discovered layered kagome metals AV$_3$Sb$_5$(A=K, Rb, Cs) have attracted much attention because of their unique combination of superconductivity, charge density wave (CDW) order, and nontrivial band topology. The CDW order with an in-plane 2x2 reconstruction is found to exhibit exotic properties, such as time-reversal symmetry breaking and rotational symmetry breaking. However, the nature of the CDW, including its dimensionality, structural pattern, and effect on electronic structure, remains elusive despite intense research efforts. Here, using angle-resolved photoemission spectroscopy, we unveil for the first time characteristic double-band splittings and band reconstructions, as well as the band gap resulting from band folding, in the CDW phase. Supported by density functional theory calculations, we unambiguously show that the CDW in AV$_3$Sb$_5$ originates from the intrinsic coexistence of Star-of-David and Tri-Hexagonal distortions. The alternating stacking of these two distortions naturally leads to three-dimensional 2x2x2 or 2x2x4 CDW order. Our results provide crucial insights into the nature and distortion pattern of the CDW order, thereby laying down the basis for a substantiated understanding of the exotic properties in the family of AV$_3$Sb$_5$ kagome metals.

Elastoresistivity in the incommensurate charge density wave phase of BaNi2(As1−xPx)2

AbstractElectronic nematicity, the breaking of the crystal lattice rotational symmetry by the electronic fluid, is a fascinating quantum state of matter. In this work, using electronic transport under strain we investigate the electronic nematicity of BaNi2(As1−xPx)2, a candidate system for charge-induced nematicity. We report a large B1g elastoresistance coefficient that is maximized at the tetragonal-to-orthorhombic transition temperature, that slightly precedes the first-order triclinic transition. An hysteretic behavior is observed in the resistance versus strain sweeps and interpreted as the pinning of orthorhombic domains. Remarkably, the elastoresistance only onsets together with a strong enhancement of the incommensurate charge density wave of the material, strongly suggesting that this electronic instability is uniaxial in nature and drive the orthorhombic transition. The absence of sizeable elastoresistance above this electronic phase clearly contrasts dynamic and static electronic nematicity. Finally, the elastoresistance temperature dependence that strongly differs from the Curie-Weiss form of iron-based superconductors reveals major differences for the respective coupling of electronic nematicity to the lattice. Our results uncover an extremely strain-sensitive platform to study electronic anisotropy induced by a charge-density-wave instability.

Electron correlations rule the phonon-driven instability in single-layer TiSe2

We investigate the controversial case of charge-density-wave (CDW) order in single layer 1T-TiSe$_2$ by employing the density functional perturbation theory with on-site Hubbard interactions. The results emphasize the crucial role of electron correlations via Hubbard corrections in order to capture the accurate electronic structure, low- and high-temperature limits of the CDW phonon mode, and temperature-charge phase diagram. We show, in close agreement with the experiments, that total phase diagram consists of both commensurate and incommensurate CDW regions, where the latter coincide with the superconductive phase and might be instrumental for its formation. In addition to the established roles of quantum lattice fluctuations and excitonic interactions, our analysis emphasizes the overlooked crucial role of the momentum dependent electron-phonon coupling and electron correlations for the CDW phase transition in single layer TiSe$_2$.

Axial-Bonding-Driven Dimensionality Effect on the Charge-Density Wave in NbSe2.

2H-NbSe2 is a prototypical charge-density-wave (CDW) system, exhibiting such a symmetry-breaking quantum ground state in its bulk and down to a single-atomic-layer limit. However, how this state depends on dimensionality and what governs the dimensionality effect remain controversial. Here, we experimentally demonstrate a robust 3 × 3 CDW phase in both freestanding and substrate-supported bilayer NbSe2, far above the bulk transition temperature. We exclude environmental effects and reveal a strong temperature and thickness dependence of Raman intensity from an axially vibrating A1g phonon mode, involving Se ions. Using first-principles calculations, we show that these result from a delicate but profound competition between the intra- and interlayer bonding formed between Se-pz orbitals. Our results suggest the crucial role of Se out-of-plane displacement in driving the CDW distortion, revealing the Se-dominated dimensionality effect and establishing a new perspective on the chemical bonding and mechanical stability in layered CDW materials.

Emergent charge order in pressurized kagome superconductor CsV3Sb5.

The discovery of several electronic orders in kagome superconductors AV3Sb5 (A means K, Rb, Cs) provides a promising platform for exploring unprecedented emergent physics1-9. Under moderate pressure (<2.2 GPa), the triple-Q charge density wave (CDW) order is monotonically suppressed by pressure, while the superconductivity shows a two-dome-like behaviour, suggesting an unusual interplay between superconductivity and CDW order10,11. Given that time-reversal symmetry breaking and electronic nematicity have been revealed inside the triple-Q CDW phase8,9,12,13, understanding this CDW order and its interplay with superconductivity becomes one of the core questions in AV3Sb5 (refs. 3,5,6). Here, we report the evolution of CDW and superconductivity with pressure in CsV3Sb5 by 51V nuclear magnetic resonance measurements. An emergent CDW phase, ascribed to a possible stripe-like CDW order with a unidirectional 4a0 modulation, is observed between Pc1 ≅ 0.58 GPa and Pc2 ≅ 2.0 GPa, which explains the two-dome-like superconducting behaviour under pressure. Furthermore, the nuclear spin-lattice relaxation measurement reveals evidence for pressure-independent charge fluctuations above the CDW transition temperature and unconventional superconducting pairing above Pc2. Our results not only shed new light on the interplay of superconductivity and CDW, but also reveal new electronic correlation effects in kagome superconductors AV3Sb5.