Charge Density Wave State Research Articles

Unveiling van Hove singularity modulation and fluctuated charge order in kagome superconductor CsV3Sb5 via time-resolved ARPES

Kagome superconductor CsV3Sb5, which exhibits intertwined unconventional charge-density wave (CDW) and superconductivity, has garnered significant attention recently. Despite extensive static studies, the nature of these exotic electronic orders remains elusive. In this study, we investigate the nonequilibrium electronic structure of CsV3Sb5 via time- and angle-resolved photoemission spectroscopy (ARPES). Our results reveal that upon laser excitation, the van Hove singularities immediately shift towards the Fermi level and subsequently oscillate in sync with a 1.3-THz coherent phonon mode. By analyzing the coherent intensity oscillations in the energy-momentum (-k) map, we find that this coherent phonon is strongly coupled with electronic bands from both Sb and V orbitals. While typically observable only in the CDW state, remarkably, we find that the 1.3-THz coherent phonon mode can be persistently excited at temperatures above TCDW, suggesting the potential existence of fluctuated CDW in CsV3Sb5. These findings enhance our understanding of the unconventional CDW in CsV3Sb5 and provide insights into the ultrafast control of kagome superconductivity. Published by the American Physical Society 2024

Effect of sulfur doping on superconductivity and charge density wave order in Kagome metal CsV3(Sb1−xSx)5

Abstract Recently, the coexistence and competition of superconductivity (SC) and charge density wave (CDW) have emerged in Kagome superconductor AV3Sb5 (A = K, Rb, Cs) under pressure, which has aroused widespread interest. Here, chemical substitution is used to introduce chemical pressure to further investigate the coexistence and competition between CDW and SC states. By preparing CsV3(Sb1−x S x )5 series single crystals and studying their crystal structure, chemical valence states, SC, and electronic transport behavior, it is found that S doping causes significant chemical pressure that is similar to axial mechanical pressure, resulting in suppression on the CDW and enhancement on SC. The T c−x relationship exhibits a double dome SC, similar to the behavior observed in the CsV3Sb5 under mechanical pressure. In addition, a negative correlation between T CDW and the disorder degree (measured by residual resistivity) is observed. This correlation is consistent with the observed translational jump in the ρ(T) curve before and after the CDW transition, that is, the temperature coefficient of resistivity does not change before and after the CDW phase transition, but only the resistivity curve shifts to a certain value. This phenomenon reveals that disorder is an important factor affecting the CDW transition of the system. Further, S doping also induces hole band filling effect that results in a decrease in the DOS at E F and consequently counterbalances the T c enhancement effect from chemical pressure to a certain extent. The electronic phase diagram of the CsV3(Sb1−x S x )5 system is accordingly established, which demonstrates the correlation between the SC, CDW, disorder degree, and other electronic nature of the system.

Understanding the superconductivity and charge density wave interaction through quasi-static lattice fluctuations

In unconventional superconductors, coupled charge and lattice degrees of freedom can manifest in ordered phases of matter that are intertwined. In the cuprate family, fluctuating short-range charge correlations can coalesce into a longer-range charge density wave (CDW) order which is thought to intertwine with superconductivity, yet the nature of the interaction is still poorly understood. Here, by measuring subtle lattice fluctuations in underdoped YBa2Cu3O6+y on quasi-static timescales (thousands of seconds) through X-ray photon correlation spectroscopy, we report sensitivity to both superconductivity and CDW. The atomic lattice shows remarkably faster relaxational dynamics upon approaching the superconducting transition at Tc ≈ 65 K. By tracking the momentum dependence, we show that the intermediate scattering function almost monotonically scales with the relaxation distance of atoms away from their average positions above Tc and in the presence of the CDW state, while this peculiar trend is reversed for other temperatures. These observations are consistent with an incipient CDW stabilized by local strain. This work provides insights into the crucial role of relaxational atomic fluctuations for understanding the electronic physics cuprates, which are inherently disordered due to carrier doping.

Proposed hydrogen kagome metal with charge density wave state and enhanced superconductivity

The d-transition kagome metals provide a novel platform for exploring correlated superconducting state intertwined with charge ordering. However, the force of charge-density-wave (CDW) and superconductivity (SC) formation, and the mechanism underlying electron pairing remain elusive. Here, utilizing our newly developed methodology based on electride states as fingerprints, we propose a novel class of hydrogen-kagome superconductors AH3Li5 (A = C, Si, P) with ideal kagome band characteristics and elucidate the electron-phonon coupling (EPC) mechanism responsible for electron pairing. The representative compressed PH3Li5 and CH3Li5 demonstrates impressive superconducting transition temperatures (Tcs) of 120.09 K and 57.18 K, respectively. Importantly, the CDW competes with SC thus resulting in a pressure-driven dome-shaped SC in CH3Li5, where the CDW order was induced by both EPC and Fermi surface nesting. Our study presents a scientific method for identifying high-Tc hydrogen-kagome metals and provides new avenues to fundamentally understand the underlying mechanism of CDW and SC, thereby guiding future experimental investigations.

Interplay between the charge density wave phase and a pseudogap under antiferromagnetic correlations

In this study, we explore the impact of short-range antiferromagnetic correlations on the charge density wave (CDW) phase in strongly correlated electron systems exhibiting the pseudogap phenomenon. Our investigation employs an n-pole approximation to consider the repulsive Coulomb interaction (U) and antiferromagnetic correlations. Considering an one-band Hubbard model to account for the Coulomb interaction and a BCS-like model for the CDW order parameter, we observed that an increase in U enhances antiferromagnetic fluctuations, resulting in a flattened re-normalized band around the antinodal point (π,0). The pseudogap manifests itself in the band structure and density of states, prompting exploration of various U and occupation number values. Our findings indicate that antiferromagnetic correlations significantly influence the CDW state, as the Fermi surface is reconstructed within the ordered phase. Furthermore, we found a Lifshitz transition inside both the CDW phase and the normal state, with the latter preceding the onset of the pseudogap.

Two-Band Electronic Reconstruction Induced via Correlation and CDW Order Effects

The emergence of a charge density wave (CDW) in transition-metal dichalcogenides opens up a route to charge order, followed by superconductivity at low temperatures. A key question here concerns how many particle electron–electron interations govern the low-energy electronic structure in the normal and CDW states. Using dynamical mean-field theory, we explore the many-body properties of an extended, two-band Hubbard model applicable to 2H-TaSe2. We reveal the electronic structure reconstruction in the normal and CDW states driven by two-band dynamical correlations. Our results demonstrate a remarkable renormalization of the Ta-5d bands crossing the Fermi level, showing a continuous reduction in the CDW gap up to an incomplete gapping, followed by a CDW to a CDW–Mott phase transition pertinent to strongly correlated transition-metal dichalcogenides.

Incoherence-to-coherence crossover observed in charge-density-wave material 1T-TiSe2

Analogous to the condensation of Cooper pairs in superconductors, the Bose–Einstein condensation (BEC) of electron–hole pairs in semiconductors and semimetals leads to an emergence of an exotic ground state — the excitonic insulator state. In this paper, we study the electronic structure of 1T-TiSe2 utilizing angle-resolved photoemission spectroscopy and alkali-metal deposition. Alkali-metal adatoms are deposited in-situ on the sample surface, doping the system with electrons. The conduction bands of 1T-TiSe2 are thereby pushed down below the Fermi energy, which enables us to characterize its temperature dependence with precision. We found that the formation of the charge density wave (CDW) in 1T-TiSe2 at ~ 205 K is accompanied by a significant increase of the band gap, supporting the existence of excitonic pairing in the CDW state of 1T-TiSe2. More importantly, by analyzing the linewidth of the single-particle excitation spectrum, we unveiled an incoherence-to-coherence crossover at 165 K, which could be attributed to a possible exciton condensation that occurs beneath the CDW transition in 1T-TiSe2. Our results not only explain the exotic transport properties of 1T-TiSe2, but also highlight the possible existence of an excitonic condensate in this semiconducting material.

Gate-Controlled Potassium Intercalation and Superconductivity in Molybdenum Disulfide.

Intercalation of guest ions into a van der Waals (vdW) gap in layered materials is a powerful route to create novel material phases and functionalities. Ionic gating is a technique to control the motions and configuration of ions for both intercalation and surface electrostatic doping. The advance of ionic gating enables the in situ probe of dynamics of ion diffusion, carrier doping, and transport properties. Here we performed in situ resistivity and Raman experiments on the potassium ion (K+) intercalation of single-crystal MoS2 and constructed a temperature-carrier density phase diagram. The K+-intercalation induces a structural transition from the prismatically coordinated phase to the octahedrally coordinated phase, where anisotropic three-dimensional superconductivity and a possible charge density wave state were observed. The present ionic gating offers a comprehensive view of the intercalated phases and proves that the electrostatically induced superconductivity is distinct from that in the intercalated phase.

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.

Phonon collapse and anharmonic melting of the 3D charge-density wave in kagome metals

The charge-density wave (CDW) mechanism and resulting structure of the AV3Sb5 family of kagome metals has posed a puzzling challenge since their discovery four years ago. In fact, the lack of consensus on the origin and structure of the CDW hinders the understanding of the emerging phenomena. Here, by employing a non-perturbative treatment of anharmonicity from first-principles calculations, we reveal that the charge-density transition in CsV3Sb5 is driven by the large electron-phonon coupling of the material and that the melting of the CDW state is attributed to ionic entropy and lattice anharmonicity. The calculated transition temperature is in very good agreement with experiments, implying that soft mode physics are at the core of the charge-density wave transition. Contrary to the standard assumption associated with a pure kagome lattice, the CDW is essentially three-dimensional as it is triggered by an unstable phonon at the L point. The absence of involvement of phonons at the M point enables us to constrain the resulting symmetries to six possible space groups. The unusually large electron-phonon linewidth of the soft mode explains why inelastic scattering experiments did not observe any softened phonon. We foresee that large anharmonic effects are ubiquitous and could be fundamental to understand the observed phenomena also in other kagome families.

Charge order near the antiferromagnetic quantum critical point in the trilayer high Tc cuprate HgBa2Ca2Cu3O8+δ

We study the transport properties of underdoped trilayer cuprate HgBa2Ca2Cu3O8+δ with doping level p = 0.10–0.12 in magnetic field up to 88 T. We report for the first time in a cuprate superconductor a dramatic change of the quantum oscillation spectrum versus temperature, which is accompanied by a sign change of the Hall effect below T ≈10 K. Based on numerical simulations, we infer a Fermi surface reconstruction in the inner plane from an antiferromagnetic state (hole pockets) to a biaxial charge density wave state (electron pockets). We show that both orders compete and share the same hotspots of the Fermi surface, and we discuss our result in the context of spin-fermion models.

Shubnikov–de Haas effect in the Falicov–Kimball model: strong correlation meets quantum oscillation

Abstract We present a comprehensive investigation of quantum oscillations (QOs) in the strongly-correlated Falicov-Kimball model (FKM). The FKM is a particularly suitable platform for probing the non-Fermi liquid state devoid of quasiparticles, affording exact Monte Carlo simulation across all parameter spaces.
In the high-correlation regime, we report the presence of prominent QOs in magnetoresistance and electron density at low temperatures within the phase separation state. The frequency behavior of these oscillations uncovers a transition in the Fermi surface as electron density diminishes, switching from hole-like to electron-like. Both types of Fermi surfaces are found to conform to the Onsager relation, establishing a connection between QOs frequency and Fermi surface area.
Upon exploring the temperature dependence of QOs amplitude, we discern a strong alignment with the Lifshitz-Kosevich (LK) theory, provided the effective mass is suitably renormalized. Notwithstanding, the substantial enhancement of the overall effective mass results in a notable suppression of the QOs amplitude within the examined temperature scope, a finding inconsistent with Fermi liquid predictions. For the most part, the effective mass diminishes as the temperature increases, but an unusual increase is observed at the proximity of the second-order phase transition instigated by thermal effects.
As the transition ensues, the regular QOs disappear, replaced by irregular ones in the non-Fermi liquid state under a high magnetic field.
We also uncover significant QOs in the insulating charge density wave state under weak interactions ($0 < U < 1$), a phenomenon we elucidate through analytical calculations.
Our findings shed light on the critical role of quasiparticles in the manifestation of QOs, enabling further understanding of their function in this context.

Correlated insulators and charge density wave states in chirally twisted triple bilayer graphene

Motivated by recent experimental observations of displacement-field-tuned correlated insulators at integer and half-integer fillings in chirally twisted triple bilayer graphene (CTTBG) [Phys.Rev.Lett.132.246501], we study the single-particle and interacting physics of CTTBG. We find that there are two inequivalent stacking orders, i.e., AB-AB-BC and AB-AB-AB, and both exhibit flat bands with nontrivial topology. We then use the Hartree–Fock approximation to calculate the rich phase diagram of CTTBG at all integer and half-integer fillings in both stacking orders and under the vertical displacement field. Under a small displacement field, the groundstates are flavor polarized states for AB-AB-BC stacking order and intervalley coherent states for AB-AB-AB stacking order at all integer and half-integer fillings. A larger displacement field will turn them into layer-polarized states. At half-integer fillings, the groundstates also exhibit charge density wave (CDW) order. For AB-AB-AB stacking, the groundstates at half-integer fillings are always 2 × 1 stripe state among a range of displacement fields. For AB-AB-BC stacking, the groundstates at half-integer fillings are also 2 × 1 stripe states under a small displacement field and a larger displacement will possibly favor further translation-symmetry-breaking, depending on filling and the direction of the displacement field. We demonstrate that the CDW states observed in the experiment can originate from the strong Coulomb interaction of the flat band electrons.

Coexisting Charge Density Waves in Twisted Bilayer NbSe2.

Twisted bilayers of 2D materials have emerged as a tunable platform for studying broken symmetry phases. While most interest has been focused toward emergent states in systems whose constituent monolayers do not feature broken symmetry states, assembling monolayers that exhibit ordered states into twisted bilayers can also give rise to interesting phenomena. Here, we use first-principles density-functional theory calculations to study the atomic structure of twisted bilayer NbSe2 whose constituent monolayers feature a charge density wave. We find that different charge density wave states coexist in the ground state of the twisted bilayer: monolayer-like 3 × 3 triangular and hexagonal charge density waves are observed in low-energy stacking regions, while stripe charge density waves are found in the domain walls surrounding the low-energy stacking regions. These predictions, which can be tested by scanning tunneling microscopy experiments, highlight the potential to create complex charge density wave ground states in twisted bilayer systems.

Charge density wave state in extremely overdoped cuprates driven by phonons

Charge density wave state in extremely overdoped cuprates driven by phonons

Quantum embedding method with transformer neural network quantum states for strongly correlated materials

The neural-network quantum states (NNQS) method is rapidly emerging as a powerful tool in quantum mechanisms. While significant advancements have been achieved in simulating simple molecules using NNQS, the ab initio simulation of complex solid-state materials remains challenging. Here in this work, we have adopted the periodic density matrix embedding theory to extend the NNQS method to deal with complex solid-state systems. Our approach notably reduces the computational problem size while maintaining high accuracy. We have validated the accuracy and efficiency of our method against traditional methodologies and experimental data in extended systems, and have investigated the magnetic ordering and charge density wave state in transition metal compounds. The findings from our research indicate that the integration of quantum embedding with intuitive chemical fragmentation can significantly enhance the NNQS simulation of realistic materials.

Surface-sensitive electronic structure of kagome superconductor CsV3Sb5

Abstract We systematically study the electronic structure of a kagome superconductor CsV3Sb5 at different temperatures covering both its charge density wave state and normal state with angle-resolved photoemission spectroscopy. We observe that the V-shaped band around Γ ¯ shows three different behaviors, referred to as α/α′, β and γ, mainly at different temperatures. Detailed investigations confirm that these bands are all from the same bulk Sb-p z origin, but they are quite sensitive to the sample surface conditions mainly modulated by temperature. Thus, the intriguing temperature dependent electronic behavior of the band near Γ ¯ is affected by the sample surface condition, rather than intrinsic electronic behavior originating from the phase transition. Our result systematically reveals the confusing electronic structure behavior of the energy bands around Γ ¯ , facilitating further exploration of the novel properties in this material.

Unconventional charge density wave in a kagome lattice antiferromagnet FeGe

FeGe is a kagome material that exhibits both charge density wave (CDW) order and magnetic order. The CDW order is developed deep inside the A-type antiferromagnetic phase in FeGe, providing a unique platform to investigate the interplay between CDW and magnetism. However, the driving mechanism of the CDW phase remains controversial. In this work, we performed high-pressure electrical transport and x-ray diffraction measurements combined with density-functional theory calculations to investigate the evolution of the CDW of FeGe under pressure. In contrast to conventional CDW materials, the CDW transition temperature of FeGe increases with increasing pressure, indicating the unconventional mechanism of CDW in this material. More interestingly, another possible CDW with a 3×3×6 superlattice emerges above 20 GPa, which may be explained by the calculated metastable CDW states under high pressure. These observations exclude the possibility of Van Hove singularities nesting as a CDW driving force. Our results unveil versatile CDW states and broaden the study of intertwined electronic states in the magnetic kagome metal FeGe. Published by the American Physical Society 2024

Directly visualizing nematic superconductivity driven by the pair density wave in NbSe2

Pair density wave (PDW) is a distinct superconducting state characterized by a periodic modulation of its order parameter in real space. Its intricate interplay with the charge density wave (CDW) state is a continuing topic of interest in condensed matter physics. While PDW states have been discovered in cuprates and other unconventional superconductors, the understanding of diverse PDWs and their interactions with different types of CDWs remains limited. Here, utilizing scanning tunneling microscopy, we unveil the subtle correlations between PDW ground states and two distinct CDW phases — namely, anion-centered-CDW (AC-CDW) and hollow-centered-CDW (HC-CDW) — in 2H-NbSe2. In both CDW regions, we observe coexisting PDWs with a commensurate structure that aligns with the underlying CDW phase. The superconducting gap size, Δ(r), related to the pairing order parameter is in phase with the charge density in both CDW regions. Meanwhile, the coherence peak height, H(r), qualitatively reflecting the electron-pair density, exhibits a phase difference of approximately 2π/3 relative to the CDW. The three-fold rotational symmetry is preserved in the HC-CDW region but is spontaneously broken in the AC-CDW region due to the PDW state, leading to the emergence of nematic superconductivity.

Strong electron-phonon coupling and multigap superconductivity in 2H/1T Janus MoSLi monolayer.

Two-dimensional (2D) Janus transition metal dichalcogenides MXY manifest novel physical properties owing to the breaking of out-of-plane mirror symmetry. Recently, the 2H phase of MoSH has been demonstrated to possess intrinsic superconductivity, whereas the 1T phase exhibits a charge density waves state. In this paper, we have systematically studied the stability and electron-phonon interaction characteristics of MoSLi. Our results have shown that both the 2H and 1T phases of MoSLi are stable, as indicated by the phonon spectrum and the abinitio molecular dynamics. However, the 1T phase exhibits an electron-phonon coupling constant that is twice as large as that of the 2H phase. In contrast to MoSH, the 1T phase of MoSLi exhibits intrinsic superconductivity. By employing the abinitio anisotropic Migdal-Eliashberg formalism, we have revealed the two-gap superconducting nature of 1T-MoSLi, with a transition temperature (Tc) of 14.8K. The detailed analysis indicates that the superconductivity in 1T-MoSLi primarily originates from the interplay between the vibration of the phonon modes in the low-frequency region and the dz2 orbital. These findings provide a fresh perspective on superconductivity within Janus structures.