Charge Density Wave Research Articles

Nonreciprocal nonlinear responses in moving charge density waves

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

Effects of frequency mixing on Shapiro-step formations in sliding charge-density-waves

A one-dimensional charge-density wave (CDW) is driven to slide by a dc electric field, carrying an electric current. In an additional ac field with frequency ωex, it is known that the sliding CDW can be synchronized to ωex, leading to the occurrence of Shapiro steps in the I–V characteristics. Motivated by a recent experiment where ac fields with two frequencies ωex and ωex′ are simultaneously applied, we theoretically investigate the effects of frequency mixing on the Shapiro-step formation. Based on the Fukuyama–Lee–Rice model, we show that in addition to the main steps induced by ωex, satellite steps characterized by ωex′ emerge. It is also found that with increasing the ac-field strength for ωex′, each step width first exhibits a damped oscillation as in the one-frequency case and then exhibits a non-monotonic behavior. The origin of these behaviors and the relevance to the associated experiment are also discussed.

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.

Intercalation-Induced Monolayer Behavior in Bulk NbSe2.

Superconductivity at the 2D limit is significant for advancing fundamental physics, leading to extensive research on monolayer two-dimensional materials. In particular, monolayer transition metal dichalcogenides such as NbSe2 exhibit Ising superconductivity due to broken in-plane inversion symmetry and strong spin-orbit coupling, which has garnered significant attention. In this letter, we adopted an organic cation intercalation technique to modulate the interlayer interaction of NbSe2 by expanding the interlayer distance, thereby making intercalated NbSe2 behave similarly to monolayer NbSe2. The interlayer distances of NbSe2 intercalated with THA+, CTA+, and TDA+ cations are almost double or triple that of pristine NbSe2. The superconducting transition temperature (Tc) of THA-NbSe2 is comparable to that of pristine NbSe2, while the charge density wave (CDW) transition temperature is higher. The Tc of intercalated NbSe2 decreases with a reduced hole concentration, and the enhanced CDW is ascribed to the dimensional reduction. Notably, the in-plane upper critical field of intercalated NbSe2 significantly exceeds the Pauli paramagnetic limit, which is similar to the Ising superconductivity observed in monolayer NbSe2. Our work demonstrates that the organic cations intercalated two-dimensional materials exhibit behavior similar to their monolayer counterparts, providing a convenient platform for exploring and modulating physical phenomena at the two-dimensional limit.

Quantum Phase Transition as a Promising Route to Enhance the Critical Current in Kagome Superconductor CsV3Sb5.

Developing strategies to systematically increase the critical current, the threshold current below which the superconductivity exists, is an important goal of materials science. Here, the concept of quantum phase transition is employed to enhance the critical current of a kagome superconductor CsV3Sb5, which exhibits a charge density wave (CDW) and superconductivity that are both affected by hydrostatic pressure. As the CDW phase is rapidly suppressed under pressure, a large enhancement in the self-field critical current (Ic, sf) is recorded. The observation of a peak-like enhancement of Ic, sf at the zero-temperature limit (Ic, sf(0)) centered at p* ≈ 20kbar, the same pressure where the CDW phase transition vanishes, further provides strong evidence of a zero-temperature quantum anomaly in this class of pressure-tuned superconductor. Such a peak in Ic, sf(0) resembles the findings in other well-established quantum-critical superconductors, hinting at the presence of enhanced quantum fluctuations associated with the CDW phase in CsV3Sb5.

Absence of electron-phonon coupling superconductivity in the bilayer phase of La3Ni2O7 under pressure

An experimental study found superconductivity in bilayer phase of La3Ni2O7, with the highest superconducting transition temperature (Tc) ∼ 80 K under pressure. Recently, some reports claimed that there exists a competitive monolayer-trilayer structural phase in La3Ni2O7 compounds. We perform the first-principles calculations and find that bilayer phase of La3Ni2O7 is energetically favorable under pressure. Although extensive studies have been done to investigate the electronic correlation and potential superconducting pairing mechanism in bilayer phase of La3Ni2O7, the phonon properties and electron-phonon coupling (EPC) in the high-pressure I4/mmm phase of La3Ni2O7 are not reported. Using the density functional theory (DFT) combined with Wannier interpolation technique, we study the phonon properties and EPC in bilayer phase of La3Ni2O7 under 29.5 GPa. Our findings reveal that EPC is insufficient to explain the observed superconducting Tc ∼ 80 K. And the calculated Fermi surface nesting may explain the experimentally observed charge density wave (CDW) transition in bilayer phase of La3Ni2O7. Our calculations substantiate that bilayer phase of La3Ni2O7 is an unconventional superconductor.

Artificial superconducting Kondo lattice in a van der Waals heterostructure

Engineering Kondo lattice with tailored functionality is desirable for elucidating the heavy fermion physics. We realize the construction of an artificial Kondo lattice/superconductor heterojunction by growing monolayer VSe2 on bulk 2H-NbSe2 with molecular beam epitaxy. Spectroscopic imaging scanning tunneling microscopy measurements show the emergence of a new charge density wave (CDW) phase with 3×\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{3}\ imes$$\\end{document}3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{3}$$\\end{document} periodicity on the monolayer VSe2. Unexpectedly, a pronounced Kondo resonance appears around the Fermi level, and distributes uniformly over the entire film, evidencing the formation of Kondo lattice. Density functional theory calculations suggest the existence of magnetic interstitial V atoms in VSe2/NbSe2, which play a key role in forming the CDW phase along with the Kondo lattice observed in VSe2. The Kondo origin is verified from both the magnetic field and temperature dependences of the resonance peak, yielding a Kondo temperature of ~ 44 K. Moreover, a superconducting proximity gap opens on monolayer VSe2, whose shape deviates from the function of one-band BCS superconductor, but is reproduced by model calculations with heavy electrons participating the pairing condensate. Our work lays the experimental foundation for studying interactions between the heavy fermion liquids and the superconducting condensate.

Temperature Induced, Reversible Switching of Ferro-Rotational Order Coupled to Superlattice Commensuralibity.

High-quality 1T-TaS2 crystals are investigated by angle-resolved photoelectron spectroscopy, Raman spectroscopy, and low-energy electron diffraction. The Ferro-Rotational Order (FRO) of the charge density wave switches configuration at the transition between the commensurate and the nearly commensurate phase. This process requires samples without built-in or externally induced strain. Moreover, temperature gradients generated by a focused laser beam can be employed in order to freeze the in-plane chirality. Based on such observations, we propose a protocol to obtain durable and nonvolatile state switching of the FRO configuration in bulk 1T-TaS2 crystals.

Quantum Geometry and Stabilization of Fractional Chern Insulators Far from the Ideal Limit.

In the presence of strong electronic interactions, a partially filled Chern band may stabilize a fractional Chern insulator (FCI) state, the zero-field analog of the fractional quantum Hall phase. While FCIs have long been hypothesized, feasible solid-state realizations only recently emerged, largely due to the rise of moiré materials. In these systems, the quantum geometry of the electronic bands plays a critical role in stabilizing the FCI in the presence of competing correlated phases. In the limit of "ideal" quantum geometry, where the quantum geometry is identical to that of Landau levels, this role is well understood. However, in more realistic scenarios only empiric numerical evidence exists, accentuating the need for a clear understanding of the mechanism by which the FCI deteriorates, moving further away from these ideal conditions. We introduce and analyze an anisotropic model of a |C|=1 Chern insulator, whereupon partial filling of its bands, an FCI phase is stabilized over a certain parameter regime. We incorporate strong electronic interaction analytically by employing a coupled-wires approach, studying the FCI stability and its relation to the quantum metric. We identify an unusual anti-FCI phase benefiting from nonideal geometry, generically subdominant to the FCI. However, its presence hinders the formation of FCI in favor of other competitive phases at fractional fillings, such as the charge density wave. Though quite peculiar, this anti-FCI phase may have already been observed in experiments at high magnetic fields. This establishes a direct link between quantum geometry and FCI stability in a tractable model far from any ideal band conditions, and illuminates a unique mechanism of FCI deterioration.

Effects of lattice instability on the thermoelectric behavior of kagome metal ScV6Sn6

Kagome metal ScV6Sn6 has been a subject of interest due to the emergence of a first-order structural phase transition with intriguing charge density wave behavior below the transition temperature Tc ∼ 92 K. To explore the thermoelectric properties and provide experimental insights into the nature of the phase transition, we have carried out a combined study by means of the electrical resistivity, Seebeck coefficient, and thermal conductivity measurements on single crystalline ScV6Sn6. Pronounced features near Tc have been characterized by all measured physical quantities. In particular, the Seebeck coefficient exhibits a marked reduction as lowering temperature across Tc, attributed to an imbalance of the contribution from different type of carriers induced by the structural phase transition. From the examination of the electronic and lattice thermal conductivities, we obtained a confirmation that the observed enhancement at Tc is essentially caused by the change of the lattice thermal conductivity, demonstrating the primary importance of lattice distortions for the heat transport of ScV6Sn6. In addition, the lattice thermal conductivity above Tc was found to increase monotonically with temperature. We associated the peculiar phenomenon with lattice fluctuations, highlighting the essence of structural instability in the kagome lattice ScV6Sn6. These results add to the knowledge about the thermal transport properties in kagome materials with a hexagonal HfFe6Ge6-type structure.

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.

Charge density waves and the effects of uniaxial strain on the electronic structure of 2H-NbSe2

Interplay of superconductivity and density wave orders has been at the forefront of research of correlated electronic phases for a long time. 2H-NbSe2 is considered to be a prototype system for studying this interplay, where the balance between the two orders was proven to be sensitive to band filling and pressure. However, the origin of charge density wave in this material is still unresolved. Here, by using angle-resolved photoemission spectroscopy, we revisit the charge density wave order and study the effects of uniaxial strain on the electronic structure of 2H-NbSe2. Our results indicate previously undetected signatures of charge density waves on the Fermi surface. The application of small amount of uniaxial strain induces substantial changes in the electronic structure and lowers its symmetry. This, and the altered lattice should affect both the charge density wave phase and superconductivity and should be observable in the macroscopic properties.

Impact of charge density waves on superconductivity and topological properties in kagome superconductors

Impact of charge density waves on superconductivity and topological properties in kagome superconductors

Cooling rate dependence of charge density wave phases in 1T-TaS2 studied by scanning tunneling microscopy and x-ray diffraction

The role of dynamics in the charge density wave (CDW) phases of 1T-TaS2, especially in accessing metastable phases, is still under scrutiny. We investigated cooling rate dependence on low-temperature CDW phases in this material by scanning tunneling microscopy and x-ray diffraction. In the majority of cases, we found the typical low temperature commensurate CDW and identified no other differences between samples that were fast cooled vs slow cooled from room temperature. In rare cases (1/18 STM experiments and 1/30 XRD experiments), we found a multi-domain structure in the low temperature CDW. The domain structure and metallic behavior revealed by STM and STS measurements of this phase are in excellent agreement with the previously reported metallic mosaic CDW phase.

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.

Phonon transport manipulation in TiSe2 via reversible charge density wave melting

Titanium diselenide (TiSe2) is a layered material that under a critical temperature of Tc ≈ 200 K features a periodic modulation of the electron density, known as charge density wave (CDW), which finds applications in quantum information and emerging electronic devices. Here, we present first-principles calculations showing the suppression of the CDW via photoexcitation and consequent stabilization of the undistorted high-temperature phase, in agreement with experimental observations. Interestingly, the unfolded CDW melting is accompanied by a sizable reduction in the thermal conductivity, κ, of up to 25% and a large entropy increase of ~10 J K−1 kg−1. The significant κ variation is almost entirely originated from photoinduced changes in the phonon–phonon scattering processes involving a high-symmetry soft phonon mode. Our results open new possibilities in the design of devices for thermal management and phonon-based logic, and suggest original applications in the of context solid-state cooling.

Unusual Geometric and Electronic Structures at Domain Boundaries in a Heterochiral Charge Density Wave Superlattice.

Domain boundaries (DBs) in charge density wave (CDW) systems not only are important for understanding the mechanism of how CDW interplays with other quantum phases but also have potential for future CDW-based nanodevices. However, current research on DBs in CDW materials has been mainly limited to those between homochiral CDW domains, whereas DBs between heterochiral CDW domains, especially in the atomic layers, remain largely unexplored. Here, we have studied the geometric and electronic states of heterochiral DBs in single-layer and bilayer 1T-NbSe2 using scanning tunneling microscopy/spectroscopy. We observe the existence of diverse CDW configurations in a single heterochiral CDW DB with atomic resolution and reveal the corresponding electronic states. In addition, interlayer stacking further enriches the electronic properties of the DB. Our results offer deep insights into the relationship between the detailed CDW nanostructures and electronic behaviors, which has significant implications for DB engineering in strongly correlated CDW systems and related nanodevices.

Theoretical Description of Pump-Probe Experiments in Charge-Density-Wave Materials out to Long Times

We describe coupled nonequilibrium electron-phonon systems semiclassically—Ehrenfest dynamics for the phonons and quantum mechanics for the electrons—using a classical Monte Carlo approach that determines the nonequilibrium response to a large pump field. The semiclassical approach is expected to be accurate, because the phonons are excited to average energies much higher than the phonon frequency, eliminating the need for a quantum description. The numerical efficiency of this method allows us to perform a self-consistent time evolution out to very long times (tens of picoseconds), enabling us to model pump-probe experiments of a charge-density-wave (CDW) material. Our system is a half-filled, one-dimensional (1D) Holstein chain that exhibits CDW ordering due to a Peierls transition. The chain is subjected to a time-dependent electromagnetic pump field that excites it out of equilibrium, and then a second probe pulse is applied after a time delay. By evolving the system to long times, we capture the complete process of lattice excitation and subsequent relaxation to a new equilibrium, due to an exchange of energy between the electrons and the lattice, leading to lattice relaxation at finite temperatures. We employ an indirect (impulsive) driving mechanism of the lattice by the pump pulse due to the direct driving of the electrons. We identify two driving regimes, where the pump can either cause small perturbations or completely invert the initial CDW order. Our work successfully describes the ringing of the amplitude mode in CDW systems that has long been seen in experiment but never successfully explained by microscopic theory. We also describe the fluence-dependent crossover that inverts the CDW order parameter and changes the phonon dynamics. Finally, we illustrate how this method can examine a number of different types of experiments including photoemission, x-ray diffraction, and two-dimensional (2D) spectroscopy. Published by the American Physical Society 2024

Experimental observation of metallic states with different dimensionality in a quasi-one-dimensional charge density wave compound

Experimental observation of metallic states with different dimensionality in a quasi-one-dimensional charge density wave compound

Nanoscale Operando Imaging of Electrically Driven Charge-Density Wave Phase Transitions.

Structural transformations in strongly correlated materials promise efficient and fast control of materials' properties via electrical or optical stimulation. The desired functionality of devices operating based on phase transitions, however, will also be influenced by nanoscale heterogeneity. Experimentally characterizing the relationship between microstructure and phase switching remains challenging, as nanometer resolution and high sensitivity to subtle structural modifications are required. Here, we demonstrate nanoimaging of a current-induced phase transformation in the charge-density wave (CDW) material 1T-TaS2. Combining electrical characterizations with tailored contrast enhancement, we correlate macroscopic resistance changes with the nanoscale nucleation and growth of CDW phase domains. In particular, we locally determine the transformation barrier in the presence of dislocations and strain, underlining their non-negligible impact on future functional devices. Thereby, our results demonstrate the merit of tailored contrast enhancement and beam shaping for advanced operando microscopy of quantum materials and devices.