Incommensurate Charge Density Wave Research Articles

Dimensional Crossover in a Charge Density Wave Material Probed by Angle-Resolved Photoemission Spectroscopy.

High-resolution angle-resolved photoemission spectroscopy data reveal evidence of a crossover from one-dimensional (1D) to three-dimensional (3D) behavior in the prototypical charge density wave (CDW) material NbSe_{3}. In the low-temperature 3D regime, gaps in the electronic structure are observed due to two incommensurate CDWs, in agreement with x-ray diffraction and electronic-structure calculations. At higher temperatures we observe a spectral weight depletion that approaches the power-law behavior expected in one dimension. From the warping of the quasi-1D Fermi surface at low temperatures, we extract the energy scale of the dimensional crossover. This is corroborated by a detailed analysis of the density of states, which reveals a change in dimensional behavior dependent on binding energy. Our results offer an important insight into the dimensionality of excitations in quasi-1D materials.

Metallic Twin Grain Boundaries Embedded in MoSe2 Monolayers Grown by Molecular Beam Epitaxy.

Twin grain boundaries in MoSe2 are metallic and undergo a metal to insulator Peierls transition at low temperature. Growth of MoSe2 by molecular beam epitaxy results in the spontaneous formation of a high density of these twin grain boundaries, likely as a mechanism to incorporate Se deficiency in the film. Using scanning tunneling microscopy, we study the grain boundary network that is formed in homoepitaxially grown MoSe2 and for MoSe2 grown heteroepitaxially on MoS2 and HOPG substrates. No statistically relevant variation of the grain boundary concentration has been found for the different substrates, indicating that the grain boundary formation is substrate independent and depends mainly on the growth conditions. Twin grain boundaries exhibit three crystallographically identical orientations, and thus they form an intersecting network. Different intersection geometries are identified that imply varying defect configurations. These intersection points act as preferential nucleation sites for vapor-deposited metal atoms, which we demonstrate on the example of selective gold cluster formation at grain boundary intersections. Scanning tunneling spectroscopy shows a band gap narrowing of MoSe2 in the immediate vicinity of the metallic grain boundary, which may be associated with lattice strain induced at the grain boundary. Tunneling noise spectra taken over the grain boundaries indicate random telegraphic noise, suggestive of pinning/depinning behavior of conductive channels in the metallic grain boundaries or their intersection points. Finally, indications for incommensurate and commensurate Peierls-driven charge density wave formation were observed in microprobe transport measurements at 205 and 227 K, respectively.

Influence of Domain Walls in the Incommensurate Charge Density Wave State of Cu Intercalated 1T-TiSe_{2}.

We report a low-temperature scanning tunneling microscopy study of the charge density wave (CDW) order in 1T-TiSe_{2} and Cu_{0.08}TiSe_{2}. In pristine 1T-TiSe_{2} we observe a long-range coherent commensurate CDW (CCDW) order. In contrast, Cu_{0.08}TiSe_{2} displays an incommensurate CDW (ICDW) phase with localized CCDW domains separated by domain walls. Density of states measurements indicate that the domain walls host an extra population of fermions near the Fermi level which may play a role in the emergence of superconductivity in this system. Fourier transform scanning tunneling spectroscopy studies suggest that the dominant mechanism for CDW formation in the ICDW phase may be electron-phonon coupling.

Competing electronic instabilities of extended Hubbard models on the honeycomb lattice: A functional renormalization group calculation with high-wave-vector resolution

We investigate the quantum many-body instabilities for electrons on the honeycomb lattice at half-filling with extended interactions, motivated by a description of graphene and related materials. We employ a recently developed fermionic functional Renormalization Group scheme which allows for highly resolved calculations of wavevector dependences in the low-energy effective interactions. We encounter the expected anti-ferromagnetic spin density wave for a dominant on-site repulsion between electrons, and charge order with different modulations for dominant pure $n$-th nearest neighbor repulsive interactions. Novel instabilities towards incommensurate charge density waves take place when non-local density interactions among several bond distances are included simultaneously. Moreover, for more realistic Coulomb potentials in graphene including enough non-local terms there is a suppression of charge order due to competition effects between the different charge ordering tendencies, and if the on-site term fails to dominate, the semi-metallic state is rendered stable. The possibility of a topological Mott insulator being the favored tendency for dominating second nearest neighbor interactions is not realized in our results with high momentum resolution.

Laser-Induced Charge-Density-Wave Transient Depinning in Chromium.

We report on time-resolved x-ray diffraction measurements following femtosecond laser excitation in pure bulk chromium. Comparing the evolution of incommensurate charge-density-wave (CDW) and atomic lattice reflections, we show that, a few nanoseconds after laser excitation, the CDW undergoes different structural changes than the atomic lattice. We give evidence for a transient CDW shear strain that breaks the lattice point symmetry. This strain is characteristic of sliding CDWs, as observed in other incommensurate CDW systems, suggesting the laser-induced CDW sliding capability in 3D systems. This first evidence opens perspectives for unconventional laser-assisted transport of correlated charges.

A charge-density-wave oscillator based on an integrated tantalum disulfide-boron nitride-graphene device operating at room temperature.

The charge-density-wave (CDW) phase is a macroscopic quantum state consisting of a periodic modulation of the electronic charge density accompanied by a periodic distortion of the atomic lattice in quasi-1D or layered 2D metallic crystals. Several layered transition metal dichalcogenides, including 1T-TaSe2, 1T-TaS2 and 1T-TiSe2 exhibit unusually high transition temperatures to different CDW symmetry-reducing phases. These transitions can be affected by the environmental conditions, film thickness and applied electric bias. However, device applications of these intriguing systems at room temperature or their integration with other 2D materials have not been explored. Here, we demonstrate room-temperature current switching driven by a voltage-controlled phase transition between CDW states in films of 1T-TaS2 less than 10 nm thick. We exploit the transition between the nearly commensurate and the incommensurate CDW phases, which has a transition temperature of 350 K and gives an abrupt change in current accompanied by hysteresis. An integrated graphene transistor provides a voltage-tunable, matched, low-resistance load enabling precise voltage control of the circuit. The 1T-TaS2 film is capped with hexagonal boron nitride to provide protection from oxidation. The integration of these three disparate 2D materials in a way that exploits the unique properties of each yields a simple, miniaturized, voltage-controlled oscillator suitable for a variety of practical applications.

Long-range charge-density-wave proximity effect at cuprate/manganate interfaces.

The interplay between charge density waves (CDWs) and high-temperature superconductivity is currently under intense investigation. Experimental research on this issue is difficult because CDW formation in bulk copper oxides is strongly influenced by random disorder, and a long-range-ordered CDW state in high magnetic fields is difficult to access with spectroscopic and diffraction probes. Here we use resonant X-ray scattering in zero magnetic field to show that interfaces with the metallic ferromagnet La2/3Ca1/3MnO3 greatly enhance CDW formation in the optimally doped high-temperature superconductor YBa2Cu3O6+δ (δ ∼ 1), and that this effect persists over several tens of nanometres. The wavevector of the incommensurate CDW serves as an internal calibration standard of the charge carrier concentration, which allows us to rule out any significant influence of oxygen non-stoichiometry, and to attribute the observed phenomenon to a genuine electronic proximity effect. Long-range proximity effects induced by heterointerfaces thus offer a powerful method to stabilize the charge-density-wave state in the cuprates and, more generally, to manipulate the interplay between different collective phenomena in metal oxides.

Direct imaging of incommensurate wave pockets in the charge-density-wave state of LaTe2

We herein report the study of the atomic structure for a fully incommensurate CDW in LaTe2 using Cs-corrected scanning transmission electron microscopy (STEM). It is directly revealed for the first time that the atomic displacements adopt an incommensurate wave-pocket structure along each Te chain. This pocket structure has a long periodicity determined by the CDW incommensurability. We can use the sinusoidal waves as the first-order approximation to characterize the atomic motions within the pocket pattern, which can yield atomic displacements in good agreement with the theoretical model commonly used for studying CDW. These facts demonstrate that the incommensurate pocket patterns should be an essential structural nature in the CDW states and play a critical role for developing the mechanism of the CDW transitions.

Strong enhancement of superconductivity at high pressures within the charge-density-wave states of2H−TaS2and2H−TaSe2

We present measurements of the superconducting and charge density wave critical temperatures (Tc and TCDW) as a function of pressure in the transition metal dichalchogenides 2H-TaSe2 and 2H-TaS2. Resistance and susceptibility measurements show that Tc increases from temperatures below 1 K up to 8.5 K at 9.5 GPa in 2H-TaS2 and 8.2 K at 23 GPa in 2H-TaSe2. We observe a kink in the pressure dependence of TCDW at about 4 GPa that we attribute to the lock-in transition from incommensurate CDW to commensurate CDW. Above this pressure, the commensurate TCDW slowly decreases coexisting with superconductivity within our full pressure range.

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

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

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

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

Interplay between multiple charge-density waves and the relationship with superconductivity inPdxHoTe3

HoTe$_{3}$, a member of the rare-earth tritelluride ($R$Te$_{3}$) family, and its Pd-intercalated compounds, Pd$_x$HoTe$_{3}$, where superconductivity (SC) sets in as the charge-density wave (CDW) transition is suppressed by the intercalation of a small amount of Pd, are investigated using angle-resolved photoemission spectroscopy (ARPES) and electrical resistivity. Two incommensurate CDWs with perpendicular nesting vectors are observed in HoTe$_{3}$ at low temperatures. With a slight Pd intercalation ($x$ = 0.01), the large CDW gap decreases and the small one increases. The momentum dependence of the gaps along the inner Fermi surface (FS) evolves from orthorhombicity to near tetragonality, manifesting the competition between two CDW orders. At $x$ = 0.02, both CDW gaps decreases with the emergence of SC. Further increasing the content of Pd for $x$ = 0.04 will completely suppress the CDW instabilities and give rise to the maximal SC order. The evolution of the electronic structures and electron-phonon couplings (EPCs) of the multiple CDWs upon Pd intercalation are carefully scrutinized. We discuss the interplay between multiple CDW orders, and the competition between CDW and SC in detail.

Commensurate and incommensurate spin-density waves in heavy electron systems

The nesting of the Fermi surfaces of an electron and a hole pocket separated by a nesting vector Q and the interaction between electrons gives rise to itinerant antiferromagnetism. The order can gradually be suppressed by mismatching the nesting and a quantum critical point (QCP) is obtained as the Néel temperature tends to zero. The transfer of pairs of electrons between the pockets can lead to a superconducting dome above the QCP (if Q is commensurate with the lattice, i.e. equal to G/2). If the vector Q is not commensurate with the lattice there are eight possible phases: commensurate and incommensurate spin and charge density waves and four superconductivity phases, two of them with modulated order parameter of the FFLO type. The renormalization group equations are studied and numerically integrated. A re-entrant SDW phase (either commensurate or incommensurate) is obtained as a function of the mismatch of the Fermi surfaces and the magnitude of |Q − G/2|.

Controlling many-body states by the electric-field effect in a two-dimensional material

To understand the complex physics of a system with strong electron-electron interactions, the ideal is to control and monitor its properties while tuning an external electric field applied to the system (the electric-field effect). Indeed, complete electric-field control of many-body states in strongly correlated electron systems is fundamental to the next generation of condensed matter research and devices. However, the material must be thin enough to avoid shielding of the electric field in the bulk material. Two-dimensional materials do not experience electrical screening, and their charge-carrier density can be controlled by gating. Octahedral titanium diselenide (1T-TiSe2) is a prototypical two-dimensional material that reveals a charge-density wave (CDW) and superconductivity in its phase diagram, presenting several similarities with other layered systems such as copper oxides, iron pnictides, and crystals of rare-earth elements and actinide atoms. By studying 1T-TiSe2 single crystals with thicknesses of 10 nanometres or less, encapsulated in two-dimensional layers of hexagonal boron nitride, we achieve unprecedented control over the CDW transition temperature (tuned from 170 kelvin to 40 kelvin), and over the superconductivity transition temperature (tuned from a quantum critical point at 0 kelvin up to 3 kelvin). Electrically driving TiSe2 over different ordered electronic phases allows us to study the details of the phase transitions between many-body states. Observations of periodic oscillations of magnetoresistance induced by the Little-Parks effect show that the appearance of superconductivity is directly correlated with the spatial texturing of the amplitude and phase of the superconductivity order parameter, corresponding to a two-dimensional matrix of superconductivity. We infer that this superconductivity matrix is supported by a matrix of incommensurate CDW states embedded in the commensurate CDW states. Our results show that spatially modulated electronic states are fundamental to the appearance of two-dimensional superconductivity.

Incommensurate charge density wave modulated by period of Hubbard superlattices

The charge structure factor of the half-filled Hubbard superlattices with one on-site repulsive site and [Formula: see text] free sites per unit cell is investigated numerically. The behaviors of charge structure reveal a kind of even–odd [Formula: see text] disparity. For even [Formula: see text], we always observe a commensurate charge density wave (CDW). For odd [Formula: see text], we observe a commensurate–incommensurate CDW transition at a critical on-site repulsion around the particle–hole symmetric point. This transition results from the competition between the local charge correlations with odd distance and even distance.

Fluctuating orders and quenched randomness in the cuprates

We study a quasi-2D classical Landau-Ginzburg-Wilson effective field theory in the presence of quenched disorder in which incommensurate charge-density wave and superconducting orders are intertwined. The disorder precludes long-range charge-density wave order, but not superconducting or nematic order. We select three representative sets of input parameters and compute the corresponding charge-density wave structure factors using both large-$N$ techniques and classical Monte Carlo simulations. Where nematicity and superconductivity coexist at low temperature, the peak height of the charge-density wave structure factor decreases monotonically as a function of increasing temperature, unlike what is seen in X-ray experiments on YBa$_2$Cu$_3$O$_{6+x}$. Conversely, where the thermal evolution of the charge-density wave structure factor qualitatively agrees with experiments, the nematic correlation length, computed to one-loop order, is shorter than the charge-density wave correlation length.

Enhancement of superconductivity at the onset of charge-density-wave order in a metal

We analyze superconductivity in the cuprates near the onset of an incommensurate charge density wave (CDW) order with momentum ${\bf Q} = (Q,0)/(0,Q)$, as observed in the experiments. We first consider a semi-phenomenological charge-fermion model in which hot fermions, separated by ${\bf Q}$, attract each other by exchanging soft CDW fluctuations. We find that in a quantum-critical region near CDW transition, $T_c = A {\bar g}_c$, where ${\bar g}_c$ is charge-fermion coupling and $A$ is the prefactor which we explicitly compute. We then consider the particular microscopic scenario in which CDW order parameter emerges as a composite field made out of primary spin-density-wave fields. We show that charge-fermion coupling ${\bar g}_c$ is of order of spin-fermion coupling ${\bar g}_s$. As the consequence, superconducting $T_c$ is substantially enhanced near the onset of CDW order. Finally we analyze the effect of an external magnetic field $H$. We show that, as $H$ increases, optimal $T_c$ decreases and the superconducting dome becomes progressively more confined to the CDW quantum-critical point. These results are consistent with the experiments.

Commensurate and incommensurate spin-density waves and the superconductivity dome in heavy electron systems

The nesting of the Fermi surfaces of an electron and a hole pocket separated by a nesting vector $\mathbf{Q}$ and the interaction between electrons gives rise to itinerant antiferromagnetism. The order can gradually be suppressed by mismatching the nesting and a quantum critical point is obtained as the N\'eel temperature tends to zero. If the vector $\mathbf{Q}$ is commensurate with the lattice (umklapp with $\mathbf{Q}=\mathbf{G}/2$), pairs of electrons can be transferred between the pockets and a superconducting dome above the quantum critical point may arise. If the vector $\mathbf{Q}$ is not commensurate with the lattice, there are eight phases that need to be considered: commensurate and incommensurate spin and charge density waves and four superconductivity phases, two of them with a modulated order parameter of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) type. The renormalization group equations are studied and numerically integrated. The phase diagram is obtained as a function of the mismatch of the Fermi surfaces and the magnitude of $|\mathbf{Q}\ensuremath{-}\mathbf{G}/2|$.

Influence of Ti doping on the incommensurate charge density wave in1T−TaS2

We report temperature-dependent transport and x-ray diffraction measurements of the influence of Ti hole doping on the charge density wave (CDW) in $1T\text{\ensuremath{-}}{\mathrm{Ta}}_{1\ensuremath{-}x}{\mathrm{Ti}}_{x}{\mathrm{S}}_{2}$. Confirming past studies, we find that even trace impurities eliminate the low-temperature commensurate (C) phase in this system. Surprisingly, the magnitude of the in-plane component of the CDW wave vector in the nearly commensurate (NC) phase does not change significantly with Ti concentration, as might be expected from a changing Fermi surface volume. Instead, the angle of the CDW in the basal plane rotates, from $11.9{}^{\ensuremath{\circ}}$ at $x=0$ to $16.4{}^{\ensuremath{\circ}}$ at $x=0.12$. Ti substitution also leads to an extended region of coexistence between incommensurate (IC) and NC phases, indicating heterogeneous nucleation near the transition. Finally, we explain a resistive anomaly originally observed by Di Salvo [F. J. Di Salvo et al., Phys. Rev. B 12, 2220 (1975)] as arising from pinning of the CDW on the crystal lattice. Our study highlights the importance of commensuration effects in the NC phase, particularly at $x\ensuremath{\sim}0.08$.

Nematic fluctuations and their wave vector in two-dimensional metals

We revisit the problem of electrons on a square lattice below half filling close to an Ising-nematic quantum critical point. For Fermi surfaces with sufficiently strong antinodal nesting, the static nematic susceptibility is maximal at the antinodal nesting wave vector within a simple RPA calculation. We present a detailed analysis of the nematic susceptibility within Eliashberg theory and show that the strong interaction between Fermions in the antinodal regions shifts the maximum of the nematic susceptibility to slightly larger wave vectors. The corresponding order is akin to the incommensurate charge-density wave with d-wave form factor found recently in some underdoped cuprate materials. At sufficiently high temperatures around $T/t \sim 0.1$ nematic fluctuations are strongest at zero wave vector.