Charge Density Wave Order Research Articles

Rigorous Results on the Ground State of the Attractive SU(N) Hubbard Model.

We study the attractive SU(N) Hubbard model with particle-hole symmetry. The model is defined on a bipartite lattice with the number of sites N_{A} (N_{B}) in the A (B) sublattice. We prove three theorems that allow us to identify the basic ground-state properties: the degeneracy, the fermion number, and the SU(N) quantum number. We also show that the ground state exhibits charge density wave order when |N_{A}-N_{B}| is macroscopically large. The theorems hold for a bipartite lattice in any dimension, even without translation invariance.

Quasi-Two-Dimensional Heterostructures (KM1 – xTe)(LaTe3) (M = Mn and Zn) with Charge Density Waves

Layered heterostructure materials with two different functional building blocks can teach us about emergent physical properties and phenomena arising from interactions between the layers. We report the intergrowth compounds KLa$M$$_{1-x}$Te$_{4}$ ($M$ = Mn, Zn; $x\approx$ 0.35) featuring two chemically distinct alternating layers [LaTe$_3$] and [K$M$$_{1-x}$Te]. Their crystal structures are incommensurate, determined by single X-ray diffraction for the Mn compound and transmission electron microscope (TEM) study for the Zn compound. KLaMn$_{1-x}$Te$_{4}$ crystallizes in the orthorhombic superspace group $Pmnm$(01/2${\gamma}$)$s$00 with lattice parameters $a$ = 4.4815(3) {\AA}, $b$ = 21.6649(16) {\AA} and $c$ = 4.5220(3) {\AA}. It exhibits charge density wave (CDW) order at room temperature with a modulation wave vector $\mathbf{q}$ = 1/2$\mathbf{b}$* + 0.3478$\mathbf{c}$* originating from electronic instability of Te-square nets in [LaTe$_{3}$] layers. The Mn analog exhibits a cluster spin glass behavior with spin freezing temperature $T_{\mathrm{f}}$ $\approx$ 5 K attributed to disordered Mn vacancies and competing magnetic interactions in the [Mn$_{1-x}$Te] layers. The Zn analog also has charge density wave order at room temperature with a similar $\mathbf{q}$-vector having the $\mathbf{c}$* component ~ 0.346 confirmed by selected-area electron diffraction (SAED). Electron transfer from [K$M_{1-x}$Te] to [LaTe$_{3}$] layers exists in KLa$M_{1-x}$Te$_{4}$, leading to an enhanced electronic specific heat coefficient. The resistivities of KLa$M_{1-x}$Te$_{4}$ ($M$ = Mn, Zn) exhibit metallic behavior at high temperatures and an upturn at low temperatures, suggesting partial localization of carriers in the [LaTe$_{3}$] layers with some degree of disorder associated with the $M$ atom vacancies in the [$M_{1-x}$Te] layers.

Robust Superconductivity in (ZnxCu1–x)0.5IrTe2

Here, we report the effect of electron doping Zn for Cu on the physical properties of Cu0.5IrTe2. Slight Zn doping concentration (x) becomes detrimental to the charge density wave (CDW) order, whil...

Holographic striped superconductor

We construct a holographic model describing the striped superconductor (SSC), which is characterized by the presence of pair density waves (PDW). We explicitly demonstrate that the SSC phase is implemented as the intertwined phase of charge density waves (CDW) order and uniform superconducting (SC) order. The interplay of PDW order, CDW order as well as the uniform SC order in SSC phase is studied. It is found that the PDW order is prominent when both CDW order and uniform SC order are balanced. The critical temperature of CDW becomes higher in the presence of the uniform SC order, but its charge density amplitude is suppressed. On the other hand, the SC order is not sensitive to the presence of CDW order. We also demonstrate that among all the possible solutions, the black hole in SSC phase has the lowest free energy and thus is thermodynamically favored.

Doping Quantum Spin Liquids on the Kagome Lattice

AbstractThe authors review recent density‐matrix renormalization group studies of lightly doped quantum spin liquids (QSLs) on the kagome lattice. While a number of distinct conducting phases, including high temperature superconductivity, have been theoretically anticipated, a tendency toward fractionalized insulating charge‐density‐wave (CDW) states is instead found. In agreement with earlier work [Jiang, Devereaux, and Kivelson, Phys. Rev. Lett. 2017, 119, 067002], results for the t‐J model reveal that, starting from a fully gapped QSL, light doping leads to CDW long‐range order with a pattern that depends on lattice geometry and doping concentration such that there is one doped‐hole per CDW unit cell, while the spin–spin correlations remain short‐ranged. Alternatively, this state can be viewed as a stripe crystal or Wigner crystal of spinless holons, rather than of doped holes. From here, by studying generalized versions of the t‐J model, these results are extended to light doping of other types of QSLs, including critical and chiral QSLs. These results suggest that doping these QSLs also leads to insulating states with long‐range CDW order. While the superconducting correlations are short‐ranged, they can be significantly enhanced by second‐neighbor electron hopping. The relevance of these numerical results to Kagome materials is also discussed.

Charge density wave and weak Kondo effect in a Dirac semimetal CeSbTe

Using angle-resolved photoemission spectroscopy (ARPES) and low-energy electron diffraction (LEED), together with density-functional theory (DFT) calculation, we report the formation of charge density wave (CDW) and its interplay with the Kondo effect and topological states in CeSbTe. The observed Fermi surface (FS) exhibits parallel segments that can be well connected by the observed CDW ordering vector, indicating that the CDW order is driven by the electron-phonon coupling (EPC) as a result of the nested FS. The CDW gap is large (∼0.3 eV) and momentum-dependent, which naturally explains the robust CDW order up to high temperatures. The gap opening leads to a reduced density of states (DOS) near the Fermi level (EF), which correspondingly suppresses the many-body Kondo effect, leading to very localized 4f electrons at 20 K and above. The topological Dirac cone at the X point is found to remain gapless inside the CDW phase. Our results provide evidence for the competition between CDW and the Kondo effect in a Kondo lattice system. The robust CDW order in CeSbTe and related compounds provide an opportunity to search for the long-sought-after axionic insulator.

Metal-to-insulator transition in Pt-doped TiSe2 driven by emergent network of narrow transport channels

Metal-to-insulator transitions (MIT) can be driven by a number of different mechanisms, each resulting in a different type of insulator—Change in chemical potential can induce a transition from a metal to a band insulator; strong correlations can drive a metal into a Mott insulator with an energy gap; an Anderson transition, on the other hand, due to disorder leads to a localized insulator without a gap in the spectrum. Here, we report the discovery of an alternative route for MIT driven by the creation of a network of narrow channels. Transport data on Pt substituted for Ti in 1T-TiSe2 shows a dramatic increase of resistivity by five orders of magnitude for few % of Pt substitution, with a power-law dependence of the temperature-dependent resistivity ρ(T). Our scanning tunneling microscopy data show that Pt induces an irregular network of nanometer-thick domain walls (DWs) of charge density wave (CDW) order, which pull charge carriers out of the bulk and into the DWs. While the CDW domains are gapped, the charges confined to the narrow DWs interact strongly, with pseudogap-like suppression in the local density of states, even when they were weakly interacting in the bulk, and scatter at the DW network interconnects thereby generating the highly resistive state. Angle-resolved photoemission spectroscopy spectra exhibit pseudogap behavior corroborating the spatial coexistence of gapped domains and narrow domain walls with excess charge carriers.

Microscopic evidence for the intra-unit-cell electronic nematicity inside the pseudogap phase in YBa2Cu4O8

Understanding the nature of the mysterious pseudogap phenomenon is one of the most important issues associated with cuprate high-Tc superconductors. Here, we report 17O nuclear magnetic resonance (NMR) studies on two planar oxygen sites in stoichiometric cuprate YBa2Cu4O8 to investigate the symmetry breaking inside the pseudogap phase. We observe that the Knight shifts of the two oxygen sites are identical at high temperatures but different below Tnem ∼ 185 K, which is close to the pseudogap temperature T*. Our result provides a microscopic evidence for intra-unit-cell electronic nematicity. The difference in quadrupole resonance frequency between the two oxygen sites is unchanged below Tnem, which suggests that the observed nematicity does not directly stem from the local charge density modulation. Furthermore, a short-range charge density wave (CDW) order is observed below T ≃ 150 K. The additional broadening in the 17O-NMR spectra because of this CDW order is determined to be inequivalent for the two oxygen sites, which is similar to that observed in case of nematicity. These results suggest a possible connection between nematicity, CDW order, and pseudogap.

Two-Dimensional Metallic Vanadium Ditelluride as a High-Performance Electrode Material.

Two-dimensional (2D) metallic transition-metal dichalcogenides (MTMDCs) are considered as ideal electrode materials for enhancing the device performances of 2D semiconducting transition-metal dichalcogenides, due to their similar atomic structures and complementary electronic properties. Vanadium ditelluride (VTe2) behaves as a fascinating material in MTMDCs family, presenting room-temperature ferromagnetism, charge density waves order, and topological property. However, its practical applications in universal electrode/energy-related fields remain unexplored. Herein, we achieved the direct synthesis of ultrathin, large-domain, and thickness-tunable 1T-VTe2 nanosheets on an easily available mica substrate by chemical vapor deposition (CVD). We further uncover that the CVD-derived 1T-VTe2 can serve as a high-performance electrode material thanks to its ultrahigh conductivity. Accordingly, a 6 times higher field-effect mobility (∼47.5 cm2 V-1 s-1) was achieved in 1T-VTe2-contacted monolayer MoS2 devices than that using a conventional Ti/Au electrode (∼8.1 cm2 V-1 s-1). Moreover, the CVD-synthesized 1T-VTe2 nanosheets are revealed to present excellent electrocatalytic activity for hydrogen evolution reaction. These results should propel the direct application of CVD-grown 2D MTMDCs as high-performance electrode materials in all 2D materials related devices.

Anomalous Hall resistivity and possible topological Hall effect in the EuAl4 antiferromagnet

We report the observation of anomalous Hall resistivity in single crystals of EuAl$_4$, a centrosymmetric tetragonal compound, which exhibits coexisting antiferromagnetic (AFM) and charge-density-wave (CDW) orders with onset at $T_\mathrm{N} \sim 15.6$ K and $T_\mathrm{CDW} \sim 140$ K, respectively. In the AFM state, when the magnetic field is applied along the $c$-axis direction, EuAl$_4$ undergoes a series of metamagnetic transitions. Within this field range, we observe a clear hump-like anomaly in the Hall resistivity, representing part of the anomalous Hall resistivity. By considering different scenarios, we conclude that such a hump-like feature is most likely a manifestation of the topological Hall effect, normally occurring in noncentrosymmetric materials known to host nontrivial topological spin textures. In view of this, EuAl$_4$ would represent a rare case where the topological Hall effect not only arises in a centrosymmetric structure, but it also coexists with CDW order.

Correlation-assisted quantized charge pumping

We investigate charge pumping in the vicinity of order-obstructed topological phases, i.e. symmetry protected topological phases masked by spontaneous symmetry breaking in the presence of strong correlations. To explore this, we study a prototypical Su-Schrieffer-Heeger model with finite-range interaction that gives rise to orbital charge density wave order, and characterize the impact of this order on the model's topological properties. In the ordered phase, where the many-body topological invariant loses quantization, we find that not only is quantized charge pumping still possible, but it is even assisted by the collective nature of the orbital charge density wave order. Remarkably, we show that the Thouless pump scenario may be used to uncover the underlying topology of order-obstructed phases.

Experimental Evidence of a Stable 2H Phase on the Surface of Layered 1T′-TaTe2

We report on the low-energy electronic structure of tantalum ditelluride (1T′-TaTe2), one of the charge density wave (CDW) materials from the group V transition metal dichalcogenides using angle-resolved photoemission spectroscopy and density functional theory (DFT). We find that the Fermi surface topology of TaTe2 is quite complicated compared to its isovalent compounds such as TaS2, TaSe2, and isostructural compound NbTe2. Most importantly, we discover that the surface electronic structure of 1T′-TaTe2 has more resemblance to the 2H-TaTe2, while the bulk electronic structure has more resemblance to the hypothetical 1T-TaTe2. These experimental observations are thoroughly compared with our DFT calculations performed on 1T-, 2H-, and 2H (monolayer)/1T-TaTe2. We further notice that the Fermi surface topology is temperature independent up to 180 K, confirming that the 2H phase on the surface is stable up to 180 K and the CDW order is not due to the Fermi surface nesting.

Higher-Order Weyl Semimetals.

We investigate higher-order Weyl semimetals (HOWSMs) having bulk Weyl nodes attached to both surface and hinge Fermi arcs. We identify a new type of Weyl node, which we dub a 2nd-order Weyl node, that can be identified as a transition in momentum space in which both the Chern number and a higher order topological invariant change. As a proof of concept we use a model of stacked higher order quadrupole insulators (QI) to identify three types of WSM phases: 1st order, 2nd order, and hybrid order. The model can also realize type-II and hybrid-tilt WSMs with various surface and hinge arcs. After a comprehensive analysis of the topological properties of various HOWSMs, we turn to their physical implications that show the very distinct behavior of 2nd-order Weyl nodes when they are gapped out. We obtain three remarkable results: (i)the coupling of a 2nd-order Weyl phase with a conventional 1st-order one can lead to a hybrid-order topological insulator having coexisting surface cones and flat hinge arcs that are independent and not attached to each other. (ii)A nested 2nd-order inversion-symmetric WSM by a charge-density wave (CDW) order generates an insulating phase having coexisting flatband surface and hinge states all over the Brillouin zone. (iii)A CDW order in a time-reversal symmetric higher-order WSM gaps out a 2nd-order node with a 1st-order node and generates an insulating phase having coexisting surface Dirac cone and hinge arcs. Moreover, we show that a measurement of charge density in the presence of magnetic flux can help to identify some classes of 2nd-order WSMs. Finally, we show that periodic driving can be utilized as a way for generating HOWSMs. Our results are relevant to metamaterials as well as various phases of Cd_{3}As_{2}, KMgBi, and rutile-structure PtO_{2} that have been predicted to realize higher order Dirac semimetals.

Strongly coupled charge, orbital, and spin order in TbTe3

We report a ground state with strongly coupled magnetic and charge density wave orders mediated via orbital ordering in the layered compound \tbt. In addition to the commensurate antiferromagnetic (AFM) and charge density wave (CDW) orders, new magnetic peaks are observed whose propagation vector equals the sum of the AFM and CDW propagation vectors, revealing an intricate and highly entwined relationship. This is especially interesting given that the magnetic and charge orders lie in different layers of the crystal structure where the highly localized magnetic moments of the Tb$^{3+}$ ions are netted in the Tb-Te stacks, while the charge order is formed by the conduction electrons of the adjacent Te-Te layers. Our results, based on neutron diffraction and resonant x-ray scattering reveal that the charge and magnetic subsystems mutually influence each other via the orbital ordering of Tb$^{3+}$ ions.

Robust superconductivity intertwined with charge density wave and disorder in Pd-intercalated ErTe3

Pd-intercalated ErTe$_3$ is studied as a model system to explore the effect of "intertwined" superconducting and charge density wave (CDW) orders. Despite the common wisdom that superconductivity emerges only when CDW is suppressed, we present data from STM and AC susceptibility measurements that show no direct competition between CDW order and superconductivity. Both coexist over most of the intercalation range, with uniform superconductivity over length scales that exceed the superconducting coherence length. This is despite persisting short-range CDW order and increased scattering from the Pd intercalation. While superconductivity is insensitive to local defects in either of the bi-directional CDWs, vestiges of the Fermi-level distortions are observed in the properties of the superconducting state.

Orbital symmetries of charge density wave order in YBa2Cu3O6+x.

Charge density wave (CDW) order has been shown to compete and coexist with superconductivity in underdoped cuprates. Theoretical proposals for the CDW order include an unconventional d-symmetry form factor CDW, evidence for which has emerged from measurements, including resonant soft x-ray scattering (RSXS) in YBa2Cu3O6+x (YBCO). Here, we revisit RSXS measurements of the CDW symmetry in YBCO, using a variation in the measurement geometry to provide enhanced sensitivity to orbital symmetry. We show that the (0 0.31 L) CDW peak measured at the Cu L edge is dominated by an s form factor rather than a d form factor as was reported previously. In addition, by measuring both (0.31 0 L) and (0 0.31 L) peaks, we identify a pronounced difference in the orbital symmetry of the CDW order along the a and b axes, with the CDW along the a axis exhibiting orbital order in addition to charge order.

Lattice dynamics of the topological Dirac semimetal LaAgSb2 with charge density wave ordering

LaAgSb$_{2}$ is a rare material, which offers the opportunity to investigate the complex interplay between charge density wave (CDW) ordering and topology protected electronic band structure. As both of these phenomena are governed by the structural symmetries, a comprehensive study of the lattice dynamics is highly desirable. In this report, we present the results of temperature and pressure dependent Raman spectroscopy and x-ray diffraction in single crystalline LaAgSb$_{2}$. Our results confirm that Raman spectroscopy is a highly sensitive tool to probe CDW ordering phenomenon, particularly the low-temperature second CDW transition in LaAgSb$_{2}$, which appears as a very weak anomaly in most experiments. The crystal orientation-dependent measurements provide the evolution of Raman modes with crystallographic symmetries and can be further studied through group symmetry analysis. The low-temperature x-ray diffraction data show the emergence of structural modulations corresponding to the CDW instability. The combined high-pressure Raman spectroscopy and synchrotron x-ray diffraction reveal multiple structural phase transitions through lowering of crystalline symmetries, which are also expected to lead to electronic topological transitions.

Hierarchy among the crystal lattice, charge density wave, and superconducting orders in transition metal dichalcogenides

Using high-energy x-ray scattering and large-scale three-dimensional (3D) structure modeling, we investigate the relationship between the crystal lattice, charge density wave (CDW), and superconducting (SC) orders in transition metal dichalcogenides (TMDs). In particular, we systematically substitute Te for Se in Ta-Se-Te solid solutions, determine changes in their crystal lattice, and relate them to changes in the CDW transition temperature, ${T}_{\mathrm{CDW}}$, and SC critical temperature, ${T}_{\mathrm{c}}$. We find that strong lattice distortions such as buckling of Ta layers are detrimental to the CDW and SC orders. The presence of a perfect lattice order in two dimensions is a prerequisite to the emergence of CDWs but insufficient to achieve a SC ordered state. For the SC order to emerge, the Ta sublattice should also appear periodic in 3D. Local chemical disorder may promote the SC order, and the perfectness of Ta coordination polyhedra is a factor contributing to its strength. A hierarchical relationship among the crystal lattice, CDW, and SC orders thus appears to exist in TMDs in a sense that different degrees of crystal lattice order-disorder promote and maintain the CDW and SC orders to a different extent, offering an opportunity to control the latter through modifying the former by rational design. Our findings are a step towards a better understanding of the correlation between lattice and electronic degrees of freedom in TMDs. We also demonstrate an efficient experimental approach to study them in fine detail.

Coexistence of Superconductivity and Charge Density Waves in Tantalum Disulfide: Experiment and Theory

The coexistence of charge density wave (CDW) and superconductivity in tantalum disulfide (2H-TaS_{2}) at low temperature is boosted by applying hydrostatic pressures to study both vibrational and magnetic transport properties. Around P_{c}, we observe a superconducting dome with a maximum superconducting transition temperature T_{c}=9.1 K. First-principles calculations of the electronic structure predict that, under ambient conditions, the undistorted structure is characterized by a phonon instability at finite momentum close to the experimental CDW wave vector. Upon compression, this instability is found to disappear, indicating the suppression of CDW order. The calculations reveal an electronic topological transition (ETT), which occurs before the suppression of the phonon instability, suggesting that the ETT alone is not directly causing the structural change in the system. The temperature dependence of the first vortex penetration field has been experimentally obtained by two independent methods. While a d wave and single-gap BCS prediction cannot describe the lower critical field H_{c1} data, the temperature dependence of the H_{c1} can be well described by a single-gap anisotropic s-wave order parameter.

Charge density wave instability and pressure-induced superconductivity in bulk 1T−NbS2

Charge-density-wave (CDW) instability and pressure-induced superconductivity in bulk 1T-NbS2 are predicted theoretically by first-principles calculations. We reveal a CDW instability towards the formation of a stable commensurate CDW order, resulting in a sqart(13)*sqart(13) structural reconstruction featured with star-of-David clusters. The CDW phase exhibits one-dimensional metallic behavior with in-plane flat-band characteristics, and coexists with an orbital-density-wave order predominantly contributed by 4d_(z^2-r^2 ) orbital from the inner Nb atoms of the star-of-David cluster. By doubling the cell of the CCDW phase along the layer stacking direction, a metal-insulator transition may be realized in the CDW phase in case the interlayer antiferromagnetic ordering and Coulomb correlation effect have been considered simultaneously. Bare electron susceptibility, phonon linewidth and electron-phonon coupling calculations suggest that the CDW instability is driven by softened phonon modes due to the strong electron-phonon coupling interactions. CDW order can be suppressed by pressure, concomitant with appearance of superconductivity. Our theoretical predictions call for experimental investigations to further clarify the transport and magnetic properties of 1T-NbS2. Furthermore, it would also be very interesting to explore the possibility to realize the CDW order coexisting with the superconductivity in bulk 1T-NbS2.