Subgap collective tunneling and its staircase structure in charge density waves

Tunneling spectra of chain materials NbSe3 and TaS3 were studied in nanoscale mesa devices. Current-voltage I-V characteristics related to all charge density waves (CDWs) reveal universal spectra within the normally forbidden region of low V, below the electronic CDW gap 2Delta. The tunneling always demonstrates a threshold Vt approximately 0.2Delta, followed, for both CDWs in NbSe3, by a staircase fine structure. T dependencies of Vt(T) and Delta(T) scale together for each CDW, while the low T values Vt(0) correlate with the CDWs' transition temperatures Tp. Fine structures of CDWs perfectly coincide when scaled along V/Delta. The results evidence the sequential entering of CDW vortices (dislocations) in the junction area with the tunneling current concentrated in their cores. The subgap tunneling proceeds via the phase channel: coherent phase slips at neighboring chains.     

Stationary Josephson current in junctions involving d-wave superconductors with charge density waves: the temperature dependence and deviations from the law of corresponding states

Stationary Josephson current I _c in symmetric and non-symmetric junctions involving d-wave superconductors with charge density waves (CDWs) was calculated. It was found that, if CDWs are weak or absent, there exists an approximate proportionality between I _c and the product of superconducting order parameters in the electrodes (the law of corresponding states) for several factors affecting those quantities, such as the temperature, T, or one of the parameters characterizing the combined CDW superconducting phase (the degree of the Fermi surface dielectric gapping and the ratio between the parent superconducting and CDW order parameters). Otherwise, the dependences I _c (T) were shown to deviate from those in the absence of CDWs, and the relevant corresponding-state dependences from linearity, the deviations being especially strong at certain rotation angles of crystalline electodes with respect to the junction plane. Hence, making use of specially designed experimental setups and analyzing the I _c (T) and corresponding-state dependences, the existence of CDWs in cuprates and other non-conventional superconductors can be detected.     

Multiband nodeless superconductivity near the charge-density-wave quantum critical point in ZrTe_(3-x)Se_x

It was found that selenium doping can suppress the charge-density-wave(CDW) order and induce bulk superconductivity in ZrTe_3. The observed superconducting dome suggests the existence of a CDW quantum critical point(QCP) in ZrTe_3-xSex near x ≈ 0.04. To elucidate the superconducting state near the CDW QCP, we measure the thermal conductivity of two ZrTe_(3-x)Se_x single crystals(x = 0.044 and 0.051) down to 80 m K. For both samples, the residual linear term κ_0/T at zero field is negligible, which is a clear evidence for nodeless superconducting gap. Furthermore, the field dependence of κ_0/T manifests a multigap behavior. These results demonstrate multiple nodeless superconducting gaps in ZrTe_(3-x)Se_x,which indicates conventional superconductivity despite of the existence of a CDW QCP.     

Revealing charge density wave formation in the LaTe2 system by angle resolved photoemission spectroscopy

We present the first direct study of charge density wave (CDW) formation in quasi-2D single layer LaTe2 using high-resolution angle resolved photoemission spectroscopy and low energy electron diffraction. CDW formation is driven by Fermi surface (FS) nesting, however, characterized by a surprisingly smaller gap ( approximately 50 meV) than seen in the double layer RTe2 compounds, extending over the entire FS. This establishes LaTe2 as the first reported semiconducting 2D CDW system where the CDW phase is FS nesting driven. In addition, the layer dependence of this phase in the tellurides and the possible transition from a stripe to a checkerboard phase is discussed.     

Scanning tunnelling microscopy of charge-density waves in transition metal chalcogenides

We have used scanning tunnelling microscopes (STMs) operating at liquid helium and liquid nitrogen temperatures to image the charge-density waves (CDWs) in transition metal chalcogenides. The layer structure dichalcogenides TaSe₂, TaS₂, NbSe₂, VSe₂, TiSe₂ and TiS₂ have been studied including representative polytype phases such as 1T, 2H and 4Hb. Experimental results are presented for the complete range of CDW amplitudes and structures observed in these materials. In most cases both the CDW and the surface atomic structure have been simultaneously imaged. Results on the trichalcogenide NbSe₃ are also included.

The formation of the CDW along with the associated periodic lattice distortion gaps the Fermi surface (FS) and modifies the local density-of-states (LDOS) detected by the tunnelling process. The tunnelling microscopes have been operated mostly in the constant current mode which maps the LDOS at the position of the tunnelling tip. The relative amplitudes and profiles of the CDW superlattice and the atomic lattice have been measured and confirm on an atomic scale the CDW structures predicted by X-ray, electron and neutron diffraction. The absolute STM deflections are larger than expected for the CDW induced modifications of the LDOS above the surface and possible enhancement mechanisms are reviewed.

In the 2H trigonal prismatic coordination phases the CDWs involve a relatively small charge transfer and the atomic structure dominates the STM images. In the 1T octahedral coordination phases the charge transfer is large and the CDW structure dominates the STM image with an anomalously large enhancement of the STM profile. Systematic comparison of the STM profiles with band structure and FS information is included.

In the case of the 4Hb mixed coordination phases at the lowest temperatures two nearly independent CDWs form in alternate sandwiches. STM studies on 4Hb crystals with both octahedral and trigonal prismatic surface sandwiches have been carried out. The STM scans detect the relative strengths of the two CDWs as well as the interactions between the two types of CDW structure.

The STM scans are also able to detect defects and domain structure in the CDW image. Several examples will be given demonstrating the potential of the STM to detect these local variations in LDOS on an atomic scale. In contrast to the layer structure crystals the linear chain compound NbSe₃ shows a complex surface atomic structure as well as the formation of two CDWs. The surface atomic structure is resolved in the STM scans and profiles have detected the presence of the CDW modulation at 77K and 4.2K. These results demonstrate the feasibility of detecting CDW structure in the presence of complex atomic structure and using materials where dynamical CDW effects can also be studied by STM.

The range of STM results presented here show that the STM scans are extremely sensitive to the detail of the CDW structure and its effect on the LDOS. Although much of this structure has been deduced from diffraction studies, the ability to examine the CDW structure on an atomic scale with the STM is new. The sensitivity of the STM method suggests potential applications to a wide range of electronic structures in materials.     

Tri-hexagonal charge order in kagome metal CsV3Sb5 revealed by 121Sb nuclear quadrupole resonance

We report ¹²¹Sb nuclear quadrupole resonance(NQR)measurements on kagome superconductor CsV₃Sb₅ with Tc=2.5 K.¹²¹Sb NQR spectra split after a charge density wave(CDW)transition at 94 K,which demonstrates a commensurate CDW state.The coexistence of the high temperature phase and the CDW phase between 91 K and 94 K manifests that it is a first order phase transition.The CDW order exhibits tri-hexagonal deformation with a lateral shift between the adjacent kagome layers,which is consistent with 2×2×2 superlattice modulation.The superconducting state coexists with CDW order and shows a conventional s-wave behavior in the bulk state.     

Spin-dependent tunneling in junctions containing metals with charge density waves in a magnetic field

The dependences of the differential tunneling conductance G on the voltage V across a junction in an external magnetic field H are calculated for two types of junctions involving normal or superconducting metals with charge density waves (CDWs). Junctions of the first type are asymmetric CDW metal (CDWM)-insulator-ferromagnet junctions. The results of calculations for these junctions demonstrate that there occurs splitting between the components of the conductance G(V) corresponding to the tunneling of electrons with spins aligned with the magnetic field H and opposite to it, as is the case with junctions containing a superconducting electrode instead of the CDWM electrode. Junctions of the second type are junctions between two normal or superconducting CDWM electrodes. For junctions with at least one normal CDWM electrode and H ≠ 0, the conductance G(V) also exhibits spin splitting. The form of the conductance G(V) for tunnel junctions of both types depends on the phase of the order parameter of the charge density waves.     

Sliding-induced decoupling and charge transfer between the coexisting Q1 and Q2 charge density waves in NbSe3

Using high-resolution x-ray scattering in the presence of an applied current, we report evidence for a dynamical decoupling between the two NbSe3 charge-density waves (CDWs), Q1 (T(C1)=145 K) and Q2 (T(C2)=59 K), coexisting below T(C2). Simultaneous and oppositely directed shifts of the relevant CDW superlattice spots develop above a threshold current which we identify as the depinning threshold I(C1) for the more strongly pinned upper CDW Q1 (I(C1) approximately 10I(C2)). In contrast with shifts induced by current conversion processes, the present effect is not current polarized and is not limited to the current-contact regions. We propose a model which explains this instability through a sliding-induced charge transfer between the two electronic reservoirs corresponding to the Q1 and Q2 CDWs.     

Emergence of Fermi pockets in a new excitonic charge-density-wave melted superconductor

A superconducting state (T(c) approximately 4.2 K) has very recently been observed upon successful doping of the charge-density-wave (CDW) ordered triangular lattice TiSe(2), with copper. Using state-of-the-art photoemission spectroscopy we identify, for the first time, momentum-space locations of doped electrons that form the Fermi sea of the superconductor. With doping, we find that kinematic nesting volume increases, whereas coherence of the CDW collective order sharply drops. In superconducting doping, as chemical potential rises, we observe the emergence of a large density of states in the form of a narrow electron pocket near the L point of the Brillouin zone with d-like character. The k-space spectral evolution directly demonstrates, for the first time, that the CDW order parameter microscopically competes with superconductivity in the same band.     

Charge-density waves and superlattices in the metallic layered transition metal dichalcogenides

The d1 layer metals TaS 2 , TaSe 2 , NbSe 2 , in all their various polytypic modifications, acquire, below some appropriate temperature, phase conditions that their electromagnetic properties have previously revealed as 'anomalous'. Our present electron-microscopic studies indicate that this anomalous behaviour usually included the adoption, at some stage, of a superlattice. The size of superlattice adopted often is forecast in the pattern of satellite spotting and strong diffuse scattering found above the transition. Our conclusions are that charge-density waves and their concomitant periodic structural distortions occur in all these 4d 1 /5d 1 dichalcogenides. We have related the observed periodicities of these CDW states to the theoretical form of the parent Fermi surfaces. Particularly for the 1T octahedrally coordinated polytypes the Fermi surface is very simple and markedly two-dimensional in character, with large near-parallel walls. Such a situation is known theoretically to favour the formation of charge and spin-density waves. When they first appear, the CDWs in the 1T (and 4Hb) polytypes are incommensurate with the lattice. This condition produes a fair amount of gapping in the density of states at the Fermi level. For the simplest case of 1T-TaSe 2 , the room temperature superlattice is realized when this existing CDW rotates into an orientation for which it then become commensurate. At this first-order transition the Fermi surface energy gapping increases beyond that generated by the incommensurate CDW, as is clearly evident in the electromagnetic properties. For the trigonal prismatically coordinated polytypes, CDW formation is withheld to low temperatures, probably because of the more complex band structures. This CDW state (in the cases measured) would seem at once commensurate, even though the transition is, from a wide variety of experiments, apparently second order. A wide range of doped and intercalated materials have been used to substantiate the presence of CDWs in these compounds, and to clarify the effect that their occurrence has on the physical properties. The observations further demonstrate the distinctiveness of the transition metal dichalcogenide layer compounds, and of the group VA metals in particular.     

Effect of charge density waves on the tunnel spectra of the Bi2Sr2CaCu2O8+δ superconductor

The differential tunnel conductance G _S of the junction between a normal metal and a superconductor with a charge density wave (CDW) is calculated as a function of the voltage V across the junction. The results are averaged over the spread of superconducting and CDW energy gaps in the nanoscale-inhomogeneous superconductor. It is shown that, if both order parameters are nonzero, a dip-hump structure is formed beyond the superconducting gap of G _S (V). If the phase of the CDW order parameter is not equal to π/2, a dip-hump structure will appear solely or mainly for one sign of the bias polarity. The results agree with the experimental data for Bi₂Sr₂CaCu₂O_8+δ and other high-temperature oxides     

Competition of charge-density waves and superconductivity in sulfur

A one-dimensional charge-density wave (CDW) instability is shown to be responsible for the formation of the incommensurate modulation of the atomic lattice in the high-pressure phase of sulfur. The coexistence of, and competition between, the CDW and the superconducting state leads to the previously observed increase of T{c} up to 17 K, which we attribute to the suppression of the CDW instability, the same phenomenology found in doped layered dichalcogenides.     

Effects of radiation damage on the charge density wave transitions in NbSe3

We have measured the electrical resistivity of NbSe₃ samples which have been radiation damaged with 2.5 MeV protons up to a defect concentration of 0.5%. We find that, unlike substitutional impurities, the defects do not destroy the charge density wave (CDW) transitions and the samples do not go superconducting. The defects become more effective scatterers below the CDW transitions so that the defect resistivity is temperature dependent. The defects pin the CDWs randomly so that carriers in the unnested regions can be scattered by the CDW. This leads to an enhancement of the defect resistivity. The resistivity of the highly damaged samples is still increasing with decreasing temperatures to below 1 K.     

Infrared signature of the charge-density-wave gap in ZrTe<Subscript>3</Subscript>

The chain-like ZrTe₃ compound undergoes a charge-density-wave (CDW) transition at T_CDW=63 K, most strongly affecting the conductivity perpendicular to the chains. We measure the temperature (T) dependence of the optical reflectivity from the far infrared up to the ultraviolet with polarized light. The CDW gap Δ(T) along the direction perpendicular to the chains is compatible for T<T_CDW with the behavior of an order parameter within the mean-field Bardeen-Cooper-Schrieffer (BCS) theory. Δ(T) also persists well above T_CDW, which emphasizes the role played by fluctuation effects.     

Superconductivity at 5.2 K in ZrTe3 polycrystals and the effect of Cu and Ag intercalation

We report the occurrence of superconductivity in polycrystalline samples of ZrTe(3) at temperature 5.2 K at ambient pressure. The superconducting state coexists with the charge density wave (CDW) phase, which sets in at 63 K. The intercalation of Cu or Ag does not have any bearing on the superconducting transition temperature but suppresses the CDW state. The feature of a CDW anomaly in these compounds is clearly seen in the DC magnetization data. Resistivity data are analyzed in order to estimate the relative loss of carriers and reduction in the nested Fermi surface area upon CDW formation in ZrTe(3) and the intercalated compounds.     

Fermi surface reconstruction in the CDW state of CeTe3 observed by photoemission

CeTe3 is a layered compound where an incommensurate charge density wave (CDW) opens a large gap ( approximately 400 meV) in optimally nested regions of the Fermi surface (FS), whereas other sections with poorer nesting remain ungapped. Through angle-resolved photoemission, we identify bands backfolded according to the CDW periodicity. They define FS pockets formed by the intersection of the original FS and its CDW replica. Such pockets illustrate very directly the role of nesting in the CDW formation but they could not be detected so far in a CDW system. We address the reasons for the weak intensity of the folded bands, by comparing different foldings coexisting in CeTe3.     

Interaction of both charge density waves in NbSe3 from interlayer tunneling experiments

An interlayer tunneling technique has been used for spectroscopy of charge density wave (CDW) energy gaps (Δ_1,2) in NbSe₃ subsequently opened at the Fermi surface on decreasing temperature at T _p1 = 145 K (CDW1) and at T _p2 = 60 K (CDW2). We found that the CDW2 formation is accompanied by an increase of the CDW1 gap below T _p2. The maximum enhancement of Δ₁, δΔ₁ is about 10%. The effect observed has been predicted theoretically as resulting from the joint phase locking of both CDWs with the underlying crystalline lattice below T _p2. The text was submitted by the authors in English.     

Incommensurate/commensurate charge-density-wave states as a source for plutonium metal behavior

Physical property behavior of plutonium (Pu) metal phases is like that of an incommensurate charge-density wave (ICDW) system where the CDW influenced distortion modulates the crystal. As incommensurates, the different Pu phases may have to be considered as superspace group structures where there is a one-dimensional modulation of the basic three-dimensional lattice. Certain Pu phases may then be classified into as many as three Bravais classes when considered in (3 + 1) dimensional space. The possible variants in Bravais class, crystals setting and bottom lines, as well as allowable differences in the number of atoms per unit cell, should permit incommensurate materials, as well as Pu phases, to appear in different variants of the basic space group structure on heating and cooling cycles. One should not expect the lower temperature phases, e.g., Pu, to return to their original distorted or modulated structures at constant rate cooling, after being distorted or modulated by CDWs in their higher temperature space group structures. This can explain the hysteresis in phase transitions noted with Pu metal and with incommensurate materials in general.

Chiral symmetry appears to be inherent to the incommensurability of a quasi-one dimensional system. All but one of the reported space group structures for Pu phases have at least a one-dimensional twofold screw axis with a center of symmetry, i.e., they show chiral symmetry. A theory suggests that chiral symmetry must permit the contraction in one or more dimensions noted with most incommensurate materials, as well as with Pu phases.

It is suggested that there is another ICDW Pu phase (αI) below ～ 60 K, and that the γ-Pu phase (Fddd) must be a composite structure. Other Pu phases appear to be composite structures also. There is evidence for a new phase, or phase mixture, which appears reproducibly between the δ and γ phases only on a cooling cycle. It is infered that this is a reappearance of the δ' phase.

Published dilatometry, internal friction and relative shear modulus results appear to confirm both incommensurate and commensurate CDW states in Pu metal phases. It is suggested that CDWs may be playing a role in f-bonding in Pu metal and that CDWs and valence fluctuations may be manifestations of the same electronic behavior.     

Superconductivity in the pseudogap state in the hot-spot model: Ginzburg-Landau expansion

Peculiarities of the superconducting state (s and d pairing) are considered in the model of the pseudogap state induced by short-range order fluctuations of the dielectric (AFM (SDW) or CDW) type, which is based on the model of the Fermi surface with “hot spots.” A microscopic derivation of the Ginzburg-Landau expansion is given with allowance for all Feynman diagrams in perturbation theory in the electron interaction with short-range order fluctuations responsible for strong scattering in the vicinity of hot spots. The superconducting transition temperature is determined as a function of the effective pseudogap width and the correlation length of short-range order fluctuations. Similar dependences are derived for the main parameters of a superconductor in the vicinity of the superconducting transition temperature. It is shown, in particular, that the specific heat jump at the transition point is considerably suppressed upon a transition to the pseudogap region on the phase diagram.