In-chain tunneling through charge-density-wave nanoconstrictions and break junctions

We have fabricated longitudinal nanoconstrictions in the charge-density wave conductor (CDW) NbSe3 using a focused ion beam and using a mechanically controlled break-junction technique. Conductance peaks are observed below the TP1=145 K and TP2=59 K CDW transitions, which correspond closely with previous values of the full CDW gaps 2Delta1 and 2Delta2 obtained from photoemission. These results can be explained by assuming CDW-CDW tunneling in the presence of an energy gap corrugation epsilon2 comparable to Delta2, which eliminates expected peaks at +/-|Delta1+Delta2|. The nanometer length scales our experiments imply indicate that an alternative explanation based on tunneling through back-to-back CDW-normal-conductor junctions is unlikely.     

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.     

Measurement of the shear strength of a charge density wave

We have explored the shear plasticity of charge density waves (CDWs) in NbSe3 samples with cross sections having a single microfabricated thickness step. Shear stresses along the step result from thickness-dependent CDW pinning. For small thickness differences the CDW depins elastically at the volume average depinning field. For large thickness differences the thicker, more weakly pinned side depins first via plastic shear, and shear plasticity contributes substantial dissipation well above the depinning field. A simple model describes the qualitative features of our data and yields a value for the CDW's shear strength of approximately 9.5 x 10(3) Nm(-2). This value is orders of magnitude smaller than the CDW's longitudinal modulus but much larger than corresponding values for flux line lattices, and in part explains the relative coherence of the CDW response.     

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.     

The phase diagram for coexisting d-wave superconductivity and charge-density waves: cuprates and beyond

Phase diagrams of d-wave superconductivity characterized by an order parameter Δ coexisting with charge-density waves (CDWs) characterized by an order parameter Σ were constructed for the two-dimensional Fermi surface (FS) appropriate to, e.g., cuprates. CDWs were considered as an origin of the pseudogap appearing at antinodal FS sections of the d(x2-y2) superconductor. Two types of the Σ-reentrance were found: with the temperature, T, and with the opening of the CDW sector, 2α. The angular plots in the momentum space for the resulting gap profile over the FS ('gap roses') were obtained. The gap patterns are rather involved, giving insight into the difficulties of the interpretation of photoemission spectra. It was shown that the Σ-Δ coexistence region exists even for the complete dielectric gapping due to the distinction between the superconducting and CDW order parameter symmetries. The checkerboard and unidirectional CDW configurations were examined, and both the phase diagrams and the behavior with T and α of the order parameters were found to differ. A more general case with a non-zero mismatch angle β between the superconducting lobes and the CDW sectors was analyzed, the case β = π/4 corresponding to the d(xy) symmetry of the superconducting order parameter. The phase diagrams were found to be sensitive to β-variations, showing that internal strains and external pressure can drastically affect the behavior of Σ(T) and Δ(T).     

Charge density wave states in phase-engineered monolayer VTe2

Charge density wave (CDW) strongly affects the electronic properties of two-dimensional (2D) materials and can be tuned by phase engineering. Among 2D transitional metal dichalcogenides (TMDs), VTe$_{2}$ was predicted to require small energy for its phase transition and shows unexpected CDW states in its T-phase. However, the CDW state of H-VTe$_{2}$ has been barely reported. Here, we investigate the CDW states in monolayer (ML) H-VTe$_{2}$, induced by phase-engineering from T-phase VTe$_{2}$. The phase transition between T- and H-VTe$_{2}$ is revealed with x-ray photoelectron spectroscopy (XPS) and scanning transmission electron microscopy (STEM) measurements. For H-VTe$_{2}$, scanning tunneling microscope (STM) and low-energy electron diffraction (LEED) results show a robust $2\sqrt 3 \times 2\sqrt 3 $ CDW superlattice with a transition temperature above 450 K. Our findings provide a promising way for manipulating the CDWs in 2D materials and show great potential in its application of nanoelectronics.     

S-Wave Superconductivity in Kagome Metal CsV_3Sb_5 Revealed by ~(121/123)Sb NQR and ~(51)V NMR Measurements

We report ~(121/123)Sb nuclear quadrupole resonance(NQR) and ~(51)V nuclear magnetic resonance(NMR) measurements on kagome metal CsV_3 Sb_5 with T_c=2.5 K.Both ~(51)V NMR spectra and ~(121/123)Sb NQR spectra split after a charge density wave(CDW) transition,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.At low temperature,electric-field-gradient fluctuations diminish and magnetic fluctuations become dominant.Superconductivity emerges in the charge order state.Knight shift decreases and 1/T_1T shows a Hebel-Slichter coherence peak just below T_c,indicating that CSV_3 Sb_5 is an s-wave superconductor.     

Negative resistance and local charge-density-wave dynamics

Charge-density-wave (CDW) dynamics is studied on a submicron length scale in NbSe(3) and o-TaS(3). Regions of negative absolute resistance are observed in the CDW sliding regime at sufficiently low temperatures. The origin of the negative resistance is attributed to the different forces that the deformed CDW and quasiparticles feel: the force on the CDW is merely caused by a difference of the electric potentials, while the quasiparticle current is governed by a difference of the electrochemical potentials.     

93Nb NMR spin echo spectroscopy in single crystal NbSe3

We report electric field induced phase displacements of the charge density wave (CDW) in a single crystal of NbSe3 using 93Nb NMR spin-echo spectroscopy. CDW polarizations in the pinned state induced by unipolar and bipolar pulses are linear and reversible up to at least E = (0.96)ET. The polarizations have a broad distribution extending up to phase angles of order 60 degrees for electric fields close to threshold. No evidence for polarizations in excess of a CDW wavelength or for a divergence in polarization near ET are observed. The results are consistent with elastic depinning models, provided that the critical regime expected in large systems is not observable.     

Chiral charge-density waves

We discovered the chirality of charge-density waves (CDW) in 1T-TiSe? by using STM and time-domain optical polarimetry. We found that the CDW intensity becomes Ia?∶Ia?∶Ia? = 1∶0.7 ± 0.1∶0.5 ± 0.1, where Ia(i) (i=1,2,3) is the amplitude of the tunneling current contributed by the CDWs. There were two states, in which the three intensity peaks of the CDW decrease clockwise and anticlockwise. The chirality in CDW results in the threefold symmetry breaking. Macroscopically, twofold symmetry was indeed observed in optical measurement. We propose the new generalized CDW chirality H(CDW) ≡ q?·(q?×q?), where q(i) are the CDW q vectors, which is independent of the symmetry of components. The nonzero H(CDW)-the triple-q vectors do not exist in an identical plane in the reciprocal space-should induce a real-space chirality in CDW system.     

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.     

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.     

Unusual spectral behavior of charge-density waves with imperfect nesting in a quasi-one-dimensional metal

Low-temperature electronic properties of the charge-density-wave system NbSe3 are reported from angle-resolved photoemission at 15 K. The effect of two instabilities q(1) and q(2) on the k-resolved spectral function is observed for the first time. With a pseudogap background, the gap spectra exhibit maxima at Delta*(1) approximately 110 meV and Delta*(2) approximately 45 meV. Imperfectly nested sections of the Fermi surface lack a Fermi-Dirac edge, and show the signature of a dispersion that is modified by self-energy effects. The energy scale is of the order of the effective gap 2 Delta*(2). The effect disappears above T2, suggesting a correlation with the charge-density-wave state.     

Raman spectra of several layer compounds with charge density waves

Raman scattering studies of the transition metal dichalcogenide layer compounds 1TTaS₂, 1TTaSe₂, 2H-TaSe₂ and 1TVSe₂ are reported. The materials were studied with commensurate and incommensurate charge density waves (CDWs) as well as in the absence of CDWs. Large qualitative changes observed in the Raman spectra are associated with the formation of CDWs and the change from an incommensurate to a commensurate phase.     

Tunable charge density wave in TiS_3 nanoribbons

Recently, modifications of charge density wave(CDW) in two-dimensional(2D) show intriguing properties in quasi-2D materials such as layered transition metal dichalcogenides(TMDCs). Optical, electrical transport measurements and scanning tunneling microscopy uncover the enormous difference on the many-body states when the thickness is reduced down to monolayer. However, the CDW in quasi-one-dimensional(1D) materials like transition metal trichalcogenides(TMTCs) is yet to be explored in low dimension whose mechanism is likely distinct from their quasi-2D counterparts.Here, we report a systematic study on the CDW properties of titanium trisulfide(TiS_3). Two phase transition temperatures were observed to decrease from 53 K(103 K) to 46 K(85 K) for the bulk and 15-nm thick nanoribbon, respectively,which arises from the increased fluctuation effect across the chain in the nanoribbon structure, thereby destroying the CDW coherence. It also suggests a strong anisotropy of CDW states in quasi-1D TMTCs which is different from that in TMDCs.Remarkably, by using back gate of-30 V ～ 70 V in 15-nm device, we can tune the second transition temperature from110 K(at-30 V) to 93 K(at 70 V) owing to the altered electron concentration. Finally, the optical approach through the impinging of laser beams on the sample surface is exploited to manipulate the CDW transition, where the melting of the CDW states shows a strong dependence on the excitation energy. Our results demonstrate TiS_3 as a promising quasi-1D CDW material and open up a new window for the study of collective phases in TMTCs.     

Interlayer tunneling spectroscopy of the field induced CDW state in graphite

Using interlayer tunneling spectroscopy we studied anomalous magnetoresistance state in graphite in pulsed magnetic fields up to 55 T. At low temperatures we found the opening of a pseudogap on tunneling spectra at fields above 17 T. The gap value is saturated above 30 T to 2Δ=70 mV. The gap feature is gradually smearing out with temperature but is still observed up to temperatures of ∼250 K. We discuss possible origin of the pseudogap as being related with the field induced charge density wave (CDW) state in analogy with that recently observed in NbSe₃ above Peierls transition temperature.     

The influence of impurities on the quasiparticle tunneling current between weakly coupled quasi-one-dimensional charge density waves

The dc and ac conductivity of a tunneling junction between two impure quasi-one-dimensional charge density wave (CDW) systems is calculated. The non-magnetic impurities are considered in the self-consistent Born approximation (SCBA). Impurities modify the density of states (DOS) of the pure CDW system for quasiparticles inside the energy region of the gap 2(T). As in the pure case, the theory predicts in addition to a tunneling current which is proportional to the product of the DOS a term proportional to the cosine of the order parameter phase difference. In the case of a normal state/CDW junction, analytical expressions are obtained forT=0 showing deviations from the pure case. The linear ac conductivity is obtained by the scaling relation between the dc and the ac response.     

Adsorbate-induced pinning of a charge-density wave in a quasi-1D metallic chains: Na on the In/Si(111)-(4x1) surface

We find that foreign adsorbates acting as local impurities can induce a metal-insulator transition by pinning a charge-density wave (CDW) on the quasi-1D metallic In/Si(111)-(4x1) chain system. Our scanning tunneling microscopy image clearly reveals the presence of a new local 4x2 structure nucleated by Na adatoms at room temperature, which turns out to be insulating with a doubled periodicity along the chains. We directly determine a CDW gap energy Delta = 105+/-8 meV by identifying a characteristic loss peak in our high-resolution electron-energy-loss spectra. We thus report the first observation of a local impurity-derived Peierls-like reconstruction of a quasi-1D system.     

Triangular lattices of charge-and spin-density waves in chemisorbed metal monolayers on the surface of diamond structure semiconductors

The electronic spectrum of a planar triangular lattice is analyzed, and the possible occurrence of charge (CDWs) and spin density waves (SDWs) in the lattice is discussed. Commensurate CDW and SDW structures of two types are considered in the weak and strong electron-electron interaction approximations. The CDW and SDW models are applied to the specific case of chemisorbed metal monolayers on the (111) surface of diamond structure semiconductors with a coverage close to 1/3.     

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.