Commensurate Charge Density Wave Research Articles

S-wave superconductivity in superconducting BaTi2Sb2O revealed by121/123Sb-NMR/nuclear quadrupole resonance measurements

We report the ${}^{121/123}$Sb-NMR/nuclear quadrupole resonance (NQR) measurements on the superconductor BaTi${}_{2}$Sb${}_{2}$O with a two-dimensional Ti${}_{2}$O square-net layer formed with Ti${}^{3+}$ (3${d}^{1}$). NQR measurements revealed that the in-plane four-fold symmetry is broken at the Sb site below ${T}_{\mathrm{A}}\ensuremath{\sim}40$ K, without an internal field appearing at the Sb site. These exclude a spin-density wave (SDW)/ charge density wave (CDW) ordering with incommensurate correlations, but can be understood with the commensurate CDW ordering at ${T}_{\mathrm{A}}$. The spin-lattice relaxation rate $1/{T}_{1}$, measured at the four-fold symmetry breaking site, decreases below superconducting (SC) transition temperature ${T}_{\mathrm{c}}$, indicative of the microscopic coexistence of superconductivity and the CDW/SDW phase below ${T}_{\mathrm{A}}$. Furthermore, $1/{T}_{1}$ of ${}^{121}$Sb-NQR shows a coherence peak just below ${T}_{\mathrm{c}}$ and decreases exponentially at low temperatures. These results are in sharp contrast with those in cuprate and iron-based superconductors, and strongly suggest that its SC symmetry is classified to an ordinary $s$-wave state.

Topological Solitons versus Nonsolitonic Phase Defects in a Quasi-One-Dimensional Charge-Density Wave

We investigated phase defects in a quasi-one-dimensional commensurate charge-density wave (CDW) system, an In atomic wire array on Si(111), using low temperature scanning tunneling microscopy. The unique fourfold degeneracy of the CDW state leads to various phase defects, among which intrinsic solitons are clearly distinguished. The solitons exhibit a characteristic variation of the CDW amplitude with a coherence length of about 4 nm, as expected from the electronic structure, and a localized electronic state within the CDW gap. While most of the observed solitons are trapped by extrinsic defects, moving solitons are also identified and their novel interaction with extrinsic defects is disclosed.

Vanishing of the metal-insulator Peierls transition in pressurized BaVS3

BaVS${}_{3}$ presents a metal-to-insulator (MI) transition at ambient pressure due to the stabilization of a 2k${}_{\mathrm{F}}$ commensurate charge density wave (CDW) Peierls ground state built on the $d{z}^{2}$ V orbitals. The MI transition vanishes under pressure at a quantum critical point (QCP) where the electronic properties exhibit a non-Fermi liquid behavior. In this paper, we determine the CDW phase diagram under pressure and show that it combines both the vanishing of the second-order Peierls transition and a commensurate-incommensurate first-order delocking transition of the 2k${}_{\mathrm{F}}$ wave vector. We explain quantitatively the drop of the MI critical temperature by the decrease of the electron-hole pair lifetime of the CDW condensate due to an enhancement of the hybridization between the $d{z}^{2}$ and $e$(${t}_{2g}$) levels of the V under pressure.

Electronic structure of two-dimensional hexagonal diselenides: Charge density waves and pseudogap behavior

We present theoretical study of electronic structure (spectral functions and Fermi surfaces) for incommensurate pseudogap and charge density wave (CDW) and commensurate CDW phases of quasi two dimensional diselenides 2H-TaSe2 and 2H-NbSe2. Incommensurate pseudogap regime is described within the scenario based on short-range order CDW fluctuations, considered within the static Gaussian random field model. In contrast e.g. to high-Tc cuprates layered dichalcogenides have several different CDW scattering vectors and electronic spectrum with two bands at the Fermi level. To this end we present theoretical background for the description of multiple scattering processes within multiple bands electronic spectrum. Thus obtained theoretical spectral functions and Fermi surfaces are compared with recent ARPES experimental data, demonstrating rather good qualitative agreement.

Possible Commensurate Phases in LuFe2O4

LuFe2O4 is a member of the RFe2O3 family (R: rare-earth metals) and has a hexagonal layered structure with the space group R 3m above 500K, where the lattice constants are a 1⁄4 0:344 and c 1⁄4 2:528 nm in the hexagonal system. It undergoes successive phase transitions below 500K owing to the charge ordering of Fe2þ and Fe3þ ions, which in the high-temperature phase randomly occupy equivalent Fe sites. It also shows a two-dimensional (2D) charge order at the wavevector k 1⁄4 ð1=3; 1=3; 0Þ below 500K, as well as a three-dimensional (3D) charge order at k 1⁄4 1⁄2ð1þ Þ=3; ð1þ Þ=3; 3=2 , with 1⁄4 0:081 below 320K, where k is defined in the hexagonal system. Ikeda et al. proposed that LuFe2O4 can be regarded as a chargeand spinfrustrated system on the basis of their experimental results. Subramanian et al. reported that the dielectric constant of LuFe2O4 at room temperature markedly decreases under a small magnetic field, implying that a strong coupling exists between a spin moment and an electric dipole at room temperature. This indicates the potential applications of LuFe2O4 in which the charge and spin degrees of freedom of electrons can be controlled. On the theoretical side, Yamada and coworkers proposed a model of the charge ordered structure in which they discussed successive transitions from the R 3m phase to the 2D commensurate charge density wave (CDW) and 3D incommensurate CDW phases. Xiang and Whangbo discussed the charge order in charge-frustrated LuFe2O4 on the basis of the results of first-principles electronic structure calculations and Monte Carlo simulations. An electronic model of a honeycomb lattice starting with a model Hamiltonian was also studied by Nasu et al. and Naka and coworkers to explain dielectric and magnetic phenomena in the RFe2O3 family as a spinand chargefrustrated system. However, the space groups in low-symmetry phases below 500K have not yet been clarified owing to their extremely small domains. In this study, we derive the space groups and unit cells in the commensurate phases induced at the ð1=3; 1=3; 0Þ and ð1=3; 1=3; 1=2Þ points in the reciprocal lattice space of the space group R 3m in LuFe2O4. Let us first define the coordinates in the real and reciprocal spaces of the space group R 3m as shown in Figs. 1(a) and 1(b), where ðaR; bR; cRÞ and ðah; bh; chÞ indicate the lattice vectors of the rhombohedral and hexagonal systems, respectively, and the asterisks indicate the reciprocal lattice vectors. It is seen from Fig. 1(b) that the points kK 1⁄4 ð1=3; 1=3; 0Þ and kH 1⁄4 ð1=3; 1=3; 1=2Þ in a hexagonal system are both located at the Brillouin zone boundary; these two points are named the Kand H-points in Koster’s book, respectively. Regarding the K-point, we denote the equivalent points as the K1–K6-points, as shown in Fig. 1(b). The K3and K5-points are the same as the K1-point except for the reciprocal lattice vectors ah and bh , whereas the K2and K6-points are the same as the K4-point except for the reciprocal lattices ah and bh , respectively. The relation between the hexagonal and rhombohedral coordinates in real space is given as ah 1⁄4 aR bR; bh 1⁄4 bR cR; ch 1⁄4 aR þ bR þ cR: ð1Þ

Competing charge density waves and temperature-dependent nesting in2H-TaSe2

Multiple charge density wave (CDW) phases in 2H-TaSe2 are investigated by high-resolution synchrotron x-ray diffraction. In a narrow temperature range immediately above the commensurate CDW transition, we observe a multi-q superstructure with coexisting commensurate and incommensurate order parameters, clearly distinct from the fully incommensurate state at higher temperatures. This multi-q ordered phase, characterized by a temperature hysteresis, is found both during warming and cooling, in contrast to previous reports. In the normal state, the incommensurate superstructure reflection gives way to a broad diffuse peak that persists nearly up to room temperature. Its position provides a direct and accurate estimate of the Fermi surface nesting vector, which evolves non-monotonically and approaches the commensurate position as the temperature is increased. This behavior agrees with our recent observations of the temperature-dependent Fermi surface in the same compound [Phys. Rev. B 79, 125112 (2009)].

Growth and superconductivity of 2 H - Ni 0.02TaSe 2 single crystals

2 H-Ni 0.02TaSe 2 single crystals were successfully grown via the iodine vapor transport technique. The typical dimension of the crystal is about 3×2×0.5 mm 3. Compared with the parent compound 2 H-TaSe 2 with a superconducting transition temperature T C = 0.14 K, the electronic transport, specific-heat and magnetization results indicate that the superconductivity of the Ni 0.02TaSe 2 single crystal is obviously enhanced ( T C = 2.79 K). In addition, it is found that the incommensurate charge-density-wave (ICDW) disappears while the commensurate charge-density-wave (CCDW) shifts to about 96.2 K with the intercalation of a little of Ni. It clearly indicates that there is a competition between superconductivity (SC) and charge-density-wave (CDW) order for 2 H-TaSe 2 system and that between SC and ICDW is more drastic.

Commensurate charge-density wave with frustrated interchain coupling inSmNiC2

Temperature-dependent x-ray diffraction on ${\text{SmNiC}}_{2}$ has shown that the orthorhombic lattice symmetry of this compound persist down to a temperature of at least 9 K, i.e., into the charge-density-wave (CDW) state below ${T}_{\text{CDW}}=148\text{ }\text{K}$ and in the ferromagnetically ordered state below ${T}_{C}=17.7\text{ }\text{K}$. The modulated crystal structure has been determined for the incommensurate CDW state with ${\mathbf{q}}_{\text{CDW}}=(0.5,0.516,0)$ at $T=60\text{ }\text{K}$. The observed atomic modulation displacements indicate that the CDW should be considered as a commensurate CDW centered on chains of Ni atoms along $\mathbf{a}$. Frustrated interchain coupling is responsible for the incommensurability of the three-dimensionally ordered CDW state.

Superconducting phase in the layered dichalcogenide1T-TaS2upon inhibition of the metal-insulator transition

When a Mott metal-insulator transition is inhibited by a small amount of disorder in the layered dichalcogenide 1T-TaS2, an inhomogeneous superconducting state arises below T=2.1 K and coexists with a nearly commensurate charge-density wave. By angle-resolved photoelectron spectroscopy, we show that it emerges from a bad metal state with strongly damped quasiparticles. Superconductivity is almost entirely suppressed by an external magnetic field of 0.1 T.

Thermal properties of 1T-TaS 2 at the onset of charge density wave states

The crystal lattice plays an essential role in the charge density wave (CDW) phase transition together with the electron system through electron–phonon interactions. The CDW in the layered compound 1T-TaS 2 at low temperatures has a commensurate phase, which causes superlattice points to appear in the Brillouin zone of the undistorted phase. Since the effect of CDWs is to directly modulate the lattice, it is evident that an investigation that looks directly at the phonon frequencies would be most instructive in examining this phenomenon. Hence the Born–von Karman formalism, in which the equilibrium conditions are fulfilled, has been employed for the calculation of phonon frequency distribution curves of 1T-TaS 2 both in the normal and in the commensurate charge density wave (CCDW) phases. A folding technique has been adopted for the calculation in the CCDW phase. The phonon distribution and some dominant phonon frequencies for both the phases have been reported. With these results the thermal properties such as specific heat capacity, Debye Waller factor and thermal conductivity have been worked out, and are compared with the available experimental results.

Electronic transport and specific heat of

The results of low temperature thermoelectric power and the specific heat of 1T-VSe2 (Vanadium diselenide) have been reported along with the electrical resistivity, and Hall coefficient of the compound. The Charge Density Wave (CDW) transition is observed near 110K temperature in all these properties. The Thermoelectric power has been measured from 15K to 300K spanning the incommensurate and commensurate CDW regions. We observed a weak anomaly at the CDW transition for the first time in the specific heat of VSe2. The linear temperature dependence of resistivity and thermoelectric power at higher temperatures suggests a normal metallic behavior and electron-phonon scattering above the CDW transition. The positive thermoelectric power and negative Hall coefficient along with strongly temperature dependent behavior in the CDW phase suggest a mixed conduction related to the strongly hybridized s-p-d bands in this compound.

Stability of nodal quasiparticles in underdopedYBa2Cu3O6+yprobed by penetration depth and microwave spectroscopy

High resolution measurements of superfluid density and broadband quasiparticle conductivity have been used to probe the low energy excitation spectrum of nodal quasiparticles in underdoped YBCO. Penetration depth is measured to temperatures as low as 0.05 K. Microwave conductivity is measured from 0.1 to 20 GHz and is a direct probe of zero-energy quasiparticles. The data are compared with predictions for a number of theoretical scenarios that compete with or otherwise modify pure d-wave superconductivity, in particular commensurate and incommensurate spin and charge density waves; d + i s and d + i d superconductivity; circulating current phases; and the BCS--BEC crossover. We conclude that the data are consistent with a pure d-wave state in the presence of a small amount of strong scattering disorder, and are able to rule out most candidate competing states either completely, or to a level set by the energy scale of the disorder, ~ 4 K. Commensurate spin and charge density orders, however, are not expected to alter the nodal spectrum and therefore cannot be excluded.

Temperature-dependent Fermi surface of2H-TaSe2driven by competing density wave order fluctuations

Temperature evolution of the $2H{\text{-TaSe}}_{2}$ Fermi surface (FS) is studied by high-resolution angle-resolved photoemission spectroscopy. High-accuracy determination of the FS geometry was possible after measuring electron momenta and velocities along all high-symmetry directions as a function of temperature with subsequent fitting to a tight-binding model. The estimated incommensurability parameter of the nesting vector agrees with that of the incommensurate charge modulations. We observe detectable nonmonotonic temperature dependence of the FS shape, which we show to be consistent with the analogous behavior of the pseudogap. These changes in the electronic structure could stem from the competition of commensurate and incommensurate charge density wave order fluctuations and could explain the puzzling reopening of the pseudogap observed in the normal state of the transition metal dichalcogenides.

Synchrotron X-ray study of charge density waves in o-TaS3

We report a synchrotron X-ray study of charge density waves (CDW) in an o-TaS3 crystal. CDW of o-TaS3 has been known to undergo a commensurate-incommensurate transition at 100 K, below which the wavevector locks in with the pristine lattice. We exploited the beamline BL02B1 of SPring-8. Temperature dependence of the Bragg peak (002) and satellite peak (1 -1 2)+q⃗ was measured from 7 K to 180 K. We found that a new phase in a temperature range of 130--50 K, where two independent CDWs coexist. These waves are incommensurate and commensurate CDWs with longitudinal wave vectors qc=0.252c* and 0.250c*, respectively. By lowering the temperature, intensity of the incommensurate CDW was decreased, while that of the commensurate CDW was increased. At 50 K, the incommensurate CDW was completely diminished. Based on the concept of discommensuration, we determined the dislocation configuration from the intensity of the two CDWs.

Commensurate–incommensurate transition of charge density waves in o-

Abstract We report a synchrotron X-ray study of charge density waves (CDWs) in an o- TaS 3 crystal. CDW of o- TaS 3 has been known to undergo a commensurate–incommensurate transition at 100 K, below which the wavevector locks in with the pristine lattice. However, the details of the commensurate–incommensurate transition remain open problems, the example being whether the discommensuration exists or not in the neighborhood of the transition. We exploited the beamline BL02B1 of SPring-8. A two-dimensional detector was placed at a distance of 1300 mm from the sample, providing an angle resolution of 0.0076°. Temperature dependence of the Bragg peak (0 0 2) and satellite peak ( 1 - 1 2 ) + q was measured from 7 to 180 K. We found that a new phase in the temperature range of 130–50 K, where two independent CDWs coexist. These waves are incommensurate and commensurate CDWs with longitudinal wave vectors q c = 0.252 c * and 0.250 c * , respectively. By lowering the temperature, intensity of the incommensurate CDW was decreased, while that of the commensurate CDW was increased. Below 50 K, the incommensurate CDW was completely diminished. Based on the concept of discommensuration, we suggested the dislocation configuration from the intensity of the two CDWs.

Field-Induced Discommensuration in Charge Density Waves in o-TaS3

We report a synchrotron X-ray study of charge density waves (CDWs) in an o-TaS3 crystal. We found that two independent CDWs coexist in the temperature range of 130 - 50 K. These waves are incommensurate and commensurate CDWs with longitudinal wave vectors qc ¼ 0:252cand 0:250c � , respectively. The temperature and electric current dependences of the intensity of the two CDW satellites were measured. We found that the commensurate CDW was converted to the incommensurate CDW at 80 K by inducing current flow. Our observation was interpreted in terms of the dynamics of topological defects. We determined the edge dislocation configuration from the electric current dependence of the intensity of the two CDWs. The result implies for the first time that discommensurations are induced in the commensurate CDW by applying an electric field.

Absence of charge-density waves on the densePb/Ge(111)−β−3×3surface

The $\text{Pb}/\text{Ge}(111)\text{\ensuremath{-}}\ensuremath{\beta}\text{\ensuremath{-}}\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ surface is generally believed to be described with a 4/3 ML (monolayer) model on which a commensurate charge-density-wave (CDW) ground state was theoretically predicted. However, our scanning tunneling microscopy imaging has shown that the surface keeps the $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ structure even at 6 K. Our angle-resolved photoemission measurements show that this surface has a well-nested Fermi surface (FS). However, the nesting vector does not match with what is required for the predicted CDW. Also, the electron filling counted from the FS is not consistent with the 4/3 ML model. The reason for the absence of the predicted CDW is because the surface is described with the 1 ML model. A FS-driven CDW also is not yielded due to the lack of a lock-in energy with the underlying lattice.

Evolution of low-lying states in a doped CDW superconductor Cu xTiSe 2

A superconducting state has recently been observed by only a slight copper doping (∼4%) of the metallic 2D commensurate charge-density-wave (CDW) phase of titanium diselenide. We have employed high-resolution photoemission spectroscopy (ARPES) to probe the evolution of low-lying states, providing evidence that the CDW in the doped system is not due to Fermi surface nesting. With increasing copper concentration, we observe a significant rise of the chemical potential and a manifold of low-lying states at the top of the Fermi sea with increasing particle–hole asymmetry. These effects taken together contribute to destabilize the observed commensurate electronic, possibly, excitonic order in the vicinity of the superconducting doping in this system.

Fermionic functional renormalization-group for first-order phase transitions: a mean-field model

First-order phase transitions in many-fermion systems are not detected in the susceptibility analysis of common renormalization-group (RG) approaches. Here, we introduce a counterterm technique within the functional renormalization-group (fRG) formalism which allows access to all stable and metastable configurations. It becomes possible to study symmetry-broken states which occur through first-order transitions as well as hysteresis phenomena. For continuous transitions, the standard results are reproduced. As an example, we study discrete-symmetry breaking in a mean-field model for a commensurate charge-density wave. An additional benefit of the approach is that away from the critical temperature for the breaking of discrete symmetries large interactions can be avoided at all RG scales.

Scanning Tunneling Microscopy Observation of a Mott-Insulator Phase at the 1T-TaSe2 Surface

We present scanning tunneling microscopy (STM) measurements at the TaSe2 surface showing a first order process leading to a surface Mott transition. This metal to insulator transition is triggered by the commensurate charge density wave (CDW) which set up at 475 K. The electronic structure rearrangement due to the new periodicity gives rise to a half filled sub-band prone to the localization phenomena. This transition results fully developed below 250 K in agreement with previous photoemission measurements.