Charge Density Wave Energy Gap Research Articles

Semiconductor-Metal Phase Transition and Emergent Charge Density Waves in 1T-ZrX2 (X = Se, Te) at the Two-Dimensional Limit.

A charge density wave (CDW) is a collective quantum phenomenon in metals and features a wavelike modulation of the conduction electron density. A microscopic understanding and experimental control of this many-body electronic state in atomically thin materials remain hot topics in materials physics. By means of material engineering, we realized a dimensionality and Zr intercalation induced semiconductor-metal phase transition in 1T-ZrX2 (X = Se, Te) ultrathin films, accompanied by a commensurate 2 × 2 CDW order. Furthermore, we observed a CDW energy gap of up to 22 meV around the Fermi level. Fourier-transformed scanning tunneling microscopy and angle-resolved photoemission spectroscopy reveal that 1T-ZrX2 films exhibit the simplest Fermi surface among the known CDW materials in TMDCs, consisting only of a Zr 4d derived elliptical electron conduction band at the corners of the Brillouin zone.

Interplay between charge density wave order and superconductivity in LaAuSb2 under pressure

We report superconductivity below ${T}_{\mathrm{c}}=0.64$ K in the charge density wave (CDW) ordered material ${\mathrm{LaAuSb}}_{2}$, from measurements of the electrical resistivity, specific heat, and ac magnetic susceptibility. To investigate the interplay between superconductivity and CDW order in ${\mathrm{LaAuSb}}_{2}$, we measured the resistivity under pressures up to 2.0 GPa and constructed the temperature-pressure phase diagram. With the application of pressure, ${T}_{\mathrm{c}}$ increases gradually before exhibiting a sudden jump at around 0.64 GPa, while the CDW order is suppressed to lower temperatures before abruptly vanishing at the same pressure. We suggest that the jump of ${T}_{\mathrm{c}}$ may be due to the enhancement of the density of states with the closure of the CDW energy gap when CDW order is suppressed. On the other hand, the normalized upper critical field ${H}_{\mathrm{c}2}$ changes little with pressure, suggesting that orbital limiting is the dominant pair-breaking mechanism in ${\mathrm{LaAuSb}}_{2}$.

Optical spectroscopy and ultrafast pump-probe study on Bi2Rh3Se2 : Evidence for charge density wave order formation

The parkerite-type ternary chalcogenide Bi$_2$Rh$_3$Se$_2$ was discovered to be a charge density wave (CDW) superconductor. However, there was a debate on whether the observed phase transition at 240 K could be attributed to the formation of CDW order. To address the issue, we performed optical spectroscopy and ultrafast pump-probe measurements on single crystal samples of Bi$_2$Rh$_3$Se$_2$. Our optical conductivity measurement reveals clearly the formation of an energy gap with associated spectral change only at low energies, yielding strong evidence for a CDW phase transition at 240 K. Time resolved pump-probe measurement provides further support for the CDW phase transition. The amplitude and relaxation time of quasiparticles extracted from the photoinduced reflectivity show strong enhancement near transition temperature, yielding further evidence for the CDW energy gap formation. Additionally, a collective mode is identified from the oscillations in the pump-probe time delay at low temperature. This mode, whose frequency decreases gradually at elevated temperature, could be naturally attributed to the amplitude mode of CDW state.

Short-range charge density wave order in 2H−TaS2

$2H\text{\ensuremath{-}}\mathrm{Ta}{\mathrm{S}}_{2}$ undergoes a charge density wave (CDW) transition at ${T}_{\mathrm{CDW}}\ensuremath{\sim}75$ K, however key questions regarding the onset of CDW order remain under debate. In this study, we explore the CDW transition through a combination of temperature and excitation-dependent Raman spectroscopy, angle resolved photoemission spectroscopy (ARPES), and density functional theory (DFT). Below ${T}_{\mathrm{CDW}}$ we identify two CDW amplitude modes that redshift and broaden with increasing temperature and one zone-folded mode that disappears above ${T}_{\mathrm{CDW}}$. Above ${T}_{\mathrm{CDW}}$, we observe a strong two-phonon mode that softens substantially upon cooling, which suggests the presence of substantial lattice distortions at temperatures as high as 250 K. This correlates with the ARPES observation of the persistence of a CDW energy gap above ${T}_{\mathrm{CDW}}$ and finite-temperature DFT calculations of the phonon band structure that indicate an instability occurring well above the CDW transition temperature. DFT also provides the atomic displacements of the CDW amplitude modes and reproduces their temperature dependence. From these observations we suggest that short range CDW order exists well above ${T}_{\mathrm{CDW}}$, which poses new questions regarding the interplay between electronic structure and vibrational modes in layered CDW materials.

Temperature dependence of resistivity at the transition to a charge density wave state in rare-earth tritellurides

About a half of the Fermi surface in rare-earth tritellurides, RTe3 becomes gapped below the transition to a charge-density-wave (CDW) state, as revealed by ARPES data. However, the observed jump in resistivity during the CDW transition is less than 20%. Previously this phenomenon was explained by hypothesizing a very slow evolution of CDW energy gap below transition temperature in RTe3 compounds, which contradicts the X-ray measurements. Here we show that this weak change in resistivity can be explained in the framework of standard mean-field temperature dependence of the CDW energy gap in agreement with X-ray data. The change of resistivity caused by CDW is weak because the decrease in conducting electron density at the Fermi level is almost compensated by the decrease in their scattering rate. We calculate resistivity in RTe3 compounds using the Boltzmann transport equation and the mean-field description of the CDW state, and obtain a good agreement with experimental data.

Putting the gap on the map

The measurement of the charge density wave energy gap in high-temperature superconducting cuprates uncovers new links between competing states.

Strain Engineering a 4a×√3a Charge Density Wave Phase in Transition Metal Dichalcogenide 1T-VSe2.

We report a rectangular charge density wave (CDW) phase in strained 1T-VSe2 thin films synthesized by molecular beam epitaxy on c-sapphire substrates. The observed CDW structure exhibits an unconventional rectangular 4a×√3a periodicity, as opposed to the previously reported hexagonal 4a×4a structure in bulk crystals and exfoliated thin layered samples. Tunneling spectroscopy shows a strong modulation of the local density of states of the same 4a×√3a CDW periodicity and an energy gap of 2ΔCDW = (9.1 ± 0.1) meV. The CDW energy gap evolves into a full gap at temperatures below 500 mK, indicating a transition to an insulating phase at ultra-low temperatures. First-principles calculations confirm the stability of both 4a×4a and 4a×√3a structures arising from soft modes in the phonon dispersion. The unconventional structure becomes preferred in the presence of strain, in agreement with experimental findings.

Optical spectroscopy study of charge density wave order in Sr3Rh4Sn13 and (Sr0.5Ca0.5)3Rh4Sn13

We perform optical spectroscopy measurement across the charge density wave (CDW) phase transitions on single-crystal samples of Sr$_{3}$Rh$_{4}$Sn$_{13}$ and (Sr$_{0.5}$Ca$_{0.5}$)$_{3}$Rh$_{4}$Sn$_{13}$. Formation of CDW energy gap was clearly observed for both single-crystal samples when they undergo the phase transitions. The existence of a Drude component in $\sigma_1(\omega)$ below \TCDW indicates that the Fermi surface is only partially gapped in the CDW state. The obtained value of 2$\Delta$/K$_{B}$T$_{CDW}$ is roughly 13 for both Sr$_{3}$Rh$_{4}$Sn$_{13}$ and (Sr$_{0.5}$Ca$_{0.5}$)$_{3}$Rh$_{4}$Sn$_{13}$ compounds. The value is considerably larger than the mean-field value based on the weak-coupling BCS theory. The observed spectral feature in (Sr$_{x}$Ca$_{1-x}$)$_{3}$Rh$_{4}$Sn$_{13}$ resembles those seen in many other CDW systems.

Superconducting energy gap of2H−NbSe2in phonon spectroscopy

We present a high energy-resolution inelastic x-ray scattering data investigation of the charge-density-wave (CDW) soft phonon mode upon entering the superconducting state in $2H$-NbSe$_2$. Measurements were done close to the CDW ordering wavevector $\mathbf{q}_{CDW}$ at $\mathbf{q}=\mathbf{q}_{CDW}+(0,0,l)$,$0.15\leq l \leq 0.5$, for $T=10\,\rm{K}$ (CDW order) and $3.8\,\rm{K}$ (CDW order + superconductivity). We observe changes of the phonon lineshape that are characteristic for systems with strong electron-phonon coupling in the presence of a superconducting energy gap $2\Delta_c$ and from which we can demonstrate an $l$-dependence of the superconducting gap. Reversely, our data imply that the CDW energy gap is strongly localized along the $c^*$ direction. The confinement of the CDW gap to a very small momentum region explains the rather low competition and easy coexistence of CDW order and superconductivity in $2H$-NbSe$_2$. However, the energy gained by opening $\Delta_{CDW}$ seems to be too small to be the driving force of the phase transition at $T_{CDW}=33\,\rm{K}$ , which is better described as an electron-phonon coupling driven structural phase transition.

Magnetic susceptibility ofYBa2Cu3O6+xcrystals: Unusual Curie behavior and small contributions from charge density waves

We report measurements of the magnetic susceptibility of twinned single crystals of YBa$_{2}$Cu$_{3}$O$_{6+x}$ from just above their superconducting transition temperatures to 300 K with magnetic fields of up to 5 T applied parallel and perpendicular to the CuO$_2$ planes at 7 values of $x$. Appropriate analysis allows the relatively small, but still important, Curie terms to be separated from other contributions to the susceptibility. Our data support a picture in which the Curie terms arise from oxygen disorder in the Cu-O chains. This agrees with published work on polycrystalline samples where the sample cooling rate was varied, but here we show that the Curie plots flatten out above 200 K. We identify small effects of charge density wave (CDW) instabilities in the temperature ($T$) derivative of the in-plane susceptibility $d\chi_{ab}(T)/dT$ and discuss their $x$-dependence. For $x=$0.67 we make a detailed comparison with published high energy X-ray diffraction data using a minimal model involving Fermi arcs, thereby obtaining values for the CDW energy gap and the Helmholtz free energy in a coherence volume. At 80 and 100 K the latter is comparable with, or smaller than $k_BT$ respectively, highlighting the probable importance of thermal fluctuations. We note that the effect of the Lorentz force on charge carriers in the Fermi arcs could provide a simple mechanism for enhancing the CDWs in high magnetic fields, as suggested by recent experiments.

Revealing multiple charge-density-wave orders inTbTe3by optical conductivity and ultrafast pump-probe experiments

Rare-earth tri-tellurium RTe$_3$ is a typical quasi-two dimensional system which exhibits obvious charge density wave (CDW) orders. So far, RTe$_3$ with heavier R ions (Dy, Ho, Er and Tm) are believed to experience two CDW phase transitions, while the lighter ones only hold one. TbTe$_3$ is claimed to belong to the latter. However in this work we present evidences that TbTe$_3$ also possesses more than one CDW order. Aside from the one at 336 K, which was extensively studied and reported to be driven by imperfect Fermi surface nesting with a wave vector $q=(2/7 c^*)$, a new CDW energy gap (260 meV) develops at around 165 K, revealed by both infrared reflectivity spectroscopy and ultrafast pump-probe spectroscopy. More intriguingly, the origin of this energy gap is different from the second CDW order in the heavier R ions-based compounds RTe$_3$ (R=Dy, Ho, Er and Tm).

Coherent dynamics of the charge density wave gap in tritellurides.

The dynamics of the transient electronic structure in the charge density wave (CDW) system RTe3 (R = rare-earth element) is studied using time- and angle-resolved photoemission spectroscopy (trARPES). Employing a three-pulse pump-probe scheme we investigate the effect of the amplitude mode oscillations on the electronic band structure and, in particular, on the CDW energy gap. We observe coherent oscillations in both lower and upper CDW band with opposite phases, whereby two dominating frequencies are modulating the CDW order parameter. This demonstrates the existence of more than one collective amplitude mode, in contrast to a simple Peierls model. Coherent control experiments of the two amplitude modes, which are strongly coupled in equilibrium, demonstrate independent control of the modes suggesting a decoupling of both modes in the transient photoexcited state.

Effect of disorder in the charge-density-wave compounds LaTe1.95and CeTe1.95−xSex(x=0and 0.16) as revealed by optical spectroscopy

We present optical spectroscopy measurements on rare-earth ditelluride single crystals of LaTe$_{1.95}$ and CeTe$_{1.95-x}$Se$_x$ (x=0 and 0.16). The measurements reveal formation of charge density wave energy gaps at rather high energy levels, e.g. 2$\Delta\sim$ 8500 \cm for LaTe$_{1.95}$, and 6800 \cm for CeTe$_{1.95}$. More strikingly, the study reveals that, different from the rare-earth tri-tellurides, the Te vacancies and disorder effect play a key role in the low-energy charge excitations of ditelluride systems. Although an eminent peak is observed between 800 and 1500 \cm in conductivity spectra for LaTe$_{1.95}$, and CeTe$_{1.95-x}$Se$_x$ (x=0. 0.16), our analysis indicates that it could not be attributed to the formation of a small energy gap, instead it could be well accounted for by the localization modified Drude model. Our study also indicates that the low-tempreature optical spectroscopic features are distinctly different from a semiconducting CDW state with entirely gapped Fermi surfaces.

Coexistence of Bulk Superconductivity and Charge Density Wave inCuxZrTe3

We report the coexistence of bulk superconductivity with T(c)=3.8 K and charge density wave (CDW) in Cu intercalated quasi-two-dimensional crystals of ZrTe(3). The Cu intercalation results in the expansion of the unit cell orthogonal to the Zr-Zr metal chains and partial filling of CDW energy gap. We present anisotropic parameters of the superconducting state. We also show that the contribution of CDW to the scattering mechanism is anisotropic in the a-b plane. The dominant scattering mechanism in the normal state for both ZrTe(3) and Cu(0.05)ZrTe(3) along the b axis is the electron-electron umklapp scattering.

Optical spectroscopy study on CeTe3: Evidence for multiple charge-density-wave orders

We performed optical spectroscopy measurement on single crystal of CeTe$_3$, a rare-earth element tri-telluride charge density wave (CDW) compound. The optical spectra are found to display very strong temperature dependence. Besides a large and pronounced CDW energy gap being present already at room temperature as observed in earlier studies, the present measurement revealed the formation of another energy gap at smaller energy scale at low temperature. The second CDW gap removes the electrons near E$_F$ which undergo stronger scattering. The study yields evidence for the presence of multiple CDW orders or strong fluctuations in the light rare-earth element tri-telluride.

Electromechanical resonators as probes of the charge density wave transition at the nanoscale inNbSe2

We study nanoelectromechanical resonators fabricated from suspended flakes of ${\text{NbSe}}_{2}$ $(\text{thickness}\ensuremath{\sim}30--50\text{ }\text{nm})$ to probe charge density wave (CDW) physics at nanoscale. Variation in elastic and electronic properties accompanying the CDW phase transition (around 30 K) are investigated simultaneously using the devices as self-sensing heterodyne mixers. Elastic modulus is observed to change by 10%, an amount significantly larger than what had been reported earlier in the case of bulk crystals. We also study the modulation of conductance by electric field effect, and examine its relation to the order parameter and the CDW energy gap at the Fermi surface.

Coherent-noncoherent tunneling crossover inNbSe3−NbSe3point contacts

Current-voltage $(IV)$ characteristics of $\mathrm{Nb}{\mathrm{Se}}_{3}\text{\ensuremath{-}}\mathrm{Nb}{\mathrm{Se}}_{3}$ artificial contacts (point contacts) formed along the ${a}^{*}$ axis have been investigated in a wide range of contact resistances and temperatures. Depending on the contact resistance, two types of $IV$ characteristics have been observed: the first type observed for low contact resistance demonstrates a conducting peak at zero bias, while the second one for large contact resistance is characterized by a large resistance maximum near the zero bias voltage. Below the second charge-density wave (CDW) transition $(Tl59\phantom{\rule{0.3em}{0ex}}\mathrm{K})$, CDW energy gap singularities were observed in the $IV$ characteristics of both types of junctions at $V={\ensuremath{\Delta}}_{p1}∕e$ and $V=2{\ensuremath{\Delta}}_{p2}∕e$, while the singularity at $V={\ensuremath{\Delta}}_{p2}∕e$ corresponding to the single particle tunneling of carriers noncondensed into the low-temperature CDW is absent. The experimental results are discussed in the frame of the model of interlayer coherent tunneling of the remaining charge carriers that are not condensed into the CDW.

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

The differential tunnel conductance GS 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 GS(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 Bi2Sr2CaCu2O8+δ and other high-temperature oxides

A theory of the energy dependent STM image of a charge density wave

taken at low-temperature (4.2 K). This layered material is in a charge density wave (CDW) state below 35 K, with a period nearly commensurate to three times the atomic lattice. The CDW energy gap is 2Δ≈70 meV, but still the material remains metallic, even superconducting below 7.2 K. The bias-dependent phase shift in the STM image, in particular the comparison between occupied and unoccupied states, was shown to be attributable to the CDW, as no phase shift was observed in the atomic pattern. This phase shift does not result in a contrast reversal, which could be expected by analogy to some semi-conductor band gaps. The electron versus hole distribution has not been solved for a CDW gap, which is quite complex due to the many-band situation near the Fermi level. In the present work we write a general expression for the local density of states (LDOS) due to a commensurate CDW. Its amplitude and phase can be related in a simple way to the band structure, if one assumes an approximate form for the surface Bloch functions. We apply the method to the example of NbSe2, where its electronic structure is taken to be two-dimensional and the CDW is exactly commensurate to 3a. The new band structure and Fermi surface in the CDW state is calculated in perturbation theory, with a suitable pseudo-potential. The energy-dependent contrast is due to new states on the order of EF±Δ, having characteristic phases. The amplitude of the CDW is largest at the particular energies (or voltages) where tunneling occurs to the high symmetry points of the Brillouin zone. At these energies, the phase of the LDOS varies considerably, which gives a number of possible motifs in the STM image. For a shift in voltage corresponding to the energy gap edges, E=EF±Δ, we find that the maxima of the corrugation are shifted along the diagonal of the conventional unit cell.

Electronic Structure of Layered and Linear Chain Materials by Scanning Probe Microscopy

ABSTRACTTransition metal impurities such as Fe, Ni, and Co can be intercalated into the van der Waals gap of layer structure dichalcogenides and these modify the charge-density wave (CDW) structure and CDW energy gaps. Ordered superlattices associated with antiferromagnetic phases can be detected by both scanning tunneling microscopy (STM) and atomic force microscopy (AFM). STM spectroscopy indicates the formation of a mixed spin-density-wave (SDW) and CDW (SDWCDW) in the doped materials. The quasi-one dimensional trichalcogenide NbSe3 exhibits two CDW transitions and the presence of dilute transition metal impurities produces ordered superlattices due to long range screening of the impurities.