Distinct Amplitude Mode Dynamics Upon Resonant and Off-resonant Excitation Across the Charge Density Wave Energy Gap in LaTe3 Investigated by Time- and Angle-resolved Photoemission Spectroscopy

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.

We conduct Angle Resolved Photoemission Spectroscopy (ARPES) investigation on 2H -TaS 2 , a prototypical incommensurate Charge Density Wave (CDW) material. A comparative study of the low-energy electronic structures of 2H -TaS 2 and two other related compounds, 2H -TaSe 2 and 2H -NbSe 2 , identifies several generic features of their CDW orders. Firstly, Fermi surface (FS) nesting alone doesn’t seem to give rise to the CDW instability in these compounds. Secondly, partial gapping of the underlying FS surface in the CDW state is common to each of these materials. Finally, the CDW energy gap, unlike the energy gap in a superconductor, is not symmetric with respect to the chemical potential.

We investigate photocurrent generation mechanisms in a pentacene single-molecule junction using subnanometer resolved photocurrent imaging under both on- and off-resonance laser excitation. By employing a wavelength-tunable laser combined with a lock-in technique, net photocurrent signals are extracted to elucidate photoinduced electron tunneling processes. Under off-resonance excitation, photocurrents are found to arise from photon-assisted tunneling, with contributions from three distinct frontier molecular orbitals at different bias voltages. In contrast, under resonance excitation, photocurrents are found to be significantly enhanced at negative bias voltages, exhibiting a spatial distribution linked to molecular electronic transitions and associated transition dipoles. This study reveals the contributions of different frontier molecular orbitals in the photon-assisted tunneling processes under off-resonance excitation, while molecular optical transitions are also found to be important at negative bias under resonance excitation. These findings could be instructive to the design and optimization of advanced optoelectronic devices.

Recent Advances in Topological Quantum Materials by Angle-Resolved Photoemission Spectroscopy

Tunneling investigation of charge density wave energy gap in IT-TaS 2

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.

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).

8. Charge-Density Waves

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

Phonon dynamics of the charge density wave (CDW) state in the Frohlich model are investigated. It is shown by analyzing the energy and wave vector dependence of the phonon self energy that in addition to the usual phase mode the amplitude mode always lies below 2Ll at the long wave length limit (Ll is the CDW energy gap), namely it is split off from the continuum lying above 2Ll. This leads to the conclusion that the energy dependence of the self energy is crucial in determining the phonon spectrum.

The pressure dependence of the de Haas – van Alphen frequency in oriented potassium samples has been investigated with pressures up to 4.6 kbar. The change of frequency with pressure is less than that expected from free-electron scaling and the Fermi surface anisotropy increases from 0.13% at zero pressure to 0.47% at 4 kbar. These results are discussed in terms of band structure calculations and the charge density wave (CDW) model of potassium. The CDW energy gap changes with pressure for the CDW model to be applicable.

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.

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.

We investigate the indistinguishability of single photons retrieved from collective Rydberg excitations in cold atomic ensembles. The Rydberg spin waves are created either by off resonant two-photon excitation to the Rydberg state or by Rydberg electromagnetically induced transparency. To assess the indistinguishability of the generated single photons, we perform Hong-Ou-Mandel experiments between the single photons and weak coherent states of light. We analyze the indistinguishability of the single photons as a function of the detection window and for photons generated by off-resonant excitation we infer high value of indistinguishability going from 89% for the full waveform to 98% for small detection windows. In the same way, we also investigate for the first time the indistinguishability of single photons generated by Rydberg EIT, showing values lower than those corresponding to single photons generated by off-resonant excitation. These results are relevant for the use of Rydberg atoms as quantum network nodes.

The Scanning tunneling microscope (STM) has been used to study the effects of Fe doping on the charge-density wave (CDW) structure in NbSe{sub 3} and 1T-TaS{sub 2}. In NbSe{sub 3} small amounts of Fe reduce both CDW gaps by 25--30% and change the relative CDW amplitudes of the high and low temperature CDWs. The CDW amplitudes remain strong on all three chains of the surface unit cell with no evident disorder. In 1T-Fe{sub 0.05}Ta{sub 0.95}S{sub 2} the Fe introduces substantial disorder in the CDW pattern, but the local CDW amplitude remains strong. The CDW energy gap is reduced by approximately 50% and the resistive anomaly at the commensurate-incommensurate transition is removed. The STM in both the image and spectroscopy modes can detect subtle changes in CDW structure due to impurities.