Collective Amplitude Mode Research Articles

Observation of room-temperature amplitude mode in quasi-one-dimensional charge-density-wave material CuTe

We have performed in-plane electrical transport and polarized Raman spectroscopy measurements on layered material CuTe to characterize the quasi-one-dimensional charge density wave (CDW). Along with the CDW formation below TCDW ∼346 K, the a-axis resistivity shows a huge hump, but the b-axis resistivity exhibits no evident anomaly, manifesting the quasi-one-dimensional character of the CDW. Concomitantly, a rapid rise in positive Hall coefficient is observed due to partial gaping out of the Fermi surface. Based on our Raman scattering measurement, we observe two Raman-active phonon modes in the non-CDW state and, additionally, one collective amplitude mode and four zone-folded modes in the CDW state. The phonon-mode shift with temperature clearly deviates from the expected anharmonic model upon approaching TCDW, suggesting strong electron–phonon coupling in driving the CDW transition. The amplitude mode even survives at room temperature and above, whose evolution can be described by a modified mean-field model, indicating a well-defined CDW order. These results, in addition to the simple formula and easy-to-exfoliate layered structure, promise CuTe as a model system to study the Peierls-like CDW physics and hold great potentials for CDW-based applications.

Higgs-mode resonance in third harmonic generation in NbN superconductors: Multiband electron-phonon coupling, impurity scattering, and polarization-angle dependence

We theoretically investigate the resonance of third harmonic generation (THG) that has been observed at frequency being half of the superconducting gap in a multiband disordered superconductor NbN. The central question is whether the dominant contribution to the THG resonance comes from the Higgs mode (the collective amplitude mode of the superconducting order parameter) or quasiparticle excitations. To resolve this issue, we analyze a realistic three-band model with effective intraband and interband phonon-mediated interactions estimated from first-principles together with nonmagnetic impurity scatterings. Using the estimated pairing interactions with multiband impurity scattering rates being varied from clean to dirty regimes, we calculate the THG susceptibility for NbN in a channel-resolved manner by means of the BCS and self-consistent Born approximations. In the dirty regime, which is close to the experimental situation, the leading contribution is given by the paramagnetic channel of the Higgs mode having almost no polarization-angle dependence, while the second leading contribution comes from the paramagnetic channel of quasiparticles generally showing significant polarization-angle dependence. The result is consistent with the recent experimental observation of no polarization-angle dependence of THG, giving firm evidence that the Higgs mode dominantly contributes to the THG resonance in NbN superconductors.

Infrared Activation of the Higgs Mode by Supercurrent Injection in Superconducting NbN.

The Higgs mode in superconductors, i.e., the collective amplitude mode of the order parameter, does not associate with charge nor spin fluctuations, therefore it does not couple to the electromagnetic field in the linear response regime. Contrary to this common understanding, here, we demonstrate that if the dc supercurrent is introduced into the superconductor, the Higgs mode becomes infrared active and is directly observed in the linear optical conductivity measurement. We observed a sharp resonant peak at ω=2Δ in the optical conductivity spectrum of a thin-film NbN in the presence of dc supercurrent, showing a reasonable agreement with the recent theoretical prediction. The method as proven by this work opens a new pathway to study the Higgs mode in a wide variety of superconductors.

Stability of the light-induced hidden charge density wave state within the phase diagram of 1T−TaS2−xSex

The femtosecond transient optical spectroscopy is employed to study the relaxation dynamics of the equilibrium and hidden metastable charge-density-wave states in single crystals of $1T\text{\ensuremath{-}}{\mathrm{TaS}}_{2\ensuremath{-}x}{\mathrm{Se}}_{x}$ as a function of the Se doping $x$. Similar to pristine $1T\text{\ensuremath{-}}{\mathrm{TaS}}_{2}$, the transition to a hidden phase is observed at low temperature after a quench with a single 50 fs laser pulse, in the commensurate Mott phase up to $x=0.6$. The photo-induced hidden-phase formation is accompanied by a notable change in the coherent phonon spectra, and particularly the collective amplitude mode. While the temperature stability of the hidden phase is only slightly dependent on the Se content, the creation-threshold fluence strongly increases with Se content from 1 to $\ensuremath{\sim}4$ mJ/${\mathrm{cm}}^{2}$, which is attributed predominantly to the change in optical absorption coefficient at the laser excitation wavelength, and not an increased barrier of the hidden state with increasing Se.

Damping of the collective amplitude mode in superconductors with strong electron-phonon coupling

We study the effect of strong electron-phonon interactions on the damping of the Higgs amplitude mode in superconductors by means of non-equilibrium dynamical mean-field simulations of the Holstein model. In contrast to the BCS dynamics, we find that the damping of the Higgs mode strongly depends on the temperature, becoming faster as the systen approaches the transition temperature. The damping at low temperatures is well described by a power-law, while near the transition temperature the damping shows exponential-like behavior. We explain this crossover by a temperature-dependent quasiparticle lifetime caused by the strong electron- phonon coupling, which smears the superconducting gap edge and makes the relaxation of the Higgs mode into quasiparticles more efficient at elevated temperatures. We also reveal that the phonon dynamics can soften the Higgs mode, which results in a slower damping.

Collective amplitude mode fluctuations in a flat band superconductor formed at a semimetal surface

We study the fluctuations of the amplitude (i.e. the Higgs-Anderson) mode in a superconducting system of coupled Dirac particles proposed as a model for possible surface or interface superconductivity in rhombohedral graphite. We show that the absence of Fermi energy and vanishing of the excitation gap of the collective amplitude mode in the model leads to a large fluctuation contribution to thermodynamic quantities such as the heat capacity. As a consequence, the mean-field theory becomes inaccurate indicating that the interactions lead to a strongly correlated state. We also present a microscopic derivation of the Ginzburg-Landau theory corresponding to this model.

Coherent structural dynamics of a prototypical charge-density-wave-to-metal transition.

Using femtosecond time-resolved x-ray diffraction, we directly monitor the coherent lattice dynamics through an ultrafast charge-density-wave-to-metal transition in the prototypical Peierls system K(0.3)MoO(3) over a wide range of relevant excitation fluences. While in the low fluence regime we directly follow the structural dynamics associated with the collective amplitude mode; for fluences above the melting threshold of the electronic density modulation we observe a transient recovery of the periodic lattice distortion. We can describe these structural dynamics as a motion along the coordinate of the Peierls distortion triggered by the prompt collapse of electronic order after photoexcitation. The results indicate that the dynamics of a structural symmetry-breaking transition are determined by a high-symmetry excited state potential energy surface distinct from that of the initial low-temperature state.

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.

Higgs Amplitude Mode in the BCS SuperconductorsNb1−xTixNInduced by Terahertz Pulse Excitation

Ultrafast responses of BCS superconductor Nb(1-x)Ti(x)N films in a nonadiabatic excitation regime were investigated by using terahertz (THz) pump-THz probe spectroscopy. After an instantaneous excitation with the monocycle THz pump pulse, a transient oscillation emerges in the electromagnetic response in the BCS gap energy region. The oscillation frequency coincides with the asymptotic value of the BCS gap energy, indicating the appearance of the theoretically anticipated collective amplitude mode of the order parameter, namely the Higgs amplitude mode. Our result opens a new pathway to the ultrafast manipulation of the superconducting order parameter by optical means.

Nonequilibrium damping of the collective motion of homogeneous cold Fermi condensates with Feshbach resonances

Collisionless damping of a condensate of cold Fermi atoms, whose scattering is controlled by a Feshbach resonance, is explored throughout the BCS and Bose-Einstein condensate (BEC) regimes when small perturbations on its phase and amplitude modes are turned on to drive the system slightly out of equilibrium. Using a one-loop effective action, we first recreate the known result that for a broad resonance the amplitude of the condensate decays as ${t}^{\ensuremath{-}1/2}$ at late times in the BCS regime, whereas it decays as ${t}^{\ensuremath{-}3/2}$ in the BEC regime. We then examine the case of an idealized narrow resonance, and find that this collective mode decays as ${t}^{\ensuremath{-}3/2}$ throughout both the BCS and BEC regimes. Although this seems to contradict earlier results that damping is identical for both broad and narrow resonances, the breakdown of the narrow resonance limit restores this universal behavior. More measurably, the phase perturbation may give a shift on the saturated value to which the collective amplitude mode decays, which vanishes only in the deep BCS regime when the phase and amplitude modes are decoupled.

Raman scattering evidence for a cascade evolution of the charge-density-wave collective amplitude mode

The two-dimensional rare-earth tritellurides undergo a unidirectional charge-density-wave (CDW) transition at high temperature and, for the heaviest members of the series, a bidirectional one at low temperature. Raman scattering experiments as a function of temperature on ${\text{DyTe}}_{3}$ and on ${\text{LaTe}}_{3}$ at 6 GPa provide a clear-cut evidence for the emergence of the respective collective CDW amplitude excitations. In the unidirectional CDW phase, we discover that the amplitude mode develops as a succession of two mean-field BCS-like transitions with different critical temperatures, which we associate with the presence of two adjacent Te planes in the structure.