Roton Energy Research Articles

Raman spectroscopy of bimagnon and trimagnon excitations and rotonlike points in a distorted triangular lattice antiferromagnet

We investigate the experimental signatures of Raman spectroscopy of bi- and tri-magnon excitations in the distorted triangular lattice antiferromagnets alpha-LCr2O4 (L=Sr, Ca). We utilize spin wave theory to analyze the nearly 120 degree spin-3/2 spiral ordered antiferromagnetic ground state to compute the single-magnon density of states, single-magnon dispersion, and bimagnon and trimagnon Raman spectra (polarized and unpolarized). It is found that Raman scattering is capable of capturing the effect of the rotonlike M and M' points on the bimagnon Raman spectrum. Our calculation confirms the connection between single-magnon rotonlike excitation energy and bimagnon Raman excitation spectrum observed experimentally. The roton energy minimum in momentum space is half of the energy of a bimagnon excitation signal. The experimental magnetic Raman scattering result displays two peaks which have a Raman shift of 15 meV and 40 meV, respectively. Theoretical modeling and analysis of the experimental spectrum of alpha-SrCr2O4 within our distorted Heisenberg Hamiltonian lattice suggests that the low-energy peak at 15 meV is associated with the bimagnon excitation, whereas the high-energy peak around 40 meV is primarily a trimagnon excitation. Based on our fitting procedure we propose a new set of magnetic interaction parameters for alpha-SrCr2O4. These parameters reproduce not only the experimental Raman spectrum, but also the inelastic neutron scattering response (including capturing high energy magnon branches). We also compute the unpolarized bimagnon and trimagnon Raman spectra for alpha-CaCr2O4. Furhtermore, we found that the polarization sensitivity of Raman spectrum can be utilized to distinguish the bi- and tri-magnon excitation channels.

Roton excitation in overpressurized superfluid He4

We carry out a theoretical investigation of overpressurized superfluid phases of He-4 by means of quantum Monte Carlo (QMC) simulations. As a function of density, we study structural and superfluid properties, and estimate the energy of the roton excitation by inverting imaginary-time density correlation functions computed by QMC, using Maximum Entropy. We estimate the pressure at which the roton energy vanishes to be about 100 bars, which we identify with the spinodal density, i.e., the upper limit for the existence of a metastable superfluid phase.

Neutral collective excitation in fractional quantum Hall effect at Jain series

We have studied collective excitation almost all of the filling fraction, in the Jain series of positive flux attachment states. In this article we have presented excitation spectrum of all positive flux attachment states for a real two dimensional electron system to get the complete scenario. The fundamental roton energy becomes zero at the filling fractions associated with four pair of magnetic flux quanta attachment composite fermion, which suggest that there is a limitation of flux attachment to the electron to form a composite fermion in fractional quantum Hall effect. The roton energy and energy gap become zero at filling fraction ν=1/2, which shows that the gapless state ν=1/2 can be naturally obtained as an extrapolation of the collective excitation of the incompressible gaped states.

Roton Excitations and the Fluid–Solid Phase Transition in Superfluid 2D Yukawa Bosons

We compute several ground state properties and the dynamical structure factor of a 0-temperature system of Bosons interacting with the 2D screened Coulomb (2D-SC) potential. We resort to the exact shadow path integral ground state (SPIGS) quantum Monte Carlo method to compute the imaginary-time correlation function of the model, and to the genetic algorithm via falsification of theories (GIFT) to retrieve the dynamical structure factor. We provide a detailed comparison of ground state properties and collective excitations of 2D-SC and 4He atoms. The roton energy of the 2D-SC system is an increasing function of density, and not a decreasing one as in 4He. This result is in contrast with the view that the roton is the soft mode of the fluid-solid transition. We uncover a remarkable quasi-universality of backflow and of other properties when expressed in terms of the amount of short range order as quantified by the height of the first peak of the static structure factor.

Phonon-roton modes of liquid4He beyond the roton in the porous medium MCM-41

We present neutron scattering measurements of the phonon-roton (P-R) mode of superfluid ${}^{4}$He confined in 47 \AA{} MCM-41 at $T=0.5$ K at wave vectors, $Q$, beyond the roton wave vector (${Q}_{R}=1.92$ \AA{}${}^{\ensuremath{-}1}$). Measurements beyond the roton require access to high wave vectors (up to $Q=4$ \AA{}${}^{\ensuremath{-}1}$) with excellent energy resolution and high statistical precision. Only one previous measurement in porous media (in aerogel) with low statistical precision has been reported. At $T=0.5$ K, we find that the P-R mode in MCM-41 extends out to wave vector $Q\ensuremath{\simeq}3.6$ \AA{}${}^{\ensuremath{-}1}$, with the same energy and zero width (within precision) as observed in bulk superfluid ${}^{4}$He. Layer modes in the roton region are also observed. Specifically, the P-R mode energy, ${\ensuremath{\omega}}_{Q}$, increases with $Q$ for $Q>{Q}_{R}$ and reaches a plateau at a maximum energy ${\ensuremath{\omega}}_{Q}=2\ensuremath{\Delta}$ where $\ensuremath{\Delta}$ is the roton energy, $\ensuremath{\Delta}=0.74$ $\ifmmode\pm\else\textpm\fi{}$ 0.01 meV in MCM-41. This upper limit means the P-R mode decays to two rotons if its energy exceeds 2$\ensuremath{\Delta}$. It also means that the P-R mode does not decay to two-layers modes. If the P-R could decay to two-layer modes, ${\ensuremath{\omega}}_{Q}$ would plateau at a lower energy, ${\ensuremath{\omega}}_{Q}=2{\ensuremath{\Delta}}_{L}$, where ${\ensuremath{\Delta}}_{L}=0.60$ meV is the energy of the roton-like minimum of the layer mode. Rather the P-R mode and the layer modes observed in porous media appear to be quite different modes with little interaction between them.

Two-dimensional dipolar Bose gas with the roton-maxon excitation spectrum

We discuss fluctuations in a dilute two-dimensional Bose-condensed dipolar gas, which has a roton-maxon character of the excitation spectrum. We calculate the density-density correlation function, fluctuation corrections to the chemical potential, compressibility, and the normal (superfluid) fraction. It is shown that the presence of the roton strongly enhances fluctuations of the density, and we establish the validity criterion of the Bogoliubov approach. At T=0 the condensate depletion becomes significant if the roton minimum is sufficiently close to zero. At finite temperatures exceeding the roton energy, the effect of thermal fluctuations is stronger and it may lead to a large normal fraction of the gas and compressibility.

Roton-Phonon Interactions in SuperfluidHe4

High-resolution neutron resonance spin-echo measurements of superfluid 4He show that the roton energy does not have the same temperature dependence as the inverse lifetime. Diagrammatic analysis attributes this to the interaction of rotons with thermally excited phonons via both four- and three-particle processes, the latter being allowed by the broken gauge symmetry of the Bose-condensate. The distinct temperature dependence of the roton energy at low temperatures suggests that the net roton-phonon interaction is repulsive.

Microscopic characterization of overpressurized superfluid4He

We have studied static and dynamical properties of superfluid ${}^{4}$He at $T=0$ K in the pressure range from $\ensuremath{-}6$ up to 87 atm well above freezing into the metastable region. Zero temperature properties have been obtained with the exact shadow path integral ground state (SPIGS) method. Information about dynamic structure factors at different pressures have been obtained from imaginary time correlation functions via the genetic inversion via falsification of theories (GIFT) method. In the full pressure range sharp roton excitations are always present in the spectral functions. The roton energy decreases at higher pressures in good agreement with experimental data also in the metastable region. The roton energies have essentially a linear trend with pressure, going from about 7.4 K near freezing to about 4.3 K at about 87 atm. The pressure at which the linear trend would extrapolate to a zero roton energy turns out to be about 170 atm. At $T=0$ K, no sign of metastable glass phase has been found; the disordered systems studied at pressures above about 87 atm readily start homogeneous nucleation processes. Our results in the metastable phase for the condensate fractions and roton gaps differ remarkably from previous ones obtained via a diffusion Monte Carlo study.

Fractional quantum Hall edge: Effect of nonlinear dispersion and edge roton

According to Wen's theory, a universal behavior of the fractional quantum Hall edge is expected at sufficiently low energies, where the dispersion of the elementary edge excitation is linear. A microscopic calculation shows that the actual dispersion is indeed linear at low energies, but deviates from linearity beyond certain energy, and also exhibits an ``edge roton minimum.'' We determine the edge exponent from a microscopic approach, and find that the nonlinearity of the dispersion makes a surprisingly small correction to the edge exponent even at energies higher than the roton energy. We explain this insensitivity as arising from the fact that the energy at maximum spectral weight continues to show an almost linear behavior up to fairly high energies. We also study, in an effective-field theory, how interactions modify the exponent for a reconstructed edge with multiple edge modes. Relevance to experiment is discussed.

Many-Body Fluctuations and the Dynamics of Liquid 4He

It has been firmly established that dynamic pair fluctuations make important contributions to medium- and short-wavelength behavior of the dynamic structure function of superfluid 4He. These fluctuations have, so far, been treated in the so-called “uniform limit approximation.” In the first part of this work we show that the full solution of the equation of motion for pair fluctuations does not significantly change the results of the time-honored uniform limit approximation. However, pair fluctuations still fall significantly short of fully accounting for the medium-wavelength structure of the elementary excitation spectrum, i.e. the roton energy, and the energy of the short wavelength plateau seen in the dynamic structure function as measured by neutron scattering. Here we show how the inclusion of dynamic triplet fluctuations produces very satisfactory agreement with experiment. Insight into these results is obtained by examining them in terms of correlated Brillouin-Wigner perturbation theory just as it did for the physics of the contributions of pair fluctuations in previous work.

Dynamics of a Two-Dimensional System of Quantum Dipoles

A detailed microscopic analysis of the dynamic structure function S(k,omega) of a two-dimensional Bose system of dipoles polarized along the direction perpendicular to the plane is presented and discussed. Starting from ground-state quantities obtained using a quantum diffusion Monte Carlo algorithm, the density-density response is evaluated in the context of the correlated basis functions (CBF) theory. CBF predicts a sharp peak and a multiexcitation component at higher energies produced by the decay of excitations. We discuss the structure of the phonon-roton peak and show that the Feynman and Bogoliubov predictions depart from the CBF result already at low densities. We finally discuss the emergence of a roton in the spectrum, but find the roton energy not low enough to make the system unstable under density fluctuations up to the highest density considered that is close to the freezing point.

PAIR EXCITATIONS AND VERTEX CORRECTIONS IN FERMI FLUIDS AND THE DYNAMIC STRUCTURE FUNCTION OF TWO-DIMENSIONAL 3He

We use the equations–of–motion approach for time–dependent pair correlations in strongly interacting Fermi liquids to develop a theory of the excitation spectrum and the single–particle self energy in such systems. We present here the fully correlated equations and their approximate solutions for 3 He . Our theory has the following properties: It reduces to both, i) the "correlated" random–phase approximation (RPA) for strongly interacting fermions if the two–particle–two–hole correlations are ignored, and, ii) to the correlated Brillouin–Wigner perturbation theory for boson quantum fluids in the appropriate limit. iii) It preserves the two first energy–weighted sum rules, and systematically improves upon higher ones. iv) A familiar problem of the standard RPA is that it predicts a roton energy that lies more than a factor of two higher than what is found in experiments. A popular cure for this is to introduce an effective mass in the Lindhard function. No such ad–hoc assumption is invoked in our work. We demonstrate that the inclusion of correlated pair–excitations improves the dispersion relation significantly. Finally, a novel form of the density response function is derived that arises from vertex corrections in the proper polarization.

High-resolution roton spectra around the superfluid transition temperature in liquid 4He

We show for the first time high-resolution excitation spectra of bulk superfluid and liquid 4He obtained in a wide energy range (0–3meV) in a broad temperature interval 0.6–2.5K. The experiments were performed at 0.4bar constant liquid pressure on the time-of-flight crystal analyser neutron spectrometer IRIS at the ISIS Facility. There is a real gap in resolution between neutron spin echo or exact-backscattering spectroscopy and other conventional time-of-flight or triple-axis-spectrometer measurements, which at the moment can only be covered by IRIS. The unique combination of high resolution and wide dynamic range accessible on this inverted geometry spectrometer allowed for a non-conventionally detailed line-shape analysis of the roton excitations and made possible the separation of the roton and the higher-energy broad components. We provide the high-resolution evidence of a remainder single-phonon response at the extrapolated roton energy above Tλ. We conclude that the superfluid phase transition manifests itself in the strong slowdown of the variation of the single-phonon line shape with increasing temperature, rather than in the total disappearance of the signal.

Quantum Monte Carlo Simulation of Overpressurized LiquidHe4

A diffusion Monte Carlo simulation of superfluid 4He at zero temperature and pressures up to 275 bar is presented. Increasing the pressure beyond freezing (approximately 25 bar), the liquid enters the overpressurized phase in a metastable state. In this regime, we report results of the equation of state and the pressure dependence of the static structure factor, the condensate fraction, and the excited-state energy corresponding to the roton. Along this large pressure range, both the condensate fraction and the roton energy decrease but do not become zero. The roton energies obtained are compared with recent experimental data in the overpressurized regime.

Two-Dimensional Bose-Einstein Condensate under Extreme Rotation

We show that a Bose-condensed gas, under extreme rotation in a 2D anisotropic trap, forms a novel elongated quantum fluid which has a roton-maxon excitation spectrum. For a sufficiently large interaction strength, the roton energy reaches zero and the system undergoes a second order quantum transition to the state with a periodic structure-rows of vortices. The number of rows increases with the interaction, and the vortices eventually form a triangular Abrikosov lattice.

Implementation of a zero-field spin-echo option at the three-axis spectrometer IN3 (ILL, Grenoble) and first application for measurements of phonon line widths in superfluid 4He

We report on a new zero-field spin-echo spectrometer (ZETA), installed at the thermal three-axis spectrometer IN3 at ILL, Grenoble. In this technique the two long precession solenoids from neutron spin echo are replaced by two pairs of magnetic resonance coils in a zero-field region. This allows easy adaptation of tilted field geometries, necessary for measurements of phonon line widths with μeV energy resolution. First test measurements of the roton line width and energy shift as well as line width of the low- Q phonon and in the “region beyond the roton” in superfluid 4He are described. The results are in agreement with the literature and show the good operation of ZETA. The implementation of ZETA at the high-flux three-axis spectrometer IN20, foreseen in the near future, will increase the count rate by typically one order of magnitude.

Roton Excitation Spectrum in Liquid Helium II

We derive a one-particle quantum equation for roton excitations by considering rotons as bound states of helium atoms. Our approach is based on a self-similar solution of the nonlinear Schr\odinger equation with a self-consistent confining potential in a roton cluster surrounded by the condensate. The symmetric vibrational excitation of the roton determines the gap in the energy spectrum of the elementary excitations in liquid He II. Analysis of the scattering process of long-wavelength neutrons from the liquid on the basis of our theory leads directly to Landau's roton spectrum of excitations with an effective roton mass and energy spectrum gap that are in quantitative agreement with the experimental data.

Roton lifetime measurement in superfluid 4He using the spin-echo option on the IN20 triple-axis spectrometer

High-resolution measurements of the temperature dependence of the roton lifetime and energy shift in superfluid 4He have been performed using the IN20 thermal neutron triple-axis spectrometer spin-echo option (TASSE). This experiment constitutes the first implementation of the spin-echo technique for inelastic neutron scattering measurements on IN20 using the optimized field-shape superconducting precession coils. An energy resolution of 0.7 μeV was achieved and the results are in agreement with previous studies. The use of additional gradient coils enables to substantially improve the energy and the momentum transfer resolution, and to match excitation dispersion slopes and curvatures. This setup is designed to reach the nano-eV energy resolution in the case of quasi-elastic scattering experiments.

High Resolution Measurements of the Temperature Dependence of the Roton Energy of Superfluid 4He

New measurements of the roton excitations in superfluid 4He have been made using the IRIS spectrometer (energy resolution ∼20 μeV at the roton energy) at the ISIS spallation neutron source. The roton energy was determined over a temperature range of 0.56 to 1.61 K. High resolution (energy resolution <1 μeV) neutron inelastic scattering measurements by Andersen et al.2 of the dependence of the 4He roton energy on temperature have shown significant deviations from the expected behaviour; the temperature variation was found to be discontinuous and slower than predicted by the established roton-roton interaction theory due to Bedell, Pines and Zawadowski (BPZ). 3 We find that our results can be described well by the BPZ theory over this temperature range and we do not observe the anomalous behaviour reported by Andersen et al. We offer some explanations as to the origin of this apparent disagreement.

Phonons, rotons, and layer modes of liquid 4He in aerogel

We report the first observation of two-dimensional layer modes in both fully filled and partially filled aerogel. Using complementary high-energy resolution and high statistical precision neutron scattering instruments, and two different 87% porous aerogel samples, we show that the three-dimensional (3D) phonon-roton excitation energies and lifetimes of liquid 4He in aerogel are the same as in bulk 4He within current precision. The layer modes are the excitations that distinguish aerogel from the bulk rather than a difference in the 3D roton energy.