Zero-sound Mode Research Articles

Dynamic structure factor for3He in two dimensions

Recent neutron scattering experiments on 3He films have observed a zero-sound mode, its dispersion relation and its merging with -and possibly emerging from- the particle-hole continuum. Here we address the study of the excitations in the system via quantum Monte Carlo methods: we suggest a practical scheme to calculate imaginary time correlation functions for moderate-size fermionic systems. Combined with an efficient method for analytic continuation, this scheme affords an extremely convincing description of the experimental findings.

TWO DIMENSIONAL AND NOVEL QUASI TWO DIMENSIONAL QUANTUM LIQUIDS

In this thesis we have used Quantum Monte Carlo techniques to study two systems that can be regarded as the archetype for neutral strongly interacting systems: 4He, and its fermionic counterpart 3He.More specifically, we have used the Path Integral Ground State and the Path Integral Monte Carlo methods to study a system of two dimensional 3He (2d-3He) and a system of 4He adsorbed on Graphene-Fluoride (GF) and Graphane (GH) at both zero and finite temperature. The purpose of the study of 4He on GF (GH) was the research of new physical phenomena, whereas in the case of 2d-3He it was the application of novel methodologies for the ab-initio study of static and dynamic properties of Fermi systems. In the case of 2d-3He we have computed the spin susceptibility as function of density which turned out to be in very good agreement with experimental data; we have also obtained the first ab-initio evaluation of the zero-sound mode and the dynamic structure factor of 2d-3He that is in remarkably good agreement with experiments. In the case of 4He adsorbed on GF (GH), we determined the zero temperature equilibrium density of the first monolayer of 4He showing also that the commensurate sqrt(3) x sqrt(3) R30 phase is unstable on both substrates; at equilibrium density we found that 4He on GF (GH) is a modulated superfluid with an anisotropic phono-rotonic spectrum; at high coverages we found an incommensurate triangular solid and, on both GF and GH, a commensurate phase at filling factor x= 2/7 that is locally stable or at least metastable. Remarkably, in this commensurate solid phase and for both GF and GH, our computations show preliminary evidence of the presence of a superfluid fraction.

Classical behavior of strongly correlated electron systems of solids near a quantum critical point

Abstract The spectra of collective excitations of electron systems situated near a Fermi-liquid quantum critical point are analyzed. Phonon-like soft and weakly damped branches of the transverse zero-sound mode are found that have extremely low effective Debye temperatures. Their contributions to the collision integral are shown to drive electron transport in the vicinity of the critical point toward a classical regime.

Fermi-liquid theory for thin arbitrarily polarized3He films

We study the thermodynamic response, effective masses, and collective excitations for thin (submonolayer) ${}^{3}$He films as a function of density and polarization using Fermi liquid theory. The Landau parameters ${f}^{\ensuremath{\uparrow}\ensuremath{\uparrow}},{f}^{\ensuremath{\uparrow}\ensuremath{\downarrow}},{f}^{\ensuremath{\downarrow}\ensuremath{\downarrow}}$ are obtained to quadratic order in the low-density $s$-wave and $p$-wave $T$-matrix interaction parameters. Values for the effective interaction components are determined by fitting zero-polarization experimental data for the cases of thin ${}^{3}$He films on graphite and also thin ${}^{3}$He films in surface states of thin superfluid ${}^{4}$He films. By fitting the interaction parameters, we can calculate the Landau parameters to all orders, and we show results for the behavior of ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{F}}_{\ensuremath{\ell}}^{\ensuremath{\uparrow}\ensuremath{\uparrow}}\phantom{\rule{4.pt}{0ex}}\text{for}\phantom{\rule{4.pt}{0ex}}\ensuremath{\ell}\ensuremath{\leqslant}30$. With knowledge of the Landau parameters we calculate the polarization dependence of the state-dependent effective masses, compressibility, spin susceptibility, and zero-sound spectra for the mobile submonolayer range of areal densities. Our results predict a dramatic decrease in the effective masses for ${}^{3}$He on graphite as a function of polarization at higher coverages. At fixed density, the compressibility is shown to decrease monotonically with increasing polarization. At small polarization the inverse spin susceptibility is largest for small density whereas at large polarization it is largest for large density. We show that zero sound will propagate at all densities and polarizations whereas spin zero sound does not propagate in these systems. The condition for thermodynamic stability in an arbitrarily polarized Fermi liquid film is derived and discussed. We show explicitly the Fermi surface distortion due to the presence of a zero-sound mode. A table of predicted values for the zero polarization Fermi liquid parameters ${F}_{0}^{\text{s}}\phantom{\rule{4.pt}{0ex}}\text{and}\phantom{\rule{4.pt}{0ex}}{F}_{1}^{\text{a}}$ is provided.

Dispersion and damping of potential surface waves in a degenerate plasma

Potential (electrostatic) surface waves (SWs) in a semi-bounded plasma with degenerate electrons are studied using the quasi-classical mean-field kinetic model. The SW spectrum and the collisionless damping rate are obtained numerically for a wide range of wavelengths. In the limit of long wavelengths, the SW frequency ω approaches the cold-plasma limit ω=ωp/2 with ωp being the plasma frequency, while at short wavelengths, the SW spectrum asymptotically approaches the spectrum of zero-sound mode propagating along the boundary. It is shown that the surface waves in this system remain weakly damped at all wavelengths (in contrast to strongly damped surface waves in Maxwellian electron plasmas), and the damping rate nonmonotonically depends on the wavelength, with the maximum (yet small) damping occurring for surface waves with wavelength of ≈5πλF, where λF is the Thomas-Fermi length. The applicability of the used approximations and of the obtained results is discussed in detail.

Two-dimensional Fermi liquids sustain surprising roton-like plasmons beyond the particle-hole band

Using inelastic neutron scattering, we have investigated the elementary excitations of an isotropic two-dimensional Fermi liquid, 3He adsorbed on graphite. We provide in this article a detailed account of the principles and methods which allowed measuring for the first time inelastic spectra on a liquid monolayer of 3He, a strong neutron absorber. We also summarise the results presented at this Conference, and review our recent experimental and theoretical work on this this interacting many-body system. At low wave-vectors, near the edge of the particle-hole band, a mode identified as the zero-sound excitation by comparison to our theoretical calculations, is found as predicted at energies much lower than in bulk 3He. The mode enters the particle-hole band, where it undergoes Landau damping. Surprisingly, however, intensity is observed in the neutron spectra at wave-vectors larger than twice the Fermi wave-vector. This new branch is interpreted as the high wave-vector continuation of the zero-sound mode, in agreement with the theory. The results open new perspectives in the understanding of the dynamics of correlated fermions.

Influence of a polarization operator’s imaginary part on dispersion equation solutions

In this paper the solutions of the zero-sound dispersion equation in the random phase approximation (RPA) are considered. The calculation of the damped zero-sound modes \omega_s(k) (complex frequency of excitation) in the nuclear matter is presented. The method is based on the analytical structure of the polarization operators \Pi(\omega,k). The solutions of two dispersion equations with \Pi(\omega,k) and with Re(\Pi(\omega,k)) are compared. It is shown that in the first case we obtain one-valued smooth solutions without "thumb-like" forms. Considering the giant resonances in the nuclei as zero-sound excitations we compare the experimental energy and escape width of the giant dipole resonance (GDR) in the nucleus A with \omega_s(k) taken at a definite wave vector k=k_A.

Second wind of the Dulong-Petit law at a quantum critical point

Renewed interest in 3He physics has been stimulated by experimental observation of non-Fermi-liquid behavior of dense 3He films at low temperatures. Abnormal behavior of the specific heat C(T) of two-dimensional liquid 3He is demonstrated in the occurrence of a T-independent term in C(T). To uncover the origin of this phenomenon, we have considered the group velocity of transverse zero sound propagating in a strongly correlated Fermi liquid. For the first time, it is shown that if two-dimensional liquid 3He is located in the vicinity of the quantum critical point associated with a divergent quasiparticle effective mass, the group velocity depends strongly on temperature and vanishes as T is lowered toward zero. The predicted vigorous dependence of the group velocity can be detected in experimental measurements on liquid 3He films. We have demonstrated that the contribution to the specific heat coming from the boson part of the free energy due to the transverse zero-sound mode follows the Dulong-Petit Law. In the case of two-dimensional liquid 3He, the specific heat becomes independent of temperature at some characteristic temperature of a few mK.

Compressibility, zero sound, and effective mass of a fermionic dipolar gas at finite temperature

The compressibility, zero-sound dispersion, and effective mass of a gas of fermionic dipolar molecules is calculated at finite temperature for one-, two-, and three-dimensional uniform systems, and in a multilayer quasi-two-dimensional system. The compressibility is nonmonotonic in the reduced temperature, $T/{T}_{F}$, exhibiting a maximum at finite temperature. This effect might be visible in a quasi-low-dimensional experiment, providing a clear signature of the onset of many-body quantum degeneracy effects. The collective mode dispersion and effective mass show similar nontrivial temperature and density dependence. In a quasi-low-dimensional system, the zero-sound mode may propagate at experimentally attainable temperatures.

Anisotropic-Fermi-liquid theory of ultracold fermionic polar molecules: Landau parameters and collective modes

We study the Fermi liquid properties of the cold atomic dipolar Fermi gases with the explicit dipolar anisotropy using perturbative approaches. Due to the explicit dipolar anisotropy, Fermi surfaces exhibit distortions of the $d_{r^2-3z^2}$-type in three dimensions and of the $d_{x^2-y^2}$-type in two dimensions. The fermion self-energy, effective mass, and Fermi velocity develop the same anisotropy at the Hartree-Fock level proportional to the interaction strength. The Landau interaction parameters in the isotropic Fermi liquids become the tri-diagonal Landau interaction matrices in the dipolar Fermi liquids which renormalize thermodynamic susceptibilities. With large dipolar interaction strength, the Fermi surface collapses along directions perpendicular to the dipole orientation. The dynamic collective zero sound modes exhibit an anisotropic dispersion with the largest sound velocity propagating along the polar directions. Similarly, the longitudinal p-wave channel spin mode becomes a propagating mode with an anisotropic dispersion in multi-component dipolar systems.

Holographic quantum liquids in 1+1 dimensions

In this paper we initiate the study of holographic quantum liquids in 1+1 dimensions. Since the Landau Fermi liquid theory breaks down in 1+1 dimensions, it is of interest to see what holographic methods have to say about similar models. For theories with a gapless branch, the Luttinger conjecture states that there is an effective description of the physics in terms of a Luttinger liquid which is specified by two parameters. The theory we consider is the defect CFT arising due to a probe D3 brane in the AdS Schwarzschild planar black hole background. We turn on a fundamental string density on the worldvolume. Unlike higher dimensional defects, a persistent dissipationless zero sound mode is found. The thermodynamic aspects of these models are considered carefully and certain subtleties with boundary terms are explained which are unique to 1+1 dimensions. Spectral functions of bosonic and fermionic fluctuations are also considered and quasinormal modes are analysed. A prescription is given to compute spectral functions when there is mixing due to the worldvolume gauge field. We comment on the Luttinger conjecture in the light of our findings.

Remarks on Fermi liquid from holography

We investigate the signatures of Fermi liquid formation in the $\mathcal{N}=4$ super Yang-Mills theory coupled to fundamental hypermultiplet at nonvanishing chemical potential for the global $U(1)$ vector symmetry. At strong 't Hooft coupling the system can be analyzed in terms of the D7-brane dynamics in the ${\mathrm{AdS}}_{5}\ifmmode\times\else\texttimes\fi{}{S}^{5}$ background. The phases with vanishing and finite charge density are separated at zero temperature by a quantum phase transition. In the case of vanishing hypermultiplet mass, Karch, Son, and Starinets discovered a gapless excitation whose speed equals the speed of sound. We find that this zero sound mode persists to all values of the hypermultiplet mass, and its speed vanishes at the point of phase transition. The value of critical exponent and the ratio of the velocities of zero and first sounds are consistent with the predictions of Landau Fermi liquid theory at strong coupling.

Zero Sound Mode in Normal LiquidHe3

Inelastic x-ray scattering has been utilized to study the elementary excitations of normal liquid 3He at the temperature T=1.10+/-0.05 K and saturated vapor pressure in the wave vector range 0.15<or=Q<or=3.15 A(-10. The present data provide direct information on the zero-sound mode in the mesoscopic wave vector range where it was expected to decay into particle-hole excitations. The obtained results show no evidence of such a decay: the zero-sound mode remains well defined in the whole explored wave number range, thus witnessing a continuous transition of the atom dynamics from the collective to the single particle regime similarly to what is usually found in simple liquids.

Collective excitations of low-density fermion-boson quantum-liquid mixtures

We investigate the collective excitations of a low temperature dilute gas mixture that consists of a Bose-Einstein condensate and a Fermi-gas that is a normal (i.e. non-superfluid) Fermi-liquid. We find that the BEC-mediated fermion-fermion interactions, as a consequence of retardation, can become repulsive and support a zero-sound mode that is essentially undamped. In addition, we find a damped zero-sound mode that can be described as a BEC-sound mode modified by fermion mediated boson-boson interactions, and we derive its decay-rate caused by Landau damping. We study the mode structure of these excitations and find avoided crossing behavior as well as a termination point. The collective mode dynamics also reveals that phase separation sets in when the fermion-mediated boson-boson interaction destroys the stability of the homogeneous BEC. We estimate the time and length scales of the onset of the phase separation, and we discuss the feasibility of experimentally probing these consequences of mediated interactions.

Singular perturbation theory for interacting fermions in two dimensions

We consider a system of interacting fermions in two dimensions beyond the second-order perturbation theory in the interaction. It is shown that the mass-shell singularities in the self-energy, arising already at the second order of the perturbation theory, manifest a non-perturbative effect: an interaction with the zero-sound mode. Resumming the perturbation theory for a weak, short-range interaction and accounting for a finite curvature of the fermion spectrum, we eliminate the singularities and obtain the results for the quasi-particle self-energy and the spectral function to all orders in the interaction with the zero-sound mode. A threshold for emission of zero-sound waves leads a non-monotonic variation of the self-energy with energy (or momentum) near the mass shell. Consequently, the spectral function has a kink-like feature. We also study in detail a non-analytic temperature dependence of the specific heat, $C(T)\propto T^2$. It turns out that although the interaction with the collective mode results in an enhancement of the fermion self-energy, this interaction does not affect the non-analytic term in $C(T)$ due to a subtle cancellation between the contributions from the real and imaginary parts of the self-energy. For a short-range and weak interaction, this implies that the second-order perturbation theory suffices to determine the non-analytic part of $C(T)$. We also obtain a general form of the non-analytic term in $C(T)$, valid for the case of a generic Fermi liquid, \emph{i.e.}, beyond the perturbation theory.

Collective modes in a dilute Bose-Fermi mixture

We here study the collective excitations of a dilute spin-polarized Bose-Fermi mixture at zero temperature, considering in particular the features arising from the interaction between the two species. We show that a propagating zero-sound mode is possible for the fermions even when they do not interact among themselves.

Dynamical response ofspin−polarized3He

We compute the longitudinal dynamical susceptibility of spin-polarized liquid helium, whose equation of state is described in a density-functional formalism, within the frame of an extended random-phase approximation. We analyze the evolution of the dispersion relation of zero sound and paramagnon peaks with increasing polarization up to 30%. We find that while the zero-sound mode is rather stable against magnetization, the structure pattern in the spin-density channel changes significantly. In particular, we predict the appearance of new magnetic collective states induced by polarization effects.

Zero sound modes of dilute Fermi gases with arbitrary spin

Zero sound modes of dilute Fermi gases with arbitrary spin

Enhancement of nucleon-nucleon cross section in sidewards flowing nuclear matter through zero sound mode excitation

We investigate the modification induced on the nucleon-nucleon cross section by screening of the interaction inside nuclear matter. The interaction is described by the relativistic one boson exchange of σ, ω and π mesons. Medium effects enter as loop corrections to the meson propagators and are characterized not only by density, but also by temperature and velocity with respect to the center of mass of the collision. The cross section displays peaks for some specific values of the velocity, corresponding to the excitation of zero-sound modes of the longitudinal ω field. The enhancement factor amounts to about 1.5 under reasonable conditions. It increases with density and is reduced at finite temperature. These findings may have verifiable consequences on the angular dependence of the measurable secondary particle distributions.

Study of normal liquid 3He using the method of collective description of interparticle interactions and a realistic form of two-body potential

Visualizing 3He liquid at zero temperature as an interacting system of quasi-particles and the quanta of its zero-sound mode, calculation of the binding energy of the system in its normal phase is made using many-body techniques with a realistic form of interparticle potential constituting both repulsive and attractive components. The new potential has a form similar to the Walecka potential used by us some time back in the study of nuclear matter, and unlike the Lennard–Jones potential, which is most commonly used for liquid 3He, it has a Fourier transform. The calculated binding energy per particle in liquid 3He is found to be −2.478 K, which exactly agrees with the experimental result −2.48 K. This shows a substantial improvement over our earlier result obtained for a contact form of interparticle potential. For the new potential, we arrive at a velocity of 203.8 m/s for the zero-sound mode by following a self-consistent method of calculation, which is close to the experimental value of 194.4 m/s obtained by Abel et al. (Phys. Rev. 147 (1966) 111). By accounting for the local field corrections, beyond the random-phase approximation, to the bare particle-hole propagator in a parametric way, we exactly reproduce the experimental result for the zero-sound mode. The present calculation also indicates the propagation of a new kind of sound wave in liquid 3He at T=0 K, with a velocity of 153.7 m/s, similar to the one found in an earlier calculation.