Helga M. Böhm

Observation of a roton collective mode in a two-dimensional Fermi liquid

Understanding the dynamics of correlated many-body quantum systems is a challenge for modern physics. Owing to the simplicity of their Hamiltonians, 4He (bosons) and 3He (fermions) have served as model systems for strongly interacting quantum fluids, with substantial efforts devoted to their understanding. An important milestone was the direct observation of the collective phonon–roton mode in liquid 4He by neutron scattering, verifying Landau’s prediction and his fruitful concept of elementary excitations. In a Fermi system, collective density fluctuations (known as ‘zero-sound’ in 3He, and ‘plasmons’ in charged systems) and incoherent particle–hole excitations are observed. At small wavevectors and energies, both types of excitation are described by Landau’s theory of Fermi liquids. At higher wavevectors, the collective mode enters the particle–hole band, where it is strongly damped. The dynamics of Fermi liquids at high wavevectors was thus believed to be essentially incoherent. Here we report inelastic neutron scattering measurements of a monolayer of liquid 3He, observing a roton-like excitation. We find that the collective density mode reappears as a well defined excitation at momentum transfers larger than twice the Fermi momentum. We thus observe unexpected collective behaviour of a Fermi many-body system in the regime beyond the scope of Landau’s theory. A satisfactory interpretation of the measured spectra is obtained using a dynamic many-body theory.

Finite temperature investigations of a two dimensional electron liquid

We investigate the spin dependent local field corrections and correlation functions of an electron layer at intermediate degeneracies. The results are obtained within the Singwi-Tosi-Land-Sjølander approximation by solving the corresponding set of coupled integral equations. Analytic expressions are given for the asymptotic limiting behavior. In addition, the free exchange-and correlation energy, which is in good agreement with Monte Carlo results at full degeneracy, is calculated for various temperatures.

Plasmon damping and proton stopping in jellium

Abstract Two-pair excitations in a homogeneous electron gas are investigated within screened second order perturbation theory. Based on a suggestion by Ichimaru [K. Utsumi and S. Ichimaru, Phys. Rev. B 22 (1980) 5203] an additional method of obtaining the effective interelectron interaction is presented. A closer inspection of the basic equation, rewritten as a selfconsistency problem, justifies the use of static screening within this model. Fit formulae for all main results are made available. Finally, an application of these calculations to the problem of proton stopping in aluminium is presented, which is in good agreement with the experiment.

Screening effects on plasmon damping in an electron liquid

Abstract Plasmon damping in the three-dimensional homogeneous electron gas is investigated within the formalism of second-order perturbation theory, concentrating on the effects of static and dynamic screening. We have found several different theoretical approaches leading to comparable results, especially in the metallic-density regime. Using a spin-dependent interaction, however, significantly improves the results of our theory towards a better agreement with the experiments.

DYNAMIC PAIR EXCITATIONS IN ALUMINUM

We present a calculation of the excitation spectrum of the electron liquid that includes time-dependent pair correlations. For the charged boson fluid these correlations provide a major mechanism for lowering the plasmon energy; here we extend that study to the much more demanding fermionic case. Based on the formalism of correlated basis functions we derive coupled equations of motion for time-dependent 1- and 2-particle correlation amplitudes. Our solution strategy for these equations ensures the fulfillment of the first two energy–weighted sum rules and, in the appropriate limit, is consistent with the bosonic version. Results are presented for the dynamic structure factor with special emphasis being put on studying the double plasmon.

Dawson—March Model for the Pair Function af a Two-dimensional Electron Liquid

Abstract Based on the functional representation for the pair function developed by Dawson and March the ground state correlations of a two-dimensional electron gas are investigated. The method appears to produce reliable results for high and intermediate densities. Although the approach contains a linearization step using first order Borns approximation, the resulting zero-distance-correlations remain positive.

Data for: Dynamic correlations in the highly dilute 2D electron liquid: loss function, critical wave vector and analytic plasmon dispersion

Abstract Correlations, highly important in low–dimensional systems, are known to decrease the plasmon dispersion of two–dimensional electron liquids. Here we calculate the plasmon properties, applying the ‘Dynamic Many-Body Theory’, accounting for correlated two–particle–two–hole fluctuations. These dynamic correlations are found to significantly lower the plasmon’s energy. For the data obtained numerically, we provide an analytic expression that is valid across a wide range both of densities and of wave vectors. Finally, we demonstrate how this can be invoked in determining the actual electron densities from measurements on an AlGaAs quantum well.

Phenomenological plasmon broadening and relation to the dispersion

Abstract Pragmatic ways of including lifetime broadening of collective modes in the electron liquid are critically compared. Special focus lies on the impact of the damping parameter onto the dispersion. It is quantitatively exemplified for the two-dimensional case, for both, the charge (‘sheet’-)plasmon and the spin-density plasmon. The predicted deviations fall within the resolution limits of advanced techniques.

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.

REEMERGENCE OF THE COLLECTIVE MODE IN 3HE AND ELECTRON LAYERS

Neutron scattering experiments on a 3He layer on graphite show an unexpected behavior of the collective mode. After having been broadened by Landau damping at intermediate wave vectors, the phonon-roton mode resharpens at large wave vectors and even emerges from the particle-hole continuum at low energies. The measured spectra cannot be explained by a random phase approximation with any static interaction. We show here that the data are well described if dynamic two-pair fluctuations are accounted for. We predict similar effects for electron layers.