Microscopic theory of fluctuations in itinerant electron systems — Ferromagnetism

A many body theoretical method for calculating the effect of low energy fluctuations on the dynamic susceptibility χ(q, ω⁺) is presented. For the case of ferromagnetism, the contribution of one internal spin fluctuation is obtained and is seen to be much larger than the temperature dependent part of the Stoner or RPA term. It leads to the observed Curie-Weiss law for χ(0, 0) (e.g. in Ni where comparison with experiment is made).     

Ferromagnetism of the repulsive atomic Fermi gas: three-body recombination and domain formation

The simplest model for itinerant ferromagnetism, the Stoner model, has so far eludedexperimental observation in repulsive ultracold fermions due to rapid three-bodyrecombination at large scattering lengths. Here we show that a ferromagnetic phase can bestabilised by imposing a moderate optical lattice. The reduced kinetic energy drop uponformation of a polarized phase in an optical lattice extends the ferromagnetic phase tosmaller scattering lengths where three-body recombination is small enough to permitexperimental detection of the phase. We also show, using time dependent density functionaltheory, that in such a setup ferromagnetic domains emerge rapidly from a paramagneticinitial state.     

Quasirelativistic electron gas

The thermodynamic potential of an electron gas described by the Darwin Lagrangian is obtained in the ring approximation. The principal relativistic corrections to the correlation energy at absolute zero of temperature are obtained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 54–57, March, 1982.     

Linear response for the electron gas

A new form is proposed for the magnetic response function of an electron gas. It is shown that including the dependence upon the pair function gives a much smaller exchange and correlation kernel than previous estimates.     

Spin-plasmon oscillations of the two-dimensional electron gas

Interaction of the spins of 2D electrons with an alternating electric field in the plane of the system is considered. It is assumed that the double spin degeneracy is eliminated by the spin-orbit splitting. It is shown that transitions between different spin states produce a narrow absorption band in the degenerate electron gas. In the frequency domain corresponding to these transitions, those frequencies are combined with two-dimensional plasmons; as a result, the plasmon spectrum is modified, and a new type of oscillations occurs, namely, a spin-plasmon polariton. The dispersion law of these oscillations is derived. The problem of the excitation of spin-plasmon polaritons by an external electromagnetic field is solved.     

Single-particle spectrum of the degenerate electron gas

The single-particle spectrum of an interacting electron gas is discussed. There is a characteristic structure in the spectral weight function at energies that differ from the quasi-particle energy by energies of the order of the plasma energy. This structure is due to the singular Coulomb potential and the plasmon part of the effective interaction at long wavelengths. For momenta deep inside the Fermi sea a new elementary excitation of appreciable strength appears. It can be interpreted as a coupled mode of holes and plasmons.     

Single-particle spectrum of the degenerate electron gas

Extensive numerical results in the Random Phase Approximation are presented for the spectral weight function, the momentum distribution, and the density of states of the degenerate electron gas over a range of metallic densities. The single-particle spectrum contains not only the damped quasiparticle but also structure due to plasmon effects. At low momenta there is a second elementary excitation of appreciable weight. The density of states has a satellite band at energies more than the plasma energy below the Fermi level. The results confirm the main features of an earlier analysis using a simplified dielectric function.     

Momentum distribution of the homogeneous electron gas

We calculate the off-diagonal density matrix of the homogeneous electron gas at zero temperature using unbiased reptation Monte Carlo calculations for various densities and extrapolate the momentum distribution and the kinetic and potential energies to the thermodynamic limit. Our results on the renormalization factor allow us to validate approximate G0W0 calculations concerning quasiparticle properties over a broad density region (1≤r(s)?10) and show that, near the Fermi surface, vertex corrections and self-consistency aspects almost cancel each other out.     

Ferromagnetism in one-dimensional Hubbard model induced by the next-nearest-neighbor hopping at electron density 3/2

Ferromagnetism in the one-dimensional Hubbard model with the next-nearest-neighbor hopping is explored by using the exact-diagonalization method in a small cluster and the equation-of-motion method in the thermodynamic limit with electron density n = 3/2. With these two complementary methods, it is found that an intermediate value of the next-nearest- neighbor hopping amplitude tl tends to stabilize the fully polarized ferromagnetic state under the condition that the on-site coulomb interaction U is sufficiently large in our model. The ground-state phase diagram of the model is presented in the tl-U plane.     

Crystallization of an electron gas

The ground state energy of an electron gas that is evaluated by the method of Padé approximants shows a singularity which may be associated with the formation of the Wigner lattice. The energy curve in the vicinity of this singularity is examined, and the pressure and the correlation energy are evaluated. Permanent address: Department of Physics, State University of New York at Buffalo, N.Y., U.S.A.     

The influences of gas and electron temperatures on electron attachment in gas electrical discharges

Various electron attachment processes are reviewed, emphasising the way in which the rates and products of some selected reactions vary with the attaching gas temperatureT _g, the temperature,T _e, and the energy of the attaching electrons. The examples illustrating the variety of reactions are the efficient dissociative attachment reaction to CCl₄, attachment to SF₆ which involves both dissociative and non-dissociative attachment, attachment to CHCl₃ which requires activation energy, and attachment to CCl₃Br which results in both Cl- and Br- product ions. A model has been presented which is able to quantitatively explain the difference influences ofT _g andT _e on the rates of some of these reactions. Also described are the unusually efficient attachment properties of the fullerene molecules C₆₀ and C₇₀ as revealed by our FALP experiments, noting that these molecules have potential importance as efficient suppressers of electrical breakdown through gases such as those used to insulate high voltage devices. We emphasise throughout this paper the importance of an understanding of the separate influences of gas and electron temperature on attachment reactions for the modelling of practical gas discharge media such as etchant plasmas. We dedicate this paper to Professor Jan Janča on the occasion of his sixtieth birthday in recognition of his major contributions to gas discharge physics.     

Magneto-excitations in the rotating two-dimensional electron gas

Summary The effects of a rigid rotation on the two-dimensional electron gas are studied. For very large wavelengths the lower branch of magneto-excitations has the dispersion relationE_(k)≈[ℏΓ (ℏΓ+ve ²|k|)]^1/2 , wherev is the filling factor and Γ the angular speed of rotation. The result holds independently of the presence of a solid phase (Wigner lattice) on the gas.

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Riassunto Si studiano gli effetti di una rotazione rigida su un gas di elettroni bidimensionale. Per lunghezze d'onda molto ampie, il ramo piú basso delle eccitazioni magnetiche ha la relazione di dispersioneE_(k)≈[ℏΓ (ℏΓ+ve ²|k|)]^1/2 dovev è il fattore di riempimento e Γ la velocità angolare di rotazione. Il risultato vale indipendentemente dalla presenza di una fase solida (reticolo di Wigner) nel gas.

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Резюме Исследуется влияние жесткого вращения на двумерный электронный газ. Для очень больших длин волн низшая ветвь магнитных возбуждений имеет дисперсионное соотношениеE_(k)≈[ℏΓ (ℏΓ+ve ²|k|)]^1/2, гдеv-фактор заполнения и Γ-угловая скорость врашения. Полученный результат оказывается справедлив в присутствии твердой фазы (решетка Вигнера).

     

Ferromagnetism in the Hubbard model

Whether spin-independent Coulomb interaction can be the origin of a realistic ferromagnetism in an itinerant electron system has been an open problem for a long time. Here we study a class of Hubbard models on decorated lattices, which have a special property that the corresponding single-electron Schrödinger equation hasN _d-fold degenerate ground states. The degeneracyN _d is proportional to the total number of sites ||. We prove that the ground states of the models exhibit ferromagnetism when the electron filling factor is not more than and sufficiently close to=N _d/(2||), and paramagnetism when the filling factor is sufficiently small. An important feature of the present work is that it provides examples of three dimensional itinerant electron systems which are proved to exhibit ferromagnetism in a finite range of the electron filling factor.     

Hartree-Fock approximation for the one-dimensional electron gas

The Hartree-Fock calculation on the one-dimensional electron gas is done on the basis of the method analogous to that applied by Bloch and Wigner and Seitz for the three-dimensional gas. The boundary conditions of the standing wave are taken for the wave function and the bare Coulomb interaction between electrons is assumed. The parameterr _s of the three-dimensional gas is replaced by the ratio between the cross-section radius and the length of the potential tube filled by the one-dimensional gas. Excepting for a special case of the excitement of an electron pair put on one electron level the excitation energies of the non-magnetic gas are found to be very much higher than these of the ferromagnetic gas. A similar relation holds between the ground state energies of the non-magnetic and magnetic gases.     

Orbital susceptibility of the low density electron gas

The orbital susceptibility of the electron gas is calculated at densities so low that the ‘Wigner crystal’ picture is valid. These results are used to construct an interpolation for the orbital susceptibility which is exact in the high density limit and nearly exact at low densities.     

Hartree-Fock ground state of the three-dimensional electron gas

In 1962, Overhauser showed that within Hartree-Fock (HF) the electron gas is unstable to a spin-density wave state. Determining the true HF ground state has remained a challenge. Using numerical calculations for finite systems and analytic techniques, we study the unrestricted HF ground state of the three-dimensional electron gas. At high density, we find broken spin symmetry states with a nearly constant charge density. Unlike previously discussed spin wave states, the observed wave vector of the spin-density wave is smaller than 2k(F). The broken-symmetry state originates from pairing instabilities at the Fermi surface, a model for which is proposed.