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Unconventional Superconducting States of an Almost Localized Fermionic Liquid with Nonstandard Quasiparticles: Generalized Gutzwiller Approach

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Kaczmarczyk J., Jędrak J., Spałek J.
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issue 2
261-266
EN
We apply the concept of generalized (almost localized) Fermi liquid and associated with it unconventional superconductivity with Cooper pairs composed of quasiparticles with the spin dependent masses (in an applied field) and with the effective field, both induced by electron correlations. The pairing among quasiparticles takes place either in reciprocal space (Sect. 2) or in real space (Sect. 3) and is induced by the kinetic exchange of either superexchange (in the generic narrow-band situation) or Kondo-type interaction (in the Kondo-lattice limit of the periodic Anderson model). While the main features of this type of Fermi liquid have been introduced earlier, we present here a picture which is applicable to both heavy-fermion and high-T_{c} superconductivity within a single narrow-band representation of correlated states. Our approach introduces a set of additional concepts (spin-dependent masses, effective fields induced by electron correlations), for which the Landau concept of the Fermi liquid represents still a workable scheme. In the limit of the Kondo lattice, we present the phase diagram incorporating the Fulde-Ferrell-Larkin-Ovchinnikov phase within the BCS-type of pairing, whereas in that of the t-J model we show that the proper choice of renormalization factors and constraints is crucial for the mean-field description of the superconducting state.
2
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Extended Hubbard Model in the Dimer Representation. II. Lattice Hamiltonian in the Large U Limit

100%
Grabiec B., Matlak M.
Acta Physica Polonica A
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2002
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vol. 101
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issue 4
549-557
EN
Using the exact decomposition of the sc lattice into a set of interacting dimers (each dimer is described by the extended Hubbard Hamiltonian) and exact solution of the dimer problem (preceding paper) we exactly find the form of the extended Hubbard model in the case of a crystal in the large U limit. We apply a new, nonperturbative approach based on the exact projection procedure onto a dimer subspace occupied by electrons in this limit (it is the only assumption). The resulting Hamiltonian is very complicated and contains a variety of multiple magnetic and nonmagnetic interactions deeply hidden in its original form (site representation). We also present a simplified version of the model to better visualize a mixture of different interactions resulting from this approach.
3
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Extended Hubbard Model in the Dimer Representation. I. Dimer Hamiltonian in the Large U Limit

100%
Grabiec B., Matlak M.
Acta Physica Polonica A
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2002
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vol. 101
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issue 4
537-548
EN
We consider the extended Hubbard model for the single cubic lattice and rewrite it in the form of interacting dimers, using the exact solution of the dimer problem. We analytically derive the second quantization form of the dimer Hamiltonian eliminating from the considerations unoccupied dimer energy levels in the large U limit (it is the only assumption). The resulting dimer Hamiltonian written with the use of the Hubbard operators and spin operators contains three terms, visualizing explicitly competing magnetic interactions (ferromagnetic, antiferromagnetic) as a generalization of the t-J model. The presented, nonperturbative method, can in principle be applied to the cluster of any size (e.g. one central atom and z its nearest neighbours). The use of the projection technique can further be applied in the case of a crystal to obtain the second quantization form of the extended Hubbard model for the sc lattice in the large U limit.
4
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A New Microscopic Calculation for the Uniform Electron Fluid

100%
Bouchebak A., Al-Sugheir M., Ghassib H.
Acta Physica Polonica A
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2011
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vol. 119
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issue 3
312-322
EN
The static fluctuation approximation is applied for the first time to an electronic system. A simple model (a uniform electron fluid) is chosen to explore the applicability of static fluctuation approximation to electrons in metals. The thermodynamic properties - the internal energy per particle, the pressure, the entropy per unit volume, the heat capacity per unit volume, and the chemical potential - are calculated over a wide range of densities within the metallic-density region. Finally, the pair-correlation function for the electron fluid is evaluated. Values of this function are then tabulated for zero-interparticle separation at several densities of interest. The results of this work are found to be in good agreement with several other many-body calculations.
5
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Numerical Simulation of Current Dependence on Well Widths in AlGaAs/GaAs/AlGaAs Double Barrier Diode Structures

100%
Rezvani A.
Acta Physica Polonica A
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2003
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vol. 103
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issue 1
47-56
EN
A numerical procedure based on the time-dependent Kohn-Sham equation with an improved boundary condition for the modeling double barrier resonant tunneling diode is presented. The dependence of current components on well widths in AlGaAs/GaAs/AlGaAs structure is studied. An oscillatory behavior was observed as the width of the well is changed. Our evaluation shows that this oscillation cannot attribute to the well-known oscillation at resonance state.
6
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Energy Loss of Excited Slow Ions in Electron Gas

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Moneta M.
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vol. 96
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issue 3-4
429-436
EN
The electronic energy loss and the straggling of the energy loss of the degenerate electron gas for excited H*-, He*-, He**-, and Li*-like ions were calculated. The results were compared with the corresponding characteristics for ions kept in the ground state. The linear response theory was used. The ion was described by the Hartree-Fock-Slater formalism and the medium by the dielectric function. The stopping and straggling effective charges Z_{ef} for the energy loss were analysed and they were found to differ from each other and to depend on the one-electron radius r_{s}, on the ion atomic number Z_{i}, and on the number of electrons N_{i} carried by the ion.
7
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Electron-Positron Interaction in Jellium: Optimization of the Perturbed Hypernetted-Chain Approach

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Stachowiak H., Boroński E.
Acta Physica Polonica A
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2006
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vol. 110
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issue 5
709-720
EN
The perturbed hypernetted-chain approach to electron-positron interaction in jellium consists in assuming the wave function of the system in the form of a Slater determinant built of single-electron functions presented asψi k(s)=w(s)φ_i k(s). s is the distance between the electron and the positron. The function w(s) is obtained by solving the equation of Gondzik and Stachowiak. The functionφ_{i k}(s) is computed by applying a self-consistent Born approximation. The idea of the paper is to modify the function w(s) in such a way as to obtain from the Born approximation as precise results as possible. It is shown that the influence of such modifications on physical predictions is small. This shows how good is the perturbed hypernetted-chain approach. The annihilation rates obtained in such a way decrease somewhat, becoming closer to experimental expectations.
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Resonant Plasmon Response of a Periodically Modulated Two-Dimensional Electron Gas

88%
Sznajder P., Piętka B., Szczytko J., Łusakowski J., Bardyszewski W.
Acta Physica Polonica A
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2012
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vol. 122
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issue 6
1090-1092
EN
We report the theoretical study of the optical response of a periodically modulated two-dimensional electron gas. The density of states is calculated within the first order of the perturbation theory and the effects of the short-range disorder are explained and discussed. We demonstrate that the magnetic field values corresponding to the characteristic narrowing of the density of states width are given by the zeros of the subsequent Laguerre polynomials. The observed increase of the density of states at the edges are interpreted as van Hove singularities. The broadening effects are shown to modify and smear out the observed effects with increasing temperature above 2 K. The plasmon dispersion relation is discussed in terms of the random phase approximation. Small changes in plasmon dispersion relation related to the periodic modulation were predicted.
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Influence of Many-Body Effects in Real Metals on Electron-Positron Momentum Distributions

88%
Boroński E.
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vol. 125
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issue 3
706-709
EN
It is shown that if one takes into account the effective mass of the electron, which in real structures is actually different than the free electron mass, the electron and positron self-energy effects may result in flatter and smaller enhancement of the electron-positron momentum distribution. Thus, the many-body effects mentioned above, among other reasons like e.g. influence of lattice potential on electron and positron wave functions, can be responsible for decreasing of the discontinuity on the Fermi momentum and a greater smearing of the Fermi surface seen in several angular correlation of positron annihilation radiation experiments.
10
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Electronic Correlations within Fermionic Lattice Models

63%
Matlak M., Grabiec B., Krawiec S.
Acta Physica Polonica A
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2007
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vol. 112
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issue 3
537-547
EN
We investigate two-site electronic correlations within generalized Hubbard model, which incorporates the conventional Hubbard model (parameters: t (hopping between nearest neighbours), U (Coulomb repulsion (attraction))) supplemented by the intersite Coulomb interactions (parameters: J^{(1)} (parallel spins), J^{(2)} (antiparallel spins)) and the hopping of the intrasite Cooper pairs (parameter: V). As a first step we find the eigenvalues E_α and eigenvectors |E_α〉 of the dimer and we represent each partial Hamiltonian E_α|E _α〉〈 E_α| (α=1,2,...,16) in the second quantization with the use of the Hubbard and spin operators. Each dimer energy level possesses its own Hamiltonian describing different two-site interactions which can be active only in the case when the level will be occupied by the electrons. A typical feature is the appearance of two generalized t-J interactions ascribed to two different energy levels which do not vanish even for U=J^{(1)}=J{(2)}=V=0 and their coupling constants are equal to ±t in this case. In the large linebreak U-limit for J^{(1)}=J^{(2)}=V=0 there is only one t-J interaction with coupling constant equal to 4t^2/|U| as in the case of a real lattice. The competition between ferromagnetism, antiferromagnetism and superconductivity (intrasite and intersite pairings) is also a typical feature of the model because it persists in the case U=J^{(1)}=J^{(2)}=V=0 and t≢0. The same types of the electronic, competitive interactions are scattered between different energy levels and therefore their thermodynamical activities are dependent on the occupation of these levels. It qualitatively explains the origin of the phase diagram of the model. We consider also a real lattice as a set of interacting dimers to show that the competition between magnetism and superconductivity seems to be universal for fermionic lattice models.
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