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Irreducible Green Functions Method Applied to Nanoscopic Systems

100%
Górski G.
Acta Physica Polonica A
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2016
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vol. 130
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issue 2
551-553
EN
The equation of motion method for the Green functions is one of the tools used in the analysis of quantum dot system coupled with the metallic and superconducting leads. We investigate modified equation of motion, based on differentiation of double-time temperature dependent Green functions both over the primary time t and secondary time t'. Our equation of motion approach allows us to obtain the Abrikosov-Suhl resonance in the particle-hole symmetric case and also in the asymmetric cases. We will apply the irreducible Green functions technique to analyses of the equation of motion applied to the dot system. This method gives a workable decoupling scheme breaking the infinite set of the Green function equations. We apply this technique to calculate the density of the states and the differential conductance of single-level quantum dot with the Coulomb repulsion attached to one metallic and one superconducting leads (N-QD-SC). Our results are compared with the previous calculations.
2
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Ferromagnetic Systems with Hopping Interaction

64%
Górski G., Mizia J.
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issue 2
336-339
EN
We analyze the influence of hopping interaction on magnetic ordering. Scattering scheme of the Hubbard III approximation with included inter-site kinetic electron-electron correlation is used. The hopping interaction and inter-site correlation lead to two spin dependent effects: the band width correction and the band-shift correction. The band-shift correction factor causes an exchange splitting between the spin-up and spin-down spectrum, and its role is similar to the exchange interaction in the classic Stoner model. The spin dependent band width correction enhanced strongly by the inter-site kinetic correlation lowers the kinetic energy of electrons by decreasing the majority spin band width for some electron occupations with respect to the minority spin band width. The results show that in the case of the symmetrical density of states there is only ferromagnetic enhancement. For the strongly asymmetrical density of states there is a ferromagnetic transition.
3
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The Influence of Potential Energy Shape on the Total Electrical Efficiency of the Energy Harvester

64%
Kucab K., Górski G.
Acta Physica Polonica A
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2017
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vol. 132
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issue 1
118-120
EN
In this theoretical work we analyze the total effective electric power versus base acceleration amplitude generated by the energy harvesting system with an electromagnetic transducer. We compare the results for both linear and nonlinear case. The transition from linear to nonlinear behavior of the system can be achieved by the change of device geometry. To improve the power efficiency of our device we also examine the dependence of crossover point of acceleration amplitudes where generated power in the nonlinear system starts to exceed the generated power in the linear regime. We have found that the crossover point can be moved towards relatively small base acceleration values by appropriate selection of system nonlinearity "strength".
4
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Phase Separation near Half-Filling Point in Superconducting Compounds

51%
Kucab K., Górski G., Mizia J.
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vol. 126
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issue 4a
A-104-A-107
EN
We present the model of superconducting ceramics using the single band extended Hubbard Hamiltonian. We investigate the simultaneous presence of antiferromagnetism and d-wave superconductivity in the coherent potential approximation applied to the on-site Coulomb repulsion U. We consider the hopping interaction, Δt, the inter-site charge-charge interaction, V (creating superconductivity), and the single site Hund type exchange interaction, F_{in} (creating antiferromagnetism). The influence of these interactions on the separation of superconducting and antiferromagnetic phases near the half-filling point is investigated. Results are compared with the experimental data for YBaCuO and NdCeCuO compounds.
5
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Alternative Equation of Motion Approach to the Single-Impurity Anderson Model

51%
Górski G., Mizia J., Kucab K.
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vol. 126
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issue 4a
A-97-A-100
EN
Solving the single-impurity Anderson model is a basic problem of solid state physics. The single-impurity Anderson model is very important, at present it is also used for systems with quantum impurities, e.g. semiconductor quantum dots and molecular transistors. Its main application is in the scheme of dynamical mean field theory describing strong correlation electron systems. To solve the single-impurity Anderson model problem we use the equation of motion Green function approach. In this report we present the novel equation of motion approximation in which we differentiate the Green function over both time variables. This differs from the commonly used equation of motion solution by Appelbaum, Penn and Lacroix where the authors take time derivative only over primary time variable. After extending calculations to higher order Green functions we find the new approximate dynamical solution of single-impurity Anderson model. The results are compared with the solutions to the single-impurity Anderson model problem at intermediate Coulomb repulsion U such as the modified iterative perturbation theory. Our approach is suitable for describing quantum dots.
6
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Modified Equation of Motion Approach for Ferromagnetic Systems

51%
Górski G., Mizia J., Kucab K.
Acta Physica Polonica A
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2015
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vol. 127
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issue 2
207-209
EN
The key problem in using the dynamical mean-field theory is finding the appropriate solution to the single impurity Anderson model. We use the modified equation of motion method based on differentiation over two time variables. In such approach we obtain correct description of the Kondo effect not only for systems symmetrical with respect to the half-filled point but also for the systems without symmetry in a half filled point and for broad range of electron concentrations like e.g. the ferromagnetic systems. For the reason of these advantages we investigate in this report dependence of the system magnetic moment on carrier concentration using our modified equation of motion method. We also analyze influence of asymmetric densities of states on ferromagnetic alignment. Our results are compared with dynamical mean-field theory-quantum Monte Carlo calculations and with Hubbard I and III approximations.
7
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Coexistence of Ferromagnetism with Spin Triplet Superconductivity

51%
Górski G., Kucab K., Mizia J.
Acta Physica Polonica A
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2009
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vol. 115
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issue 1
141-143
EN
The experimental results for ZrZn_2, URhGe, and in some pressure ranges also for UGe_2, showed that the ferromagnetic superconductors are weak itinerant ferromagnets. Guided by these results we describe the phenomenon of coexistence between equal spin triplet pairing superconductivity and ferromagnetism using the extended Stoner model, which includes in Hamiltonian the on-site Coulomb interaction, U, and occupation dependent hopping integral. We use the Hartree-Fock approximation and the Green functions technique. In the Hartree-Fock approximation the on-site Coulomb interaction plays the role of the on-site exchange (Hund's) field. All inter-site interactions will have included the inter-site kinetic correlation, 〈c_{iσ}^{+}c_{jσ}〉, within the Hartree-Fock approximation. We introduce the pressure-dependence to the hopping integral. Numerical results are compared with experimental data for ZrZn_2. The kinetic correlation creates the superconductivity without help of negative values of the Coulomb interactions. The model can explain stimulation of triplet superconductivity by the weak itinerant ferromagnetism. This effect was observed experimentally in ZrZn_2. Numerical analysis also confirms the experimental effect of decrease in critical temperatures (Curie and superconducting) with increasing external pressure.
8
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Band Magnetism with Inter-Site Correlations and Interactions

51%
Mizia J., Górski G., Kucab K.
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vol. 126
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issue 4a
A-30-A-32
EN
We introduce the Hamiltonian to describe narrow band electrons. The physics of driving forces towards ferromagnetism is re-examined. Using different approximations it has been shown that the magnetic moments created by inter-site interaction and inter-site kinetic correlation decrease quickly with temperature. As a result of these interactions and the realistic density of states the Curie temperatures calculated after fitting magnetic moments to their low temperature values are realistic. In the past the Curie temperatures calculated using only the on-site interaction were much higher than the experimental temperatures.
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