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Acta Physica Polonica A
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2007
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vol. 111
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issue 4
527-536
EN
We argue that in a strongly correlated electron system collective instanton excitations of the phase field (dual to the charge) arise with a great degree of stability, governed by gauge flux changes by an integer multiple of 2π. By unraveling consequences of the nontrivial topology of the charge gauge U(2) group, we found that the pinning of the chemical potential and the zero-temperature divergence of charge compressibility define a novel "hidden" quantum criticality on verge of the Mott transition governed by the protectorate of stable topological numbers rather than the Landau paradigm of the symmetry breaking.
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Fermi Gas with 4-Fermion BCS-type Interaction

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EN
A gas of spin 1/2 fermions with an interaction V + W = - Σ_{k,k'}g_{kk'}b*_{k} b*_{-k}b_{k'}b_{-k'} + Σ_{k} γ_{k}b*_{k}b_{k}, where b_{k}=a_{k+}a_{k-} and a_{kσ},a*_{k'σ'} satisfy Fermi anticommutation relations, is investigated. The trial ground state |G〉 is similar in form to the BCS ground state, with b*_{k} b*_{-k} replacing a*_{k+} a*_{-k-}, but because the excitation energies are not simply additive, the trial density matrix \rho_0 differs from the BCS one. The expectation values 〈G|H|G〉 and Tr(Hρ_{0}) are minimized, revealing the presence of a second-order phase transition, with T_{c} > T_{c(BCS)} for appropriately adjusted γ_{k}. It is shown that the minimization procedure applied leads to an expression for the free energy density of H, which is asymptotically exact in the infinite-volume limit. Comparison with experimental data on high-temperature superconductors is made and for a particular choice of \gamma_k qualitative agreement is found with the temperature dependence of the order parameter of the BSCCO superconductor.
EN
In the framework of the Eliashberg formalism, we have calculated the thermodynamic properties of the superconducting state in K_{3}C_{60} (the critical temperature T_C = 19.50 K). We have obtained the following results: (i) The critical value of the Coulomb pseudopotential is equal to 0.387. (ii) The values of the ratios R_1 ≡ 2Δp(0)/k_{B}T_C and R_2 ≡ ΔC(T_C)/C^{N}(T_C) are bigger than in the BCS model; R_1 = 4.01 and R_2 = 1.58. (iii) The electron effective mass m*_{e} reaches the highest value for T = T_C; [m*_{e}]_max = 2.86 m_{e}, where m_{e} is the bare electron mass. Additionally, we have given the analytical expressions for T_C, Δ(T), R_1 and R_2.
EN
The form of the density of states for a tight-binding model with the first and the next-nearest neighbour hoppings for a rectangular planar lattice and a shift of the chemical potential are calculated. This is newly and comprehensively formulated integral form illustrated numerically, helpful in approach to two-dimensional superconducting models. In some particular cases the complete analytical forms of the density of states are obtained. It is shown that for all cases the density of states has a single van Hove singularity of the logarithmic type at the identically defined point. The proper approximate analytical representations are found. The difference between the exact numerical and approximate analytical forms is evaluated and illustrated.
Acta Physica Polonica A
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1992
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vol. 82
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issue 6
967-974
EN
The ab initio self-consistent linear muffin-tin orbital calculations in the atomic sphere approximation have been performed for the ordered CrPt_{3} (AuCu_{3}-type structure) alloy. The band structure and the densities of electronic states are presented. The para- and ferrimagnetic phases were considered. The spin-polarized calculations have confirmed the experimental observation of small antiparallel induced magnetic moment on a platinum atom.
EN
Within the anisotropic BCS model the temperature dependence of the electron Raman light scattering in normal metals and superconductors is investigated. In either case analytical expressions describing the intensity of scattered light as a function of the Raman frequency and temperature are derived.
EN
We explore the Andreev tunnelling through the strongly correlated quantum dot embedded between the normal and superconducting electrodes. For a small external voltage |eV| <∆_s the electron arriving from the normal lead can be converted into a pair on the quantum dot and further propagates in the superconducting lead while simultaneously the hole is reflected back to the normal electrode. Conductance of such anomalous current is very sensitive to the particle-hole mixing of the quantum dot spectrum. We analyze the influence of the proximity effect and the Coulomb interactions on the differential Andreev conductance focusing on the extreme limit ∆_s → ∞.
EN
The concept of topological excitations and the related ground state degeneracy are employed to establish an effective theory of the superconducting state evolving from the Mott insulator for high-T_c cuprates. The theory includes the effects of the relevant energy scales with the emphasis on the Coulomb interaction $U$ governed by the electromagnetic U(1) compact group. The results are obtained for the layered t-t'-t_⊥-U-J system of strongly correlated electrons relevant for cuprates. Casting the Coulomb interaction in terms of composite-fermions via the gauge flux attachment facility, we show that instanton events in the Matsubara "imaginary time", labelled by a topological winding numbers, governed by gauge flux changes by an integer multiple of 2π, are essential configurations of the phase field dual to the charge. The impact of these topological excitations is calculated for the phase diagram, which displays the "hidden" quantum critical point on verge of the Mott transition that is given by a divergence of the charge compressibility.
EN
The work describes the properties of the high-pressure superconducting state in phosphor: p∈ {20, 30, 40, 70} GPa. The calculations were performed in the framework of the Eliashberg formalism, which is the natural generalization of the BCS theory. The exceptional attention was paid to the accurate presentation of the used analysis scheme. With respect to the superconducting state in phosphor it was shown that the observed not-high values of the critical temperature ([T_{C}]_{p=30GPa}^{max}=8.45 K) result not only from the low values of the electron-phonon coupling constant, but also from the very strong depairing Coulomb interactions. Additionally the inconsiderable strong-coupling and retardation effects force the dimensionless ratios R_{Δ}, R_{C}, and R_{H} - related to the critical temperature, the order parameter, the specific heat, and the thermodynamic critical field - to take the values close to the BCS predictions.
Acta Physica Polonica A
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2012
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vol. 121
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issue 4
738-743
EN
The spin-rotationally invariant SU(2)×U(1) approach to the Hubbard model is extended to accommodate the charge degrees of freedom. Both U(1) and SU(2) gauge transformation are used to factorize the charge and spin contribution to the original electron operator in terms of the emergent gauge fields. By tracing out gauge bosons the form of paired states is established and the role of antiferromagnetic correlations is explicated. We argue that in strongly correlated electron system collective instanton excitations of the phase field (dual to the charge) arise with a great degree of stability, governed by gauge flux changes by an integer multiple of 2π. Furthermore, it is shown that U(1) and SU(2) gauge fields play a similar role as phonons in the BCS theory: they act as the the "glue" for fermion pairing.
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vol. 126
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issue 1
342-343
EN
In the paper the temperature dependence of the thermodynamic critical field (H_c) for the alkali-metal-doped fullerides K_3C_{60} and Rb_3C_{60} has been considered. The numerical calculations have been conducted in the framework of the Migdal-Eliashberg formalism. It has been shown that the obtained numerical values of H_c agree with the experimental data. Finally, the dimensionless ratio: R_{H} ≡ T_cC^{N} (T_c)/H^{2}_c(0) has been calculated, where T_c is the critical temperature and C^{N} denotes the specific heat in the normal state. The theoretical analysis has proved that for the considered fullerides the parameter R_{H} is beyond the BCS prediction. In particular: R_{H}=0.143 for K_3C_{60}, and R_{H}=0.145 for Rb_3C_{60}.
EN
We discuss a direct effect of the energy band splitting due to the antisymmetric spin-orbit coupling on the superconducting phase transition. Employing the square lattice tight-binding model we show a significant contribution of the spin-split energy band to the pair-breaking effect in the weak- and intermediate-coupling non-centrosymmetric superconductors. We establish a general tendency of the spin-orbit coupling to suppress the critical temperature of the spin singlet and triplet states. For the weak-coupling systems we report a possible development of sharp maxima of the critical temperature for the band fillings which support the spin-orbit coupling induced Fermi surface singularities of the density of states. We note that the initial suppression of the most stable triplet state becomes comparable to the suppression of other triplet states in the intermediate-coupling regime of superconductivity.
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vol. 126
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issue 1
344-345
EN
At present, hydrides are considered as a one of the most interesting high-temperature superconductors with the classical electron-phonon pairing mechanism. In the present paper, we have analyzed the dependence of the thermodynamic critical magnetic field (H_c) on the temperature for the chlorine halide superconductor. The calculations have been made in the framework of the Eliashberg formalism for the following pressure values: p_{1}=320 GPa and p_{2}=360 GPa. We have shown that H_c increases strongly with the increase of the pressure: [H_c(0)]_{p_{2}}/[H_c(0)]_{p_{1}}= 1.43. Furthermore, the dimensionless ratio: R_{H} ≡ T_cC^{N}(T_c)/H_c^{2}(0), where T_c and C^{N} denote the critical temperature and the specific heat of the normal state, differs from the value predicted by the Bardeen-Cooper-Schrieffer theory. In particular: [R_{H}]_{p_{1}}=0.166 and [R_{H}]_{p_{2}}=0.158.
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EN
In the presented work the dependence of the thermodynamic critical field (H_{C}) on the temperature for the YNi_2B_2C superconductor was determined in the framework of the Eliashberg formalism. The numerical calculations were conducted with the use of the modified transport Eliashberg function. It has been stated that the normalized field function H_{C}(T)/H_{C}(0) correctly reproduces the experimental data.
EN
The basic thermodynamic parameters of the superconducting state in YNi_2 B_2 C were calculated in the framework of the one-band Eliashberg model. The effective Eliashberg function, determined on the basis of the transport function, was used during calculations. It was shown that the dimensionless ratios are equal to: R_1 ≡ 2Δp(0)/k_{B} T_{C} = 3.87, R_2 ≡ ΔC(T_{C})/C^{N}(T_{C}) = 1.79 and R_3 ≡ T_{C} C^{N}(T_{C}) / H_{C}^2(0) = 0.159. The value R_1 fairly agrees with the experimental data whereas R_2 and R_3 agree very well.
EN
We study the equilibrium and non-equilibrium properties of the strongly correlated quantum dot coupled between normal and superconducting leads. The effect of electron pair coherence, Coulomb interactions, and d-wave anisotropy of the order parameter are discussed with a particular account of their influence on a charge tunneling through the quantum dot.
EN
In this paper we shall present the results of numerical calculations of the superconducting characteristics (temperature dependence of the gap function and specific heat) for few different symmetries of the order parameter in relativistic theory of superconductivity. We shall discuss relevance of the results to describe newly discovered superconductors, particularly those containing heavy elements with strong spin-orbit coupling.
EN
We study the charge tunneling via the quantum dot coupled to normal and superconducting leads, where the superconducting electrode has either an isotropic or anisotropic (of d-wave symmetry) energy gap. We use the single impurity Anderson model and apply the nonequilibrium Green function formalism to determine the differential tunneling conductance. The influence of the proximity effect between the quantum dot and superconductor on the transport properties of the system manifests itself in the Andreev conductance.
EN
The detailed study of the selected thermodynamic properties of the superconducting phase in the molecular hydrogen under the pressure at 428 GPa has been presented. For the increasing value of the Coulomb pseudopotential μ^{*}∈〈0.08,0.15〉, the following results have been obtained: (i) the critical temperature decreases from 179 K to 141 K, (ii) the ratio R_{1}≡ 2Δ(0)/k_{B}T_{C} differs noticeably from the BCS value: R_{1}∈〈4.71,3.60〉; (iii) the electron effective mass is large and grows slightly together with the temperature ([m^{*}_{e}/m_{e}]_{max}=2.2 for T = T_{C}).
EN
We investigate charge tunneling through the strongly correlated quantum dot placed between the metallic and superconducting leads. For small voltages |V| ≤ Δ/e applied across the junction the current is transmitted by the anomalous mechanism of the Andreev reflections. Such transport is sensitive to the strong Coulomb interactions which can be responsible for the charging effect and, at low temperatures, for appearance of the Kondo resonance. We analyze their signatures in the differential Andreev conductance.
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