Radius dependent shift of surface plasmon frequency in large metallic nanospheres: theory and experiment

Theoretical description of oscillations of electron liquid in large metallic nanospheres (with radius of few tens nm) is formulated within random-phase-approximation semiclassical scheme. Spectrum of plasmons is determined including both surface and volume type excitations. It is demonstrated that only surface plasmons of dipole type can be excited by homogeneous dynamical electric field. The Lorentz friction due to irradiation of electro-magnetic wave by plasmon oscillations is analyzed with respect to the sphere dimension. The resulting shift of resonance frequency turns out to be strongly sensitive to the sphere radius. The form of e-m response of the system of metallic nanospheres embedded in the dielectric medium is found. The theoretical predictions are verified by a measurement of extinction of light due to plasmon excitations in nanosphere colloidal water solutions, for Au and Ag metallic components with radius from 10 to 75 nm. Theoretical predictions and experiments clearly agree in the positions of surface plasmon resonances and in an emergence of the first volume plasmon resonance in the e-m response of the system for limiting big nanosphere radii, when dipole approximation is not exact

On Possibility of Realization of d- or p-Wave Symmetry States in Anisotropic Superconductors

We consider a model of high-T$\text{}_{c}$ superconductors with an anisotropic boson-mediated pairing mechanism corresponding to the nearest-neighbor interactions, and the one-particle dispersion relation characterized by 2D Fermi surface nesting. Based upon the tight-binding or t-J approaches with half-filling we show that the effective pairing potential coefficients and the dispersion relation, which can be characterized by the parameterη=2t$\text{}_{1}$/t$\text{}_{0}$, have a diverse and mutually competing influence on the values of transition temperatures. The spin-singlet d-wave symmetry superconducting state is realized for small values ofη, whereas for sufficiently large values, the spin-triplet p-wave symmetry superconducting state should be formed. The specific heat jump and the isotope shift, as functions of the parameter η, are evaluated for the d- and p-wave symmetry

Competition mechanism between singlet and triplet superconductivity in the tight-binding model with anisotropic attractive potential

Based upon the tight-binding formalism a model of a high-Tc superconductor with isotropic and anisotropic attractive interactions is considered analytically. Symmetry facets of the group C4v are included within a method of successive transformations of the reciprocal space. Complete sets of basis functions of C4v irreducible representations are given. Plausible spin-singlet and spin-triplet superconducting states are classified with regard to the chosen basis functions. It is displayed that pairing interaction coefficients and the dispersion relation, which can be characterized by the parameter η= 2t1/t0, have a diverse and mutually competing influence on the value of the transition temperature. It is also shown that in the case of a nearly half-filled conduction band and an anisotropic pairing interaction the spin-singlet d-wave symmetry superconducting state is realized for small values of the parameter η, whereas in the opposite limit, for sufficiently large values, the spin-triplet p-wave symmetry superconducting state has to be formed. This result cannot be obtained within the Van Hove scenario or BCS-type approaches, where the p-wave symmetry superconducting state absolutely dominates. The specific heat jump and the isotope shift as functions of the parameter η are assessed and discussed for the d-wave symmetry singlet and the p-wave symmetry triplet states

Islands of stability of the d-wave order parameter in s-wave anisotropic superconductors

In this paper we find and present on diagrams in the coordinates of η=2t 1/t 0 (the ratio of the second and the first nearest neighbor hopping integrals) and n (the carrier concentration) the areas of stability for the superconducting spin-singlet s- and d-wave and the spin-triplet p-wave order parameters hatching out during the phase transition from the normal to the superconducting phase. The diagrams are obtained for an anisotropic two-dimensional superconducting system with a relatively wide partially-filled conduction band. We study a tight-binding model with an attractive nearest neighbor interaction with the amplitude V 1, and the on-site interaction (with the amplitude V 0) taken either as repulsive or attractive. The problem of the coexistence of the s-, p- and d-wave order parameters is addressed and solved for chosen values of the ratio V 0/V 1. A possible island of stability of the d-wave order parameter in the s-wave order parameter environment for a relatively strong on-site interaction is revealed. The triple points, around which the s-, d-, and p-wave order parameters coexist, are localized on diagrams. It is shown that results of the calculations performed for the two-dimensional tight-binding band model are dissimilar with some obtained within the BCS-type approximation. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 200874.20.Rp Pairing symmetries (other than s-wave), 74.62.Yb Other effects,

PARAMETRIC EQUATIONS FOR THE ENERGY GAP. EXTENDED BCS CASE

The generalised form of the gap equation which comprises also some non-BCS approaches is defined and solved. The parametric gap equations have been derived in a few equivalent cases and discussed in_ dissimilar limits. It is shown that the relations between the critical temperature and zero-temperature energy gap can be extended for all systems under consideration. The main benefits and incontestable advantage of the presented method are demonstrated with regard to the general BCS case

Competition mechanism between singlet and triplet superconductivity in the tight-binding model with anisotropic attractive potential

Based upon the tight-binding formalism a model of a high-T c superconductor with isotropic and anisotropic attractive interactions is considered analytically. Symmetry facets of the group C 4v are included within a method of successive transformations of the reciprocal space. Complete sets of basis functions of C 4v irreducible representations are given. Plausible spin-singlet and spin-triplet superconducting states are classified with regard to the chosen basis functions. It is displayed that pairing interaction coefficients and the dispersion relation, which can be characterized by the parameter η= 2t 1/t 0, have a diverse and mutually competing influence on the value of the transition temperature. It is also shown that in the case of a nearly half-filled conduction band and an anisotropic pairing interaction the spin-singlet d-wave symmetry superconducting state is realized for small values of the parameter η, whereas in the opposite limit, for sufficiently large values, the spin-triplet p-wave symmetry superconducting state has to be formed. This result cannot be obtained within the Van Hove scenario or BCS-type approaches, where the p-wave symmetry superconducting state absolutely dominates. The specific heat jump and the isotope shift as functions of the parameter η are assessed and discussed for the d-wave symmetry singlet and the p-wave symmetry triplet states. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2006