Scaling of Coulomb pseudo-potential in s-wave narrow-band superconductors

The Coulomb pseudo-potential $\mu^*$ is extracted by fitting the numerically calculated transition temperature $T_c$ of the Eliashberg-Nambu equation which is extended to incorporate the narrow-band effects, that is, the vertex correction and the frequency dependence of the screened Coulomb interaction. It is shown that even for narrow-band superconductors, where the fermi energy $\epsilon_F$ is comparable with the phonon frequency $\omega_{ph}$, the Coulomb pseudo-potential is a pertinent parameter, and is still given by $\mu^* = \mu/[1+\mu \ln(\epsilon_F/\omega_{ph})]$, provided $\omega_{ph}$ is appropriately scaled.Comment: 5 pages, 3 figures, accepted for publication by Phys. Rev.

Entropy in the Kerr-Newman Black Hole

Entropy of the Kerr-Newman black hole is calculated via the brick wall method with maintaining careful attention to the contribution of superradiant scalar modes. It turns out that the nonsuperradinat and superradiant modes simultaneously contribute to the entropy with the same order in terms of the brick wall cutoff $\epsilon$. In particular, the contribution of the superradiant modes to the entropy is negative. To avoid divergency in this method when the angular velocity tends to zero, we propose to intr oduce a lower bound of angular velocity and to treat the case of the angular momentum per unit mass $a=0$ separately. Moreover, from the lower bound of the angular velocity, we obtain the $\theta$-dependence structure of the brick wall cutoff, which natu rally requires an angular cutoff $\delta$. Finally, if the cutoff values, $\epsilon$ and $\delta$, satisfy a proper relation between them, the resulting entropy satisfies the area law.Comment: 16 pages, Latex, no figures, References are included, Subsection A and B are reduced to subsection A, Abstract is rewritten, Minor corrections are include

Plasmonic properties of metallic nanostructures

Based on the plasmon hybridization theory, this thesis provides physical understanding of the plasmonic nature of metallic nanostructures. Metallic films and nanoshell particles exhibit bonding and antibonding plasmon resonances formed by hybridization of plasmon resonances associated with the two surfaces confining the metal. For both structures the lower energy bonding plasmon resonance is characterized by symmetric alignment of the charge densities. This thesis presents a physically intuitive explanation for why the repulsive symmetric charge alignment results in a low energy bonding plasmon. It also shows that the plasmon dispersion for a planar thin film can be obtained from the plasmon resonances of a metallic nanoshell in the limit of infinite radius. After clarifying the nature of plasmon modes of thin metal films, the optical properties of an individual nanohole in a thin metallic film are examined theoretically and experimentally. Subwavelength holes, one of the most important structures in nanophotonics, give rise to extraordinary transmission when patterened in arrays. The individual holes provided a site for excitation of the underlying thin film surface plasmons. It is shown that both hole diameter and film thickness determine the energy of the optical resonance. I also show that the hole plasmon resonance (HPR) depends strongly on the polarization of the incident light due to the optical coupling between antibonding film plasmon modes and perpendicularly polarized light to the film surface. The hybridization scheme is extended to the coherent coupling between the localized plasmons of a nanoshell and the excitons of J-aggregate molecules adsorbed on the metallic nanoparticle surface. Timing the nanoshell plasmon resonant energies across the exciton energy of the J-aggregate obtains hybridized energies for plasmon-exciton coupling. The coupling strength depends on the specific plasmon mode of the nanoshell coupled to the exciton mode of the J-aggregate. Experimental data of optical extinction spectra is reproduced by using Mie theory, and the plasmon-exciton coupling of nanoshell/J-aggregate complexes systems can be quantitatively as well as qualitatively understood based on Gans theory. The plasmon hybridization theory can be also applied to various shapes of nanopartides using particular coordinate systems. This thesis investigate the optical properties of metallic toroidal nanoparticles using the plasmon hybridization theory. For incident light polarized in the plane of the torus, a low energy dipolar plasmon resonance and a high energy resonance contributed by several higher order torus modes appear in the optical spectra. The low energy node is highly tunable with the aspect ratio in terms of two characteristic radii of tori. For perpendicular polarization, the plasmon resonance is weakly dependent on the aspect ratio because the excited higher order torus modes are closely spaced. Optical spectra calculated by plasmon hybridization method show excellent agreement with numerical finite difference time domain calculation results