We present a simple and intuitive picture, an electromagnetic analog of molecular orbital theory, that describes the plasmon response of complex nanostructures of arbitrary shape. Our model can be understood as the interaction or "hybridization" of elementary plasmons supported by nanostructures of elementary geometries. As an example, the approach is applied to the important case of a four-layer concentric nanoshell, where the hybridization of the plasmons of the inner and outer nanoshells determines the resonant frequencies of the multilayer nanostructure.

We apply the recently developed plasmon hybridization method to nanoparticle dimers, providing a simple and intuitive description of how the energy and excitation cross sections of dimer plasmons depend on nanoparticle separation. We show that the dimer plasmons can be viewed as bonding and antibonding combinations, i.e., hybridization of the individual nanoparticle plasmons. The calculated plasmon energies are compared with results from FDTD simulations.

Using time-dependent density functional theory, we present a fully quantum mechanical investigation of the plasmon resonances in a nanoparticle dimer as a function of interparticle separation. We show that for dimer separations below 1 nm quantum mechanical effects, such as electron tunneling across the dimer junction and screening, significantly modify the optical response and drastically reduce the electromagnetic field enhancements relative to classical predictions. For larger separations, the dimer plasmons are well described by classical electromagnetic theory.

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We show that the plasmon resonances in single metallic nanoshells and multiple concentric metallic shell particles can be understood in terms of interaction between the bare plasmon modes of the individual surfaces of the metallic shells. The interaction of these elementary plasmons results in hybridized plasmons whose energy can be tuned over a wide range of optical and infrared wavelengths. The approach can easily be generalized to more complex systems, such as dimers and small nanoparticle aggregates.

Using the TDLDA method, we investigate how the polarizability of the d electrons of the gold atoms influences the electronic and optical properties of metallic nanoshells. It is shown that a polarizable jellium background can introduce a significant shift of the plasmon resonances. The results of the study show that the theoretically calculated optical absorption spectra for gold nanoshells with a gold sulfide core are in excellent agreement with experimental data.

The Spin-Chern (Cs) was originally introduced on finite samples by imposing spin boundary conditions at the edges. This definition lead to confusing and contradictory statements. On one hand the original paper by Sheng and collaborators revealed robust properties of Cs against disorder and certain deformations of the model and, on the other hand, several people pointed out that Cs can change sign under special deformations that keep the bulk Hamiltonian gap open. Because of the later findings, the Spin-Chern number was dismissed as a true bulk topological invariant and now is viewed as something that describes the edge where the spin boundary conditions are imposed. In this paper, we define the Spin-Chern number directly in the thermodynamic limit, without using any boundary conditions. We demonstrate its quantization in the presence of strong disorder and we argue that Cs is a true bulk topological invariant whose robustness against disorder and smooth deformations of the Hamiltonian have important physical consequences. The properties of the Spin-Chern number remain valid even when the time reversal invariance is broken. The existence of the edge channels is due to the nontrivial topology of the bulk energy bands and two nontrivial topological invariants were proposed to describe this topology, virtually in the same time: the Z 2 invariant proposed by Kane and Mele 5 and the Spin-Chern number proposed by Sheng and collaborators 6 (first mentioned in Ref. 4). In this paper we focus on the later invariant, which came under sustained scrutiny because it promised a finer classification of the Spin-Hall insulators. This was later argued not to be the case. 7,8The Spin-Chern number was computed by integrating the Berry curvature generated by imposing twisted boundary conditions on a finite sample. The numerical evidence given in Ref. 6 implied that C s is a robust topological invariant. It was later observed, however, that one can continuously deform the model using spin rotations that keep the Hamiltonian's gap unchanged but switch the sign of the Spin-Chern number.7,8 This argument shows that sometime the structure proposed in Ref. 6 fails to be a smooth fiber bundle and that C s may not be well defined over the entire Spin-Hall zone of the phase diagram. The current understanding is that, whenever one crosses certain zones of the parameter space, C s jumps, but these jumps are always by an even number. Therefore, one can still use C s to formulate a Z 2 classification of the Spin-Hall insulators and to efficiently compute the Z 2 invariant. For this reason, the interest in the Spin-Chern number continues to be strong. For example, an efficient algorithm for numerical evaluations of C s was proposed by Fukui and Hatsugai, 9 and later the algorithm was used to map C s for aperiodic systems.10 But other works totally dismiss the Spin-Chern number. 7,11For example Ref. 11 states that C s loses its meaning when the spin is not conserved.In this paper we re-define the Spin-Chern number, this time directly for an infin...