Theory of Plasmonic Nanostructures : Plasmon-Polaritons and Light-Induced Transport

Abstract

In the first part, we investigate plasmon-polaritons in cubic metacrystals of spherical metallic nanoparticles. The triple degenerate surface plasmons on the nanoparticles couple to form collective plasmons through the Coulomb-dipole-dipole interaction. The collective plasmons extend over the entire metamaterial. By hybridization of the collective plasmons with photons, they form plasmon polaritons. The latter are hybrid light-matter eigenstates of the metamaterial. Using a formalism based on Hamiltonian operators, we derive general analytical expressions for the calculation of the plasmon and plasmon-polariton dispersions. This formalism includes retardation effects of the dipolar interaction and takes into account the dielectric properties of the nanoparticles and the surrounding material. Our model can also be applied to metamaterials made of two dielectrics if one of them has a polarization-based resonance with correspondingly high efficiency of Mie scattering. With this model, we predict polaritonic splittings in the range from NIR to Vis light. These splittings depend on the polarization, lattice symmetry, and direction of propagation. Comparing our predictions with conventional finite element simulation in the frequency domain provides an excellent agreement.In the second part, we investigate with time-dependent density functional theory (TDDFT) the electronic system responses of dimers of gold clusters coupled with vacuum, n-alkane dithiol (ADT) or oligo-p-phenylene-ethynylene dithiol (OPE) for various excitations. We obtain the response to periodic excitations in the frequency range from IR to UV light by Fourier transforming the response to a kick excitation. We concentrate on electric field enhancement (FE) and characterize the AC charge transport for molecules of different lengths and the corresponding distances of vacuum. For the vacuum structures, we reproduce the distance dependence of the FE between the gold tetrahedrons. The investigation of the induced charge density allows us to estimate the different transport mechanisms: Besides charge transfer, there is the mechanism of polarization of the coupling medium. The limiting frequency for the charge transfer through OPE molecules is below ħω<2eV and for the smallest ADT below ħω<3eV. At frequencies above the limiting frequency polarization of the molecules dominates the transport. We calculate the complex admittance fand characterize the AC behavior by the phase of the admittance. The currents of well-conducting structures show only small phase shifts in the area between the gold structures for frequencies below 2.5eV/ħ. With increasing length of the ADTs the phase indicates a decreasingly capacitive behavior for frequencies between 3.5eV<ħω<5eV. For most OPEs the capacitive behavior dominates for frequencies between 2eV<ħω<4.5eV. We observe inductive behavior only for OPEs with 2 and 3 phenylene rings at ħω=4.5eV.We obtain the time dependent response by using single-cycle pulses as excitation. We use a selection of structures used to investigate the periodic excitation. For sufficiently large amplitudes, we can describe the transferred charge in the structure with 22.9Å vacuum between the gold clusters by fitting and integrating the current in the center between the gold clusters with the Fowler-Nordheim expression. We perform further analysis with Simple Man’s Models (SMMs) with different quantum descriptions of the probability of electrons tunneling out of the gold clusters. The SMM, based on the Keldysh expression for the tunneling probability, describes the results for the vacuum or contact structures at the larger amplitudes. The Fowler-Nordheim based SMM reproduces the TDDFT results for large amplitudes; however, only for the structures with smaller distances between the gold clusters. The SMMs based on a single level transport model reproduce the simulation results for the structures with smaller distances between the gold clusters for all amplitudes. We find evidence of resonance behavior in the contact structure. For the gold clusters coupled with n-propane dithiol (ADT3), we find a three-level transport mechanism after an initial polarization of the molecule. The steps are 1. recombination of the charge carriers on both ends of the molecule,2. charging of both ends of the molecule3. recombination of the charge carriers in the middle of the molecule, similar to a p-n transition.This scheme explains1. the transport as a mixture of polarization and charge transfer in the periodic excitation of this structure, and2. the delay between the molecular current compared to the currents of the gold clusters.For the gold clusters coupled with ADT3, we investigate the dependence of the amount of transported charges on the CEP studied. We find the maximum of transferred charges for CEP between -80° and -50°. Most charge carriers follow the external electric field. On average, the fastest charge carriers only need 8as to pass the molecule.