Theory of Plasmonic Nanostructures: Plasmon-Polaritons and Light-Induced Transport
Creators: name: Lamowski, Simon
Publisher: name: Zenodo
Year: 2021

description: This dissertation deals with two aspects of the theory of plasmonic nanostructures: With 1. the plasmon-polaritons in cubic metacrystals and 2. the light-induced charge transport between two metallic nanoparticles. In the first part of the thesis, 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 and the corresponding eigenmodes. 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. Then the distances have to be adjusted so that the wavelength for Bragg scattering is smaller than the corresponding wavelength of Mie scattering [M. Rybin et al., Nat. Commun. 6, 1-6 (2015)]. With this model, we predict polaritonic splittings in the range from near-infrared light to visible 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 quantitative agreement. Additionally, our model has the advantages of analytical insights and significantly less computational effort. Experimental work on a cubic metamaterial with microwaves found a polarization-dependent reflection along the double axis of rotation of the simple cubic metacrystal [M. A. Gorlach et al., Phys. Rev. B 93, 93-96 (2016)]. This measurement supports our prediction for nanostructured metamaterials with excitations in the near-infrared to the visible light range. 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 external excitations. We obtain the response to periodic excitations in the frequency range from infrared to ultraviolet light by Fourier transforming the response to a so-called kick excitation. For the system responses, we concentrate on electric field enhancement and characterize the alternating current charge transport for molecules of different lengths and the corresponding distances in the case of vacuum. For the vacuum structures, we reproduce the known distance dependence of the field amplification between the gold tetrahedrons. The field amplification at the base of the nanopyramids is an indicator of the conductivity of the structure. The investigation of the frequency-dependent 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 &lt; 2 eV and for the smallest ADT below ħω &lt; 3 eV, but at frequencies above the limiting frequency polarization of the molecules dominates the transport. The induced potential is similar to the induced charge density. It, therefore, shows a stacked dipole potential for structures with charge transport dominated by polarization. In contrast, for structures with charge transport dominated by charge transfer, the induced potential is that of a single dipole in the simulation cell. Our calculations show a continuous behavior of the induced potential within the contacts. We calculate the complex admittance for the different structures and characterize their alternating current behavior by the phase of the admittance. The currents of well-conducting structures (especially with small distances between the gold clusters) show only small phase shifts in the area between the gold structures for frequencies below 2.5 eV /ħ. The phase of the admittance shows inconclusive behavior for the vacuum-coupled clusters. With increasing length of the ADTs the phase indicates an increasingly inductive behavior for frequencies between 3.5 eV &lt; ħω &lt; 5.0 eV. For most OPEs the capacitive behavior dominates for frequencies between 2.0 eV &lt; ħω &lt; 4.5 eV. We observe explicit inductive behavior only for OPEs with two and three phenylene rings at ħω = 4.5 eV. In summary, we find clear differences from the resistive behavior for molecular contacts in the frequency range under consideration. While we study the frequency dependence with the periodic excitation, we obtain the time dependence by using single-cycle pulses as excitation. Here the main focus is on the dependence of charge transport on the amplitude and the carrier envelope phase (CEP) of the single-cycle pulse. For this purpose, we use a selection of structures used to investigate the periodic excitation. For sufficiently large amplitudes, we can describe the transferred charge in the one structure with 22.9 Å vacuum between the gold clusters with a Fowler-Nordheim model 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 mechanical 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 well for the vacuum or contact structures at the larger amplitudes. The Fowler-Nordheim based SMM reproduces the TDDFT results well for large amplitudes; however, only for the simulated structures with the smaller distances between the gold clusters. The SMMs based on a single level transport model quantitatively 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, 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 molecule 3. recombination of the charge carriers in the middle of the molecule, similar to a p-n transition. This scheme explains first the transport as a mixture of polarization and charge transfer in the periodic excitation of this structure, and second, the delay between the molecular current compared to the currents of the gold clusters. For the gold clusters coupled with n-propane dithiol (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 °. With our simulations, we can show that most charge carriers follow the external electric field. On average, the fastest charge carriers only need 8 as to pass the molecule.