Quantum mechanical analysis of nonlinear optical response of interacting graphene nanoflakes

Abstract

We propose a distant-neighbor quantum-mechanical (DNQM) approach to study the linear and nonlinear optical properties of graphene nanoflakes (GNFs). In contrast to the widely used tight-binding description of the electronic states that considers only the nearest-neighbor coupling between the atoms, our approach is more accurate and general, as it captures the electron-core interactions between all atoms in the structure.Therefore, as we demonstrate, the DNQM approach enables the investigation of the optical coupling between two closely separated, but chemically unbound GNFs. We also find that the optical response of GNFs depends crucially on their shape, size, and symmetry properties.Specifically, increasing the size of nanoflakes is found to shift their accommodated quantum plasmon oscillations to lower frequency. Importantly, we show that by embedding a cavity into GNFs, one can change their symmetry properties, tune their optical properties, or enable otherwise forbidden second-harmonic generation processes.

Two-Dimensional Materials with Giant Optical Nonlinearities near the Theoretical Upper Limit

“…In addition, Kleinman symmetry is obeyed, meaning that all permutations among γαβ are equal in this limit . Note that centrosymmetric crystals such as graphene have a second-order response if the inversion symmetry is broken via making finite-size flakes, introducing a substrate, , applying a DC electric field, or considering the photon momentum (going beyond dipole approximation) …”

“…In addition, Kleinman symmetry is obeyed, meaning that all permutations among γαβ are equal in this limit. 45 Note that centrosymmetric crystals such as graphene have a second-order response if the inversion symmetry is broken via making finite-size flakes, 49 introducing a substrate, 50,51 applying a DC electric field, 52 or considering the photon momentum (going beyond dipole approximation). 53 A general expression for χ γαβ (2) (ω 1 , ω 2 ) containing only microscopic quantities such as transition dipole moments and energy levels can be obtained using perturbation theory and density matrices.…”

$T$-matrix method for calculation of second-harmonic generation in clusters of spherical particles

“…Note that the aforementioned numerical techniques are less accurate when the size of the scatterer is of the order of a few nanometers or less. In this case, quantum effects could become predominant, and classical numerical methods have to be supplemented with quantum mechanical techniques [38][39][40][41].…”

Atomic-Scale Defects Might Determine the Second Harmonic Generation from Plasmonic Graphene Nanostructures

“…We now turn to the second harmonic generation from GNFs with and without carbon atom vacancy defects. An ideal defect-free T-type GNF has been thoroughly studied in the literature. ,,, It is characterized by a high resonant hyperpolarizability and permits an efficient second harmonic generation in the far field. In sheer contrast, α (2) (2ω) = 0 for the defect-free C-type and H-type GNFs; i.e., no second harmonic generation is possible in the far field because of the centrosymmetric geometry of these nanoparticles.…”

“…As representative examples, we study the nonlinear second-order response of the circular (C-type, N c = 5520 carbon atoms), hexagonal (H-type, N c = 5514 carbon atoms), and triangular (T-type, N c = 5556 carbon atoms) GNFs often considered in the context of graphene plasmonics as prototypical nanoantennas allowing enhancement of the incident electromagnetic field and thus of the nonlinear effects. ,,,− The geometry of the nanostructures with the carbon atom layer located in the ( x , y )-plane is sketched in Figure . The H-type and T-type GNFs have armchair edges reducing the localized plasmon decay via edge scattering. , The charge doping with 100 (C-type), 20 (H-type), and 20 (T-type) electrons added to the neutral nanostructure, and the large enough size of the nanostructures (∼10 nm), allow one to obtain well-defined dipolar plasmon resonances in the optical response of the defect-free GNFs , as shown in Figure .…”