Time-Dependent Response of Carbon Nano-Structures

The progress of nanotechnology has led to the development of nanometer scale devices such as nano-antennas, molecular junctions, and others. The calculation of such devices' electromagnetic response becomes a challenge as it requires the integration of the classical form of Maxwell's equations with the quantum equations governing the electronic structure. To that end, Time-Dependent Density Functional Theory (TDDFT) reliably predicts the optical and electronic properties of molecules in the presence of external fields. However, most TDDFT formalisms only account for the electrostatic scalar potential, ignoring the presence of induced magnetic fields, and the retardation effects which follow. Disregarding the vector potential leads to an incorrect characterization of electronic structures exceeding certain size-to-wavelength ratio, the wavelength being that of the external electromagnetic field. In this work, the inclusion of induced vector potentials in the time-dependent Kohn-Sham equation is explored in both the Coulomb and Lorentz gauges. Although the Coulomb gauge is the commonly adapted gauge-fixing condition in TDDFT, the Lorentz gauge is shown to be just as effective in characterizing the response of electronic structures, bypassing the need for a projection scheme of the current density, via Helmholtz decomposition. In both gauges, fully incorporating the scalar and vector potentials can be computationally costly due to the retardation effects. Specifically, direct evaluation of the retarded integrals with their intrinsic dependence on past densities creates a computational bottleneck. To overcome this difficulty, highly efficient FFT-based integral methods utilizing multilevel schemes are employed. Carbon systems reaching the nanometric regime are explored in both gauges and various properties, appearing as a consequence of the newly incorporated induced fields, are demonstrated.