Farhad Karimi

Dielectric function and plasmons in graphene: A self-consistent-field calculation within a Markovian master-equation formalism

We introduce a method for calculating the dielectric function of nanostructures with an arbitrary band dispersion and Bloch wave functions. The linear response of a dissipative electronic system to an external electromagnetic field is calculated by a self-consistent-field approach within a Markovian master equation formalism (SCF-MMEF) coupled with full-wave electromagnetic equations. The SCF-MMEF accurately accounts for several concurrent scattering mechanisms. The method captures interband electron-hole-pair generation, as well as the interband and intraband electron scattering with phonons and impurities. We employ the SCF-MMEF to calculate the dielectric function, complex conductivity, and loss function for supported graphene. From the loss-function maximum, we obtain plasmon dispersion and propagation length for different substrate types [nonpolar diamondlike carbon (DLC) and polar SiO

Theory of Exciton Energy Transfer in Carbon Nanotube Composites

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Basis functions for solution of non-homogeneous wave equation

and hBN], impurity densities, carrier densities, and temperatures. Plasmons on the two polar substrates are suppressed below the highest surface phonon energy, while the spectrum is broad on the nonpolar DLC. Plasmon propagation lengths are comparable on polar and nonpolar substrates and are on the order of tens of nanometers, considerably shorter than previously reported. They improve with fewer impurities, at lower temperatures, and at higher carrier densities.

Plasmons in graphene nanoribbons

We compute the exciton transfer (ET) rate between semiconducting single-wall carbon nanotubes (SWNTs). We show that the main reasons for the wide range of measured ET rates reported in the literature are (1) exciton confinement in local quantum wells stemming from disorder in the environment and (2) exciton thermalization between dark and bright states due to intratube scattering. The SWNT excitonic states are calculated by solving the Bethe–Salpeter equation using tight-binding basis functions. The ET rates due to intertube Coulomb interaction are computed via Fermi’s golden rule. In pristine samples, the ET rate between parallel (bundled) SWNTs of similar chirality is very high (∼1014 s–1), while the ET rate for dissimilar or nonparallel tubes is considerably lower (∼1012 s–1). Exciton confinement reduces the ET rate between same-chirality parallel SWNTs by 2 orders of magnitude but has little effect otherwise. Consequently, the ET rate in most measurements will be on the order of 1012 s–1, regardless o...

Quantum Transport Simulation of High-Power 4.6-μm Quantum Cascade Lasers

In this note we extend the Differential Transfer Matrix Method (DTMM) for a second-order linear ordinary differential equation to the complex plane. This is achieved by separation of real and imaginary parts, and then forming a system of equations having a rank twice the size of the real-valued problem. The method discussed in this paper also successfully removes the problem of dealing with essential singularities, which was present in the earlier formulations. Then we simplify the result for real-valued problems and obtain a new set of basis functions, which may be used instead of the WKB solutions. These basis functions not only satisfy the initial conditions perfectly, but also, may approach the turning points without the divergent behavior, which is observed in WKB solutions. Finally, an analytical transformation in the form of a matrix exponential is presented for improving the accuracy of solutions.