Analytical and numerical solutions for a two-dimensional exciton in momentum space

Theoretical Quantum Model of Two-Dimensional Propagating Plexcitons

When plasmonic excitations of metallic interfaces and nanostructures interact with electronic excitations in semiconductors, new states emerge that hybridize the characteristics of the uncoupled states. The engendered properties make these hybrid states appealing for a broad range of applications, ranging from photovoltaic devices to integrated circuitry for quantum devices. Here, through quantum modeling, the coupling of surface plasmon polaritons and mobile two-dimensional excitons such as those in atomically thin semiconductors is examined with emphasis on the case of strong coupling. Our model shows that at around the energy crossing of the dispersion relationships of the uncoupled species, they strongly interact and polariton states --propagating plexcitons -- emerge. The temporal evolution of the system where surface plasmon polaritons are continuously injected into the system is simulated to gain initial insight on potential experimental realizations of these states. The results show a steady state that is dominated by the lower-energy polariton. The study theoretically further establishes the possible existence of propagating plexcitons in atomically thin semiconductors and provides important guidance for the experimental detection and characterization of such states for a wide range of optoelectronic technologies.

Nonlinear optics in the electron-hole continuum in 2D semiconductors: two-photon transition, second harmonic generation and valley current injection

We investigate two-photon transitions to the electron-hole scattering continuum in monolayer transition-metal dichalcogenides, and identify two contributions to this nonlinear optical process with opposite circularly polarized valley selection rules. In the non-interacting limit, the competition between the two contributions leads to a crossover of the selection rule with the increase of the two-photon energy. With the strong Coulomb interaction between the electron and hole, the two contributions excite electron-hole scattering states in orthogonal angular momentum channels, while the strength of the transition can be substantially enhanced by the interaction. Based on this picture of the two-photon transition, the second harmonic generation (SHG) in the electron-hole continuum is analyzed, where the Coulomb interaction is shown to greatly alter the relative strength of different cross-circular polarized SHG processes. Valley current injection by the quantum interference of one-photon and two-photon transition is also investigated in the presence of the strong Coulomb interaction, which significantly enhances the injection rate.

Berry Phase Modification to the Energy Spectrum of Excitons

By quantizing the semiclassical motion of excitons, we show that the Berry curvature can cause an energy splitting between exciton states with opposite angular momentum. This splitting is determined by the Berry curvature flux through the k-space area spanned by the relative motion of the electron-hole pair in the exciton wave function. Using the gapped two-dimensional Dirac equation as a model, we show that this splitting can be understood as an effective spin-orbit coupling effect. In addition, there is also an energy shift caused by other "relativistic" terms. Our result reveals the limitation of the venerable hydrogenic model of excitons, and it highlights the importance of the Berry curvature in the effective mass approximation.

Electrostatically shielded quantum confined stark effect inside polar nanostructures

The effect of electrostatic shielding of the polarization fields in nanostructures at high carrier densities is studied. A simplified analytical model, employing screened, exponentially decaying polarization potentials, localized at the edges of a QW, is introduced for the ES-shielded quantum confined Stark effect (QCSE). Wave function trapping within the Debye-length edge-potential causes blue shifting of energy levels and gradual elimination of the QCSE red-shifting with increasing carrier density. The increase in the e-h wave function overlap and the decrease of the radiative emission time are, however, delayed until the "edge-localization" energy exceeds the peak-voltage of the charged layer. Then the wave function center shifts to the middle of the QW, and behavior becomes similar to that of an unbiased square QW. Our theoretical estimates of the radiative emission time show a complete elimination of the QCSE at doping densities >/=10(20) cm(-3), in quantitative agreement with experimental measurements.