Fractional dimensionality and fractional derivative spectra of interband optical transitions

Giant Gating Tunability of Optical Refractive Index in Transition Metal Dichalcogenide Monolayers

We report that the refractive index of transition metal dichacolgenide (TMDC) monolayers, such as MoS₂, WS₂, and WSe₂, can be substantially tuned by >60% in the imaginary part and >20% in the real part around exciton resonances using complementary metal-oxide-semiconductor (CMOS) compatible electrical gating. This giant tunablility is rooted in the dominance of excitonic effects in the refractive index of the monolayers and the strong susceptibility of the excitons to the influence of injected charge carriers. The tunability mainly results from the effects of injected charge carriers to broaden the spectral width of excitonic interband transitions and to facilitate the interconversion of neutral and charged excitons. The other effects of the injected charge carriers, such as renormalizing bandgap and changing exciton binding energy, only play negligible roles. We also demonstrate that the atomically thin monolayers, when combined with photonic structures, can enable the efficiencies of optical absorption (reflection) tuned from 40% (60%) to 80% (20%) due to the giant tunability of the refractive index. This work may pave the way toward the development of field-effect photonics in which the optical functionality can be controlled with CMOS circuits.

Spatiotemporal accessible solitons in fractional dimensions

We report solutions for solitons of the "accessible" type in globally nonlocal nonlinear media of fractional dimension (FD), viz., for self-trapped modes in the space of effective dimension 2<D≤3 with harmonic-oscillator potential whose strength is proportional to the total power of the wave field. The solutions are categorized by a combination of radial, orbital, and azimuthal quantum numbers (n,l,m). They feature coaxial sets of vortical and necklace-shaped rings of different orders, and can be exactly written in terms of special functions that include Gegenbauer polynomials, associated Laguerre polynomials, and associated Legendre functions. The validity of these solutions is verified by direct simulations. The model can be realized in various physical settings emulated by FD spaces; in particular, it applies to excitons trapped in quantum wells.

Exciton-dominated Dielectric Function of Atomically Thin MoS2 Films

We systematically measure the dielectric function of atomically thin MoS₂ films with different layer numbers and demonstrate that excitonic effects play a dominant role in the dielectric function when the films are less than 5–7 layers thick. The dielectric function shows an anomalous dependence on the layer number. It decreases with the layer number increasing when the films are less than 5–7 layers thick but turns to increase with the layer number for thicker films. We show that this is because the excitonic effect is very strong in the thin MoS₂ films and its contribution to the dielectric function may dominate over the contribution of the band structure. We also extract the value of layer-dependent exciton binding energy and Bohr radius in the films by fitting the experimental results with an intuitive model. The dominance of excitonic effects is in stark contrast with what reported at conventional materials whose dielectric functions are usually dictated by band structures. The knowledge of the dielectric function may enable capabilities to engineer the light-matter interactions of atomically thin MoS₂ films for the development of novel photonic devices, such as metamaterials, waveguides, light absorbers, and light emitters.

Trion X+ in vertically coupled type II quantum dots in threading magnetic field

We analyze the energy spectrum of a positively charged exciton confined in a semiconductor heterostructure formed by two vertically coupled, axially symmetrical type II quantum dots located close to each other. The electron in the structure is mainly located inside the dots, while the holes generally move in the exterior region close to the symmetry axis. The solutions of the Schrödinger equation are obtained by a variational separation of variables in the adiabatic limit. Numerical results are shown for bonding and anti-bonding lowest-lying of the trion states corresponding to the different quantum dots morphologies, dimensions, separation between them, thicknesses of the wetting layers, and the magnetic field strength.