By taking account of the electric-field-induced charge screening, a self-consistent calculation within the framework of the tight-binding approach is employed to obtain the electronic band structure of gated multilayer phosphorene and the charge densities on the different phosphorene layers. We find charge density and screening anomalies in single-gated multilayer phosphorene and electron-hole bilayers in dual-gated multilayer phosphorene. Due to the unique puckered lattice structure, both intralayer and interlayer charge screenings are important in gated multilayer phosphorene. We find that the electric-field tuning of the band structure of multilayer phosphorene is distinctively different in the presence and absence of charge screening. For instance, it is shown that the unscreened band gap of multilayer phosphorene decreases dramatically with increasing electric-field strength. However, in the presence of charge screening, the magnitude of this band-gap decrease is significantly reduced and the reduction depends strongly on the number of phosphorene layers. Our theoretical results of the band-gap tuning are compared with recent experiments and good agreement is found.

Electro-optical modulators, which use an electric voltage (or an electric field) to modulate a beam of light, are essential elements in present-day telecommunication devices. Using a self-consistent tight-binding approach combined with the standard Kubo formula, we show that the optical conductivity and the linear dichroism of few-layer phosphorene can be modulated by a perpendicular electric field. We find that the field-induced charge screening plays a significant role in modulating the optical conductivity and the linear dichroism. Distinct absorption peaks are induced in the conductivity spectrum due to the strong quantum confinement along the out-of-plane direction and to the field-induced forbidden-to-allowed transitions. The field modulation of the linear dichroism becomes more pronounced with increasing number of phosphorene layers. We also show that the Faraday rotation is present in few-layer phosphorene even in the absence of an external magnetic field. This optical Hall effect is induced by the reduced lattice symmetry of few-layer phosphorene. The Faraday rotation is greatly influenced by the field-induced charge screening and is strongly dependent on the strength of perpendicular electric field and on the number of phosphorene layers.

We investigate the energy levels and persistent currents of MoS 2 quantum rings having different shapes and edge types in the presence of a perpendicular magnetic field by means of the tight-binding approach. We find states localized at the inner and outer boundaries of the ring. These energy levels exhibit different magnetic field dependences for the inner and outer ring states due to their different localization properties. They both exhibit the usual Aharanov-Bohm oscillations but with different oscillation periods. In the presence of spin-orbit coupling, we show distinct spin and charge persistent currents for inner and outer ring states. We find well-defined spin currents with negligibly small charge currents. This is because the local currents of spin-up and -down states flow in opposite directions.

We investigate theoretically the linear dichroism and the Faraday rotation of strained few-layer phosphorene, where strain is applied uniaxially along the armchair or zigzag direction of the phosphorene lattice. We calculate the optical conductivity tensor of uniaxially strained few-layer phosphorene by means of the Kubo formula within the tight-binding approach. We show that the linear dichroism and the Faraday rotation of few-layer phosphorene can be significantly modulated by the applied strain. The modulation depends strongly on both the magnitude and direction of strain and becomes more pronounced with increasing number of phosphorene layers. Our results are relevant for mechano-optoelectronic applications based on optical absorption and Hall effects in strained few-layer phosphorene.