The electronic and optical properties of phosphorene co-doped with vanadium and nonmetallic atoms (B, C, N and O) are investigated by employing first-principles calculations based on density functional theory. It is found that the geometrical, electronic and optical properties are affected distinctly by these dopants. Significant local lattice distortions are observed in all of the V–X (X = B, C, N or O) co-doped systems. All the substituted systems retain their semiconducting character, but their band gaps become smaller than that of primitive phosphorene. This indicates that impurity doping is an effective way to modulate the band gap of phosphorene for different applications in electronic devices. Obvious covalent interactions exist between the impurities and their adjacent phosphorus atoms. In these doped systems, an interesting redshift phenomenon and significant anisotropy are observed in their optical properties. Our theoretical investigations suggest an alternative method towards modulating the electronic and optical properties of phosphorene, and predict potential applications of phosphorene in nanoelectronic and optical devices.

The O-doping effects for monolayer molybdenum disulfide (MoS2MoS2) are systematically investigated by first-principle calculations. It is shown that the geometrical, electronic and optical properties are affected distinctively by the oxygen dopant. Structural analysis reveals a local contraction along c   axis in the substituted cases. The substitution of oxygen for a sulfur atom in monolayer MoS2MoS2 leads to a transition from a direct K–K band gap to an indirect Γ  –K band gap. And, the value of band gap decreases with increasing doping concentration. In addition, for the pure MoS2MoS2, strong covalent chemical bonds are formed on the Mo–S bonds, which is ascribed to the strong hybridization between Mo-4d and S-3p orbitals. After oxygen doping, the covalent bonding of Mo–S is distinctively weakened. More electrons are transferred from Mo to O because of the larger electronegativity of O, and the atomic populations of O atoms become larger than that of S atoms. Optical properties are also found to be affected distinctively by the oxygen dopant. An interesting blue-shift of the absorption threshold is observed in the O-doped systems.The O-doped monolayer molybdenum disulfide (MoS2) with different O-doping concentrations are systematically investigated by first-principle calculations. The geometrical, electronic and optical properties are found to be affected distinctively by the oxygen dopant. The substitution of oxygen for a sulfur atom in monolayer MoS2 leads to a transition from an direct K–K band gap to an indirect Γ–K band gap. An interesting blue-shift of the absorption threshold is observed in the O-doped systems.

Highlights•Detailed magnetization structures of all the magnetization plateaus are uncovered.•Some plateaus with the same magnetization have different spin configurations.•Three D-h magnetization diagrams and phase diagrams are determined.•Phase boundaries can be exactly determined by energy level crossing.•A phase transition line (D=J) not recognized previously is detected.By the infinite time-evolving block decimation (iTEBD) algorithm, the magnetization process of the spin-32 bond-alternating Ising chain with single-ion anisotropy (D) is investigated. Magnetization plateaus including detailed magnetization structures of three different cases are uncovered, and three rich ground-state phase diagrams are explicitly determined. Especially, for the uniform antiferromagnetic case, a phase transition line at D=J, which divides the Mz=0 (Mz=12) plateau into two phases, are detected by the magnetization structure and the ground-state energy, and a updated phase diagram is proposed. Such a transition line was not recognized by the average magnetization previously. A same transition line (D=J  ) is also detected in the phase diagram of the antiferromagnetic-ferromagnetic alternating case. Magnetization plateaus are found to be easily induced for the classical Ising systems without quantum fluctuations, and the single-ion anisotropy plays a key role in the formation of Mz=12 and 1 plateaus in the present model.

Highlights•A Δ–h magnetization phase diagram is determined by two-site entanglement.•The 1/3 plateau phase can be understood by the Haldane mechanism.•Except for the KT transition, all the other QPTs are determined to be second-order.•The KT point, where the 1/3 plateau phase vanishes, is numerically determined.The magnetization and quantum phase transitions (QPTs) in a spin-(12, 1) XXZ chain under external magnetic field are investigated by the infinite time-evolving block-decimation method. A Δ−h magnetization phase diagram including three different ground-state phases, i.e.  , a ferromagnetic phase, a 13 plateau phase, and a spin-fluid phase, is determined. The Kosterlitz–Thouless (KT) point, where the 13 plateau phase vanishes, is determined to be (Δc=−0.53, hc=0.23). Except for the KT transition, all the other QPTs belong to the second-order category. By the logarithm behavior of the bipartite entanglement, the central charge in the whole critical spin-fluid phase is evaluated to be c  =1. It is found that the Haldane mechanism (picture) can be used to understand the formation of the 13 plateau state in the present model. Strong enough longitudinal antiferromagnetic correlation is found to be necessary for the appearance of such a Haldane plateau.