Fully relativistic first-principles calculations based on density functional theory are performed to study the spin-orbit-induced spin splitting in monolayer systems of the transition-metal dichalcogenides MoS2, MoSe2, WS2, and WSe2. All these systems are identified as direct-band-gap semiconductors. Giant spin splittings of 148\char21{}456 meV result from missing inversion symmetry. Full out-of-plane spin polarization is due to the two-dimensional nature of the electron motion and the potential gradient asymmetry. By suppression of the Dyakonov-Perel spin relaxation, spin lifetimes are expected to be very long. Because of the giant spin splittings, the studied materials have great potential in spintronics applications.

“Two-dimensional (2D) materials as electrodes” is believed to be the trend for future Li-ion and Na-ion battery technologies. Here, by using first-principles methods, we predict that the recently reported borophene (2D boron sheets) can serve as an ideal electrode material with high electrochemical performance for both Li-ion and Na-ion batteries. The calculations are performed on two experimentally stable borophene structures, namely β₁₂ and χ₃ structures. The optimized Li and Na adsorption sites are identified, and the host materials are found to maintain good electric conductivity before and after adsorption. Besides advantages including small diffusion barriers and low average open-circuit voltages, most remarkably, the storage capacity can be as high as 1984 mA h g⁻¹ in β₁₂ borophene and 1240 mA h g⁻¹ in χ₃ borophene for both Li and Na, which are several times higher than the commercial graphite electrode and are the highest among all the 2D materials discovered to date. Our results highly support that borophenes can be appealing anode materials for both Li-ion and Na-ion batteries with extremely high power density.

Using first-principles calculations, we propose a two-dimensional diluted magnetic semiconductor: monolayer MoS${}_2$ doped by transition metals. Doping of transition metal atoms from the IIIB to VIB groups results in nonmagnetic states, since the number of valence electrons is smaller or equal to that of Mo. Doping of atoms from the VIIB to IIB groups becomes energetically less and less favorable. Magnetism is observed for Mn, Fe, Co, Zn, Cd, and Hg doping, while for the other dopants from these groups it is suppressed by Jahn-Teller distortions. Analysis of the binding energies and magnetic properties indicates that (Mo,$X$)S${}_2$ ($X=\text{Mn}$, Fe, Co, and Zn) are promising systems to explore two-dimensional diluted magnetic semiconductors.