Black phosphorus (BP), an elemental semiconductor, has attracted tremendous interest because it exhibits a wealth of interesting electronic and optoelectronic properties in equilibrium condition. The nonequilibrium electronic structures of bulk BP under a periodic field of laser remain unexplored, but can lead to intriguing topological optoelectronic properties. Here we show that, under the irradiation of circularly polarized light (CPL), BP exhibits a photon-dressed Floquet-Dirac semimetal state, which can be continuously tuned by changing the direction, intensity, and frequency of the incident laser. The topological phase transition from type-I to type-II Floquet-Dirac fermions manifests a new form of type-III phase, which exists in a wide range of intensities and frequencies of the incident laser. Furthermore, topological surface states exhibit nonequilibrium electron transport in a direction locked by the helicity of CPL. Our findings not only deepen our understanding of fundamental properties of BP in relation to topology but also extend optoelectronic device applications of BP to the nonequilibrium regime.

Planar borophene, the truly 2D monolayer boron, has been independently successfully grown on Ag(1 1 1) by two groups (2016 Nat. Chem . 8 563 and 2015 Science 350 1513), which has received widespreading attentions. The superconducting property has not been unambiguously observed, which is unexpected because light element boron should have strong electron–phonon coupling. To resolve this puzzle, we show that the superconducting transition temperature T _c of β ₁₂ borophene is effectively suppressed by the substrate-induced tensile strain and electron doping via first principles calculations. The biaxial tensile strain of 2% induced by Ag(1 1 1) significantly reduces T _c from 14 K to 2.95 K; electron doping of 0.1 e ⁻ per boron atom further shrinks T _c to 0.09 K. We also predict that the superconducting transition temperature in β ₁₂ can be enhanced to 22.82 K with proper compressive strain (−1%) and 18.97 K with hole doping (0.1 h ⁺ per boron). Further studies indicate that the variation of T _c is closely related to the density of states of σ bands near the Fermi surface. Our results help to explain the challenges to experimentally probe superconductivity in substrate-supported borophene.

Intrinsic valley polarization can be obtained in VSe ₂ monolayers with broken inversion symmetry and time reversal symmetry. First-principles investigations reveal that the magnitude of the valley splitting in magnetic VSe ₂ induced by spin–orbit coupling reaches as high as 78.2 meV and can be linearly tuned by biaxial strain. Besides conventional polarized light, hole doping or illumination with light of proper frequency can offer effective routes to realize valley polarization. Moreover, spin–orbit coupling in monolayer VSe ₂ breaks not only the valley degeneracy but also the three-fold rotational symmetry in band structure. The intrinsic and tunable valley splitting and the breaking of optical isotropy bring additional benefits to valleytronic and optoelectronic applications.

Single-layer transition-metal dichalcogenides (TMDs) such as MoS₂ and MoSe₂ exhibit unique electronic band structures ideal for hosting many exotic spin-orbital orderings. It has been widely accepted that Rashba spin splitting (RSS) is linearly proportional to the external field in heterostructure interfaces or to the potential gradient in polar materials. Surprisingly, an extraordinary nonlinear dependence of RSS is found in semiconducting TMD monolayers under a gate field. In contrast to small and constant RSS in polar materials, the potential gradient in non-polar TMDs gradually increases with the gate bias, resulting in nonlinear RSS with a Rashba coefficient an order-of-magnitude larger than the linear one. Most strikingly, under a large gate field MoSe₂ demonstrates the largest anisotropic spin splitting among all known semiconductors to our knowledge. Based on the k·p model via symmetry analysis, we identify that the third-order contributions are responsible for the large nonlinear Rashba splitting. The gate tunable spin splitting found in semiconducting pristine TMD monolayers promises future spintronics applications in that spin polarized electrons can be generated by external gating in an experimentally accessible way.