We present a newtype 2-dimensional (2D) magnetic semiconductor based on transition-metal dichalcogenides VX₂ (X = S, Se and Te) via first-principles calculations. The obtained indirect band gaps of monolayer VS₂, VSe₂, and VTe₂ given from the generalized gradient approximation (GGA) are respectively 0.05, 0.22, and 0.20 eV, all with integer magnetic moments of 1.0 μ_B. The GGA plus on-site Coulomb interaction U (GGA + U) enhances the exchange splittings and raises the energy gap up to 0.38~0.65 eV. By adopting the GW approximation, we obtain converged G0W0 gaps of 1.3, 1.2, and 0.7 eV for VS₂, VSe₂, and VTe₂ monolayers, respectively. They agree very well with our calculated HSE gaps of 1.1, 1.2, and 0.6 eV, respectively. The gap sizes as well as the metal-insulator transitions are tunable by applying the in-plane strain and/or changing the number of stacking layers. The Monte Carlo simulations illustrate very high Curie-temperatures of 292, 472, and 553 K for VS₂, VSe₂, and VTe₂ monolayers, respectively. They are nearly or well beyond the room temperature. Combining the semiconducting energy gap, the 100% spin polarized valence and conduction bands, the room temperature T_C, and the in-plane magnetic anisotropy together in a single layer VX₂, this newtype 2D magnetic semiconductor shows great potential in future spintronics.

Topological surface states in PbTaSe ₂ show fully gapped superconductivity, making it a potential topological superconductor.

Superconductivity in topological band structures is a platform for realizing Majorana bound states and other exotic physical phenomena such as emergent supersymmetry. This potential nourishes the search for topological materials with intrinsic superconducting instabilities, in which Cooper pairing is introduced to electrons with helical spin texture such as the Dirac surface states of topological insulators, forming a time-reversal symmetric topological superconductor on the surface. We employ first-principles calculations and angle-resolved photoemission spectroscopy experiments to reveal that ${\mathrm{PbTaSe}}_2$, a noncentrosymmetric superconductor, possesses a nonzero ${\mathbb{Z}}_2$ topological invariant and fully spin-polarized Dirac surface states. Moreover, we analyze the phonon spectrum of ${\mathrm{PbTaSe}}_2$ to show how superconductivity emerges in this compound due to a stiffening of phonons by the Pb intercalation, which diminishes a competing charge-density-wave instability. By combining our findings on the topological band structure and the superconducting electron pairing, our work establishes ${\mathrm{PbTaSe}}_2$ as a stoichiometric superconductor with topological Dirac surface states. This type of intrinsic topological Dirac superconductors holds great promise for studying aspects of topological superconductors such as Majorana zero modes.

The electronic structure and magnetocrystalline anisotropy energy of strained fcc ${\mathrm{Fe}}_3{\mathrm{O}}_4$ have been studied by using the linear muffin-tin orbital method within density functional theory. A uniaxial strain applied along the [001] direction of the magnetite is considered. It is found that the applied strain would initially reduce the calculated band gap of the majority spin and then turn the half-metallic behavior in the cubic limit into the normal metallic state at high in-plane strains of -1.3% and 2.1%. The calculated fourth-order anisotropy constant $K_1$ of cubic ${\mathrm{Fe}}_3{\mathrm{O}}_4$ is in fair agreement with the experimental value. The magnitude of $K_1$ appears to be suppressed under large extensive lateral strains. The second order uniaxial anisotropy constant $K_{\mathrm{out}}$ is positive for extensive in-plane strains and is negative for compressive in-plane strains. The positive value of $K_{\mathrm{out}}$ minus the shape anisotropy indicates that an ${\mathrm{Fe}}_3{\mathrm{O}}_4$ film under an extensive in-plane strain larger than 0.2% would show the perpendicular magnetization, in good agreement with recent experiments on ${\mathrm{Fe}}_3{\mathrm{O}}_4$ films on MgO(100) and CoO(100). Interestingly, site decomposition shows that the A- and B-site Fe atoms in the strained magnetite have comparable anisotropy energies but with the opposite signs, while the oxygen’s contribution is negligible. This implies that under an extensive lateral strain, the B-site irons would favor perpendicular magnetization while the A-site irons would prefer an in-plane magnetization. The total $K_{\mathrm{out}}$ is dictated by that of the B-site irons due to their number being twice that of the A-site irons.

Two-dimensional (2D) honeycomb lattices beyond graphene promise new physical properties such as quantum spin Hall effect. While there have been claims of growth of such lattices (silicene, germanene, stanene), their existence needs further support and their preparation and characterization remain a difficult challenge. Our findings suggest that two distinct phases associated with germanene, the analog of graphene made of germanium (Ge) instead of carbon, can be grown on Ag(111) as observed by scanning tunneling microscopy, low-energy electron diffraction, and angle-resolved photoemission spectroscopy. One such germanene exhibits an atom-resolved alternatively buckled full honeycomb lattice, which is tensile strained and partially commensurate with the substrate to form a striped phase (SP). The other, a quasifreestanding phase (QP), is also consistent with a honeycomb lattice with a lattice constant incommensurate with the substrate but very close to the theoretical value for freestanding germanene. The SP, with a lower atomic density, can be driven into the QP and coexist with the QP by additional Ge deposition. Band mapping and first-principles calculations with proposed SP and QP models reveal an interface state exists only in the SP but the characteristic σ band of freestanding germanene emerges only in the QP—this leads to an important conclusion that adlayer-substrate commensurability plays a key role to affect the electronic structure of germanene. The evolution of the dual germanene phases manifests the competitive formation of Ge-Ge covalent and Ge-Ag interfacial bonds.