We study the conduction band spin splitting that arises in transition metal dichalcogenide (TMD) semiconductor monolayers such as MoS 2 , MoSe 2 , WS 2 , and WSe 2 due to the combination of spin-orbit coupling and lack of inversion symmetry. Two types of calculation are done. First, density functional theory (DFT) calculations based on plane waves that yield large splittings, between 3 and 30 meV. Second, we derive a tight-binding model that permits to address the atomic origin of the splitting. The basis set of the model is provided by the maximally localized Wannier orbitals, obtained from the DFT calculation, and formed by 11 atomiclike orbitals corresponding to d and p orbitals of the transition metal (W, Mo) and chalcogenide (S, Se) atoms respectively. In the resulting Hamiltonian, we can independently change the atomic spin-orbit coupling constant of the two atomic species at the unit cell, which permits to analyze their contribution to the spin splitting at the high symmetry points. We find that-in contrast to the valence band-both atoms give comparable contributions to the conduction band splittings. Given that these materials are most often n-doped, our findings are important for developments in TMD spintronics.

We study the electronic structure of a heterojunction made of two monolayers of MoS 2 and WS 2 . Our first-principles density functional calculations show that, unlike in the homogeneous bilayers, the heterojunction has an optically active band gap, smaller than the ones of MoS 2 and WS 2 single layers. We find that the optically active states of the maximum valence and minimum conduction bands are localized on opposite monolayers, and thus the lowest energy electron-holes pairs are spatially separated. Our findings portray the MoS 2 -WS 2 bilayer as a prototypical example for band-gap engineering of atomically thin two-dimensional semiconducting heterostructures.

Understanding the interaction between water and ceria surfaces is crucial in many catalytic applications. For the clean CeO2(111) surface, density functional theory (DFT) calculations using different generalized gradient approximations (GGAs) to the exchange-correlation functional and the DFT­(GGA)+U method have found that the most stable configuration is on top of a surface cerium atom. However, they disagree on the nature of the adsorption state, with water molecularly adsorbed with one or two Os–H hydrogen bonds (Os indicates a surface oxygen atom) or as a hydroxyl pair (OsHads–OHads), with only one recent report suggesting that these two structures are very close in energy. In this work, we studied the adsorption of water on CeO2(111) employing different approximations to exchange and correlation within DFT, namely, the Perdew–Burke–Ernzerhof (PBE) GGA, DFT­(PBE)+U, the Heyd–Scuseria–Ernzerhof (HSE06) hybrid functional, and van der Waals (vdW) density functionals [DFT­(vdW-DF/vdW-DF2)+U] with optimized exchange functionals (for vdW-DF, optB86b, revPBE, and optPBE; for vdW-DF2, rPW86). All of these methods predict close energies (10–100 meV range) for the two lowest-energy structures, the molecular structure with one Os–H bond and the hydroxyl pair. Our calculations show that these two species should be distinguishable by their infrared (IR) spectra. In particular, a rocking libration at 850 cm–1 could be used as an IR fingerprint to reveal the presence of the molecular structure. We found that the inclusion of vdW interactions increases binding energies by ∼0.18 eV, bringing them closer to the available experimental values.

The chirality of molecular structures is paramount in many phenomena, including enantioselective reactions, molecular self-assembly, biological processes and light or electron-spin polarization. Flat prochiral molecules, which are achiral in the gas phase or solution, can exhibit adsorption-induced chirality when deposited on surfaces. The whole array of such molecular adsorbates is naturally racemic as spontaneous global mirror-symmetry breaking is disfavoured. Here we demonstrate a chemical method of obtaining flat prochiral molecules adsorbed on the solid achiral surface in such a way that a specific adsorbate handedness globally dominates. An optically pure helical precursor is flattened in a cascade of on-surface reactions, which enables chirality transfer. The individual reaction products are identified by high-resolution scanning-probe microscopy. The ultimate formation of globally non-racemic assemblies of flat molecules through stereocontrolled on-surface synthesis allows for chirality to be expressed in as yet unexplored types of organic-inorganic chiral interfaces.