Recent progress in large-area synthesis of monolayer molybdenum disulphide, a new two-dimensional direct-bandgap semiconductor, is paving the way for applications in atomically thin electronics. Little is known, however, about the microstructure of this material. Here we have refined chemical vapour deposition synthesis to grow highly crystalline islands of monolayer molybdenum disulphide up to 120 μm in size with optical and electrical properties comparable or superior to exfoliated samples. Using transmission electron microscopy, we correlate lattice orientation, edge morphology and crystallinity with island shape to demonstrate that triangular islands are single crystals. The crystals merge to form faceted tilt and mirror twin boundaries that are stitched together by lines of 8- and 4-membered rings. Density functional theory reveals localized mid-gap states arising from these 8-4 defects. We find that mirror twin boundaries cause strong photoluminescence quenching whereas tilt boundaries cause strong enhancement. Meanwhile, mirror twin boundaries slightly increase the measured in-plane electrical conductivity, whereas tilt boundaries slightly decrease the conductivity.

We have experimentally determined the energies of the ground and first four excited excitonic states of the fundamental optical transition in monolayer WS2, a model system for the growing class of atomically thin two-dimensional semiconductor crystals. From the spectra, we establish a large exciton binding energy of 0.32 eV and a pronounced deviation from the usual hydrogenic Rydberg series of energy levels of the excitonic states. We explain both of these results using a microscopic theory in which the non-local nature of the effective dielectric screening modifies the functional form of the Coulomb interaction. These strong but unconventional electron-hole interactions are expected to be ubiquitous in atomically thin materials.

Python-based simulations of chemistry framework (PYSCF) is a general-purpose electronic structure platform designed from the ground up to emphasize code simplicity, so as to facilitate new method development and enable flexible computational workflows. The package provides a wide range of tools to support simulations of finite-size systems, extended systems with periodic boundary conditions, low-dimensional periodic systems, and custom Hamiltonians, using mean-field and post-mean-field methods with standard Gaussian basis functions. To ensure ease of extensibility, PYSCF uses the Python language to implement almost all of its features, while computationally critical paths are implemented with heavily optimized C routines. Using this combined Python/C implementation, the package is as efficient as the best existing C or Fortranbased quantum chemistry programs. In this paper, we document the capabilities and design philosophy of the current version of the PYSCF package.

We present a microscopic theory of neutral excitons and charged excitons (trions) in monolayers of transition metal dichalcogenides, including molybdenum disulfide. Our theory is based on an effective mass model of excitons and trions, parametrized by ab initio calculations and incorporating a proper treatment of screening in two dimensions. The calculated exciton binding energies are in good agreement with high-level many-body computations based on the Bethe-Salpeter equation. Furthermore, our calculations for the more complex trion species compare very favorably with recent experimental measurements, and provide atomistic insight into the microscopic features which determine the trion binding energy.2

Transition metal dichalcogenide (TMDC) crystals exhibit new emergent properties at monolayer thickness 1,2 , notably strong many-body e ects mediated by Coulomb interactions 3-6. A manifestation of these many-body interactions is the formation of excitons, bound electron-hole pairs, but higher-order excitonic states are also possible. Here we demonstrate the existence of four-body, biexciton states in monolayer WSe 2. The biexciton is identified as a sharply defined state in photoluminescence at high exciton density. Its binding energy of 52 meV is more than an order of magnitude greater than that found in conventional quantum-well structures 7. A variational calculation of the biexciton state reveals that the high binding energy arises not only from strong carrier confinement, but also from reduced and non-local dielectric screening. These results open the way for the creation of new correlated excitonic states linking the degenerate valleys in TMDC crystals, as well as more complex many-body states such as exciton condensates or the recently reported dropletons 8. TMDC crystals, including MoS 2 , MoSe 2 , WS 2 and WSe 2 , are semiconductors that form layered structures with a plane of hexagonal metal atoms surrounded by two planes of chalcogen atoms in trigonal prismatic coordination. At monolayer thickness, these crystals exhibit direct band gaps at the K and K points in the Brillouin zone 1,2 , and recent studies have revealed the possibility of selectively accessing the K or K valley through the use of circularly polarized light 9-12 , as well as the existence of an associated valley Hall effect 13. Importantly, many-body Coulomb interactions in these monolayer TMDC crystals have been found to be particularly strong. This leads to excitonic optical transitions in the materials, with exciton binding energies of several hundred meV (refs 3-6). In the presence of free charges, stable charged excitons (trions) have also been identified and exhibit binding energies of tens of meV (refs 12,14-16). In view of the prominence of these two-and three-body excitonic states, it is natural to ask whether two-dimensional (2D) TMDC materials, just as for the much-studied zero-and one-dimensional nanostructures 7,17-21 , also support the formation of stable biexcitons 22,23. Here we demonstrate the presence of biexcitons in monolayer WSe 2 through the discovery of a sharp new emission peak under pulsed laser excitation. We further probe the properties of the biexciton state through measurements of its ultrafast dynamics, valley polarization and thermal stability. We establish a biexciton binding energy of 52 meV. This unusually high binding energy is compatible with results of a variational analysis of biexcitonic states performed using a non-locally screened Coulomb potential to describe the interactions of charges in the atomically thin 2D material.