A two-dimensional honeycomb lattice harbours a pair of inequivalent valleys in the k-space electronic structure, in the vicinities of the vertices of a hexagonal Brillouin zone, K±. It is particularly appealing to exploit this emergent degree of freedom of charge carriers, in what is termed 'valleytronics'. The physics of valleys mimics that of spin, and will make possible devices, analogous to spintronics, such as valley filter and valve, and optoelectronic Hall devices, all very promising for next-generation electronics. The key challenge lies with achieving valley polarization, of which a convincing demonstration in a two-dimensional honeycomb structure remains evasive. Here we show, using first principles calculations, that monolayer molybdenum disulphide is an ideal material for valleytronics, for which valley polarization is achievable via valley-selective circular dichroism arising from its unique symmetry. We also provide experimental evidence by measuring the circularly polarized photoluminescence on monolayer molybdenum disulphide, which shows up to 50% polarization.

Graphene is an intriguing material with properties that are distinct from those of other graphitic systems. The first samples of pristine graphene were obtained by 'peeling off' and epitaxial growth. Recently, the chemical reduction of graphite oxide was used to produce covalently functionalized single-layer graphene oxide. However, chemical approaches for the large-scale production of highly conducting graphene sheets remain elusive. Here, we report that the exfoliation-reintercalation-expansion of graphite can produce high-quality single-layer graphene sheets stably suspended in organic solvents. The graphene sheets exhibit high electrical conductance at room and cryogenic temperatures. Large amounts of graphene sheets in organic solvents are made into large transparent conducting films by Langmuir-Blodgett assembly in a layer-by-layer manner. The chemically derived, high-quality graphene sheets could lead to future scalable graphene devices.

We perform a first principles calculation of the anomalous Hall effect in ferromagnetic bcc Fe. Our theory identifies an intrinsic contribution to the anomalous Hall conductivity and relates it to the k-space Berry phase of occupied Bloch states. This dc conductivity has the same origin as the well-known magneto-optical effect, and our result accounts for experimental measurement on Fe crystals with no adjustable parameters.