The realization of long-range ferromagnetic order in two-dimensional van der Waals crystals, combined with their rich electronic and optical properties, could lead to new magnetic, magnetoelectric and magneto-optic applications. In two-dimensional systems, the long-range magnetic order is strongly suppressed by thermal fluctuations, according to the Mermin-Wagner theorem; however, these thermal fluctuations can be counteracted by magnetic anisotropy. Previous efforts, based on defect and composition engineering, or the proximity effect, introduced magnetic responses only locally or extrinsically. Here we report intrinsic long-range ferromagnetic order in pristine CrGeTe atomic layers, as revealed by scanning magneto-optic Kerr microscopy. In this magnetically soft, two-dimensional van der Waals ferromagnet, we achieve unprecedented control of the transition temperature (between ferromagnetic and paramagnetic states) using very small fields (smaller than 0.3 tesla). This result is in contrast to the insensitivity of the transition temperature to magnetic fields in the three-dimensional regime. We found that the small applied field leads to an effective anisotropy that is much greater than the near-zero magnetocrystalline anisotropy, opening up a large spin-wave excitation gap. We explain the observed phenomenon using renormalized spin-wave theory and conclude that the unusual field dependence of the transition temperature is a hallmark of soft, two-dimensional ferromagnetic van der Waals crystals. CrGeTe is a nearly ideal two-dimensional Heisenberg ferromagnet and so will be useful for studying fundamental spin behaviours, opening the door to exploring new applications such as ultra-compact spintronics.

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.

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Van der Waals coupling is emerging as a powerful method to engineer physical properties of atomically thin two-dimensional materials. In coupled graphene-graphene and graphene-boron nitride layers, interesting physical phenomena ranging from Fermi velocity renormalization to Hofstadter's butterfly pattern have been demonstrated. Atomically thin transition metal dichalcogenides, another family of two-dimensional-layered semiconductors, can show distinct coupling phenomena. Here we demonstrate the evolution of interlayer coupling with twist angles in as-grown molybdenum disulfide bilayers. We find that the indirect bandgap size varies appreciably with the stacking configuration: it shows the largest redshift for AA-and AB-stacked bilayers, and a significantly smaller but constant redshift for all other twist angles. Our observations, together with ab initio calculations, reveal that this evolution of interlayer coupling originates from the repulsive steric effects that leads to different interlayer separations between the two molybdenum disulfide layers in different stacking configurations.

Topological insulators are an emerging class of materials that host highly robust in-gap surface or interface states while maintaining an insulating bulk. Most advances in this field have focused on topological insulators and related topological crystalline insulators in two dimensions and three dimensions, but more recent theoretical work has predicted the existence of one-dimensional symmetry-protected topological phases in graphene nanoribbons (GNRs). The topological phase of these laterally confined, semiconducting strips of graphene is determined by their width, edge shape and terminating crystallographic unit cell and is characterized by a [Formula: see text] invariant (that is, an index of either 0 or 1, indicating two topological classes-similar to quasi-one-dimensional solitonic systems). Interfaces between topologically distinct GNRs characterized by different values of [Formula: see text] are predicted to support half-filled, in-gap localized electronic states that could, in principle, be used as a tool for material engineering. Here we present the rational design and experimental realization of a topologically engineered GNR superlattice that hosts a one-dimensional array of such states, thus generating otherwise inaccessible electronic structures. This strategy also enables new end states to be engineered directly into the termini of the one-dimensional GNR superlattice. Atomically precise topological GNR superlattices were synthesized from molecular precursors on a gold surface, Au(111), under ultrahigh-vacuum conditions and characterized by low-temperature scanning tunnelling microscopy and spectroscopy. Our experimental results and first-principles calculations reveal that the frontier band structure (the bands bracketing filled and empty states) of these GNR superlattices is defined purely by the coupling between adjacent topological interface states. This manifestation of non-trivial one-dimensional topological phases presents a route to band engineering in one-dimensional materials based on precise control of their electronic topology, and is a promising platform for studies of one-dimensional quantum spin physics.

Monolayer transition metal dichalcogenide (TMDC) crystals, as direct-gap materials with unusually strong light-matter interaction, have attracted much recent attention. In contrast to the initial understanding, the minima of the conduction band are predicted to be spin split. Because of this splitting and the spin-polarized character of the valence bands, the lowest-lying excitonic states in WX 2 (X=S, Se) are expected to be spin-forbidden and optically dark. To date, however, there has been no direct experimental probe of these dark band-edge excitons, which strongly influence the light emission properties of the material. Here we show how an in-plane magnetic field can brighten the dark excitonic states and allow their properties to be revealed experimentally in monolayer WSe 2 . In particular, precise energy levels for both the neutral and charged dark excitons were obtained and compared with ab-initio calculations using the GW-BSE approach. Greatly increased emission and valley lifetimes were observed for the brightened dark states as a result of their spin configuration. These studies directly probe the excitonic spin manifold and provide a new route to tune the optical and valley properties of these prototypical twodimensional semiconductors.The electronic and optical properties of ultrathin TMDC crystals in the MX 2 (M = Mo, W, X = S, Se) family have attracted much recent attention. These 2D semiconductors exhibit a direct bandgap at monolayer thickness 1, 2 , have strong and anomalous excitonic interactions [3][4][5] , and offer the potential for highly efficient light emission. The materials also provide an ideal platform for access to the valley degree of freedom, since the optical selection rules provide a

The physical properties of two-dimensional van der Waals (2D vdW) crystals depend sensitively on the interlayer coupling, which is intimately connected to the stacking arrangement and the interlayer spacing. For example, simply changing the twist angle between graphene layers can induce a variety of correlated electronic phases 1-8 , which can be controlled further in a continuous manner by applying hydrostatic pressure to decrease the interlayer spacing 3 . In the recently discovered 2D magnets 9,10 , theory suggests that the interlayer exchange coupling strongly depends on layer separation, while the stacking arrangement can even change the sign of the magnetic exchange, thus drastically modifying the ground state 11-15 . Here, we demonstrate pressure tuning of magnetic order in the 2D magnet CrI3. We probe the magnetic states using tunneling 16,17 and scanning magnetic circular dichroism microscopy measurements 10 . We find that the interlayer magnetic coupling can be more than doubled by hydrostatic pressure. In bilayer CrI3, pressure induces a transition from layered antiferromagnetic to ferromagnetic phases. In trilayer CrI3, pressure can create coexisting domains of three phases, one ferromagnetic and two distinct antiferromagnetic. The observed changes in magnetic order can be explained by changes in the stacking arrangement. Such coupling between stacking order and magnetism provides ample opportunities for designer magnetic phases and functionalities. discussion.

Bandgap engineering is used to create semiconductor heterostructure devices that perform processes such as resonant tunnelling and solar energy conversion. However, the performance of such devices degrades as their size is reduced. Graphene-based molecular electronics has emerged as a candidate to enable high performance down to the single-molecule scale. Graphene nanoribbons, for example, can have widths of less than 2 nm and bandgaps that are tunable via their width and symmetry. It has been predicted that bandgap engineering within a single graphene nanoribbon may be achieved by varying the width of covalently bonded segments within the nanoribbon. Here, we demonstrate the bottom-up synthesis of such width-modulated armchair graphene nanoribbon heterostructures, obtained by fusing segments made from two different molecular building blocks. We study these heterojunctions at subnanometre length scales with scanning tunnelling microscopy and spectroscopy, and identify their spatially modulated electronic structure, demonstrating molecular-scale bandgap engineering, including type I heterojunction behaviour. First-principles calculations support these findings and provide insight into the microscopic electronic structure of bandgap-engineered graphene nanoribbon heterojunctions.