Extremely large magnetoresistance (XMR) was recently discovered in WTe2, triggering extensive research on this material regarding the XMR origin. Since WTe2 is a layered compound with metal layers sandwiched between adjacent insulating chalcogenide layers, this material has been considered to be electronically two-dimensional (2D). Here we report two new findings on WTe2: (1) WTe2 is electronically 3D with a mass anisotropy as low as 2, as revealed by the 3D scaling behavior of the resistance R(H, θ) = R(ε θ H) with ε θ = (cos 2 θ + γ −2 sin 2 θ) 1/2 , θ being the magnetic field angle with respect to c-axis of the crystal and γ being the mass anisotropy; (2) the mass anisotropy γ varies with temperature and follows the magnetoresistance behavior of the Fermi liquid state. Our results not only provide a general scaling approach for the anisotropic magnetoresistance but also are crucial for correctly understanding the electronic properties of WTe2, including the origin of the remarkable 'turn-on' behavior in the resistance versus temperature curve, which has been widely observed in many materials and assumed to be a metal-insulator transition.

A hallmark of materials with extremely large magnetoresistance (XMR) is the transformative turnon temperature behavior: when the applied magnetic field H is above certain value, the resistivity versus temperature ρ(T ) curve shows a minimum at a field dependent temperature T * , which has been interpreted as a magnetic-field-driven metal-insulator transition or attributed to an electronic structure change. Here, we demonstrate that ρ(T ) curves with turn-on behavior in the newly discovered XMR material WTe2 can be scaled as MR ∼ (H/ρ0) m with m ≈ 2 and ρ0 being the resistivity at zero-field. We obtained experimentally and also derived from the observed scaling the magnetic field dependence of the turn-on temperature T * ∼ (H − Hc) ν with ν ≈ 1/2, which was earlier used as evidence for a predicted metal-insulator transition. The scaling also leads to a simple quantitative expression for the resistivity ρ * ≈ 2ρ0 at the onset of the XMR behavior, which fits the data remarkably well. These results exclude the possible existence of a magnetic-field-driven metal-insulator transition or significant contribution of an electronic structure change to the lowtemperature XMR in WTe2. This work resolves the origin of the turn-on behavior observed in several XMR materials and also provides a general route for a quantitative understanding of the temperature dependence of MR in both XMR and non-XMR materials.

We report the observation of an isolated charged impurity in graphene and present direct evidence of the close connection between the screening properties of a 2D electron system and the influence of the impurity on its electronic environment. Using scanning tunneling microscopy and Landau level spectroscopy, we demonstrate that in the presence of a magnetic field the strength of the impurity can be tuned by controlling the occupation of Landau-level states with a gate voltage. At low occupation the impurity is screened, becoming essentially invisible. Screening diminishes as states are filled until, for fully occupied Landau levels, the unscreened impurity significantly perturbs the spectrum in its vicinity. In this regime we report the first observation of Landau-level splitting into discrete states due to lifting the orbital degeneracy.

Two-dimensional electron systems in the presence of a magnetic field support topologically ordered states, in which the coexistence of an insulating bulk with conducting one-dimensional chiral edge states gives rise to the quantum Hall effect. For systems confined by sharp boundaries, theory predicts a unique edge-bulk correspondence, which is central to proposals of quantum Hall-based topological qubits. However, in conventional semiconductor-based two-dimensional electron systems, these elegant concepts are difficult to realize, because edge-state reconstruction due to soft boundaries destroys the edge-bulk correspondence. Here we use scanning tunnelling microscopy and spectroscopy to follow the spatial evolution of electronic (Landau) levels towards an edge of graphene supported above a graphite substrate. We observe no edge-state reconstruction, in agreement with calculations based on an atomically sharp boundary. Our results single out graphene as a system where the edge structure can be controlled and the edge-bulk correspondence is preserved.

Environmental monitoring through gas sensors is paramount for the safety and security of industrial workers and for ecological protection. Graphene is among the most promising materials considered for next-generation gas sensing due to its properties such as mechanical strength and flexibility, high surface-to-volume ratio, large conductivity, and low electrical noise. While gas sensors based on graphene devices have already demonstrated high sensitivity, one of the most important figures of merit, selectivity, remains a challenge. In the past few years, however, surface functionalization emerged as a potential route to achieve selectivity. This review surveys the recent advances in the fabrication and characterization of graphene and reduced graphene oxide gas sensors chemically functionalized with aromatic molecules and polymers with the goal of improving selectivity toward specific gases as well as overall sensor performance.