In graphene, which is an atomic layer of crystalline carbon, two of the distinguishing properties of the material are the charge carriers' two-dimensional and relativistic character. The first experimental evidence of the two-dimensional nature of graphene came from the observation of a sequence of plateaus in measurements of its transport properties in the presence of an applied magnetic field. These are signatures of the so-called integer quantum Hall effect. However, as a consequence of the relativistic character of the charge carriers, the integer quantum Hall effect observed in graphene is qualitatively different from its semiconductor analogue. As a third distinguishing feature of graphene, it has been conjectured that interactions and correlations should be important in this material, but surprisingly, evidence of collective behaviour in graphene is lacking. In particular, the quintessential collective quantum behaviour in two dimensions, the fractional quantum Hall effect (FQHE), has so far resisted observation in graphene despite intense efforts and theoretical predictions of its existence. Here we report the observation of the FQHE in graphene. Our observations are made possible by using suspended graphene devices probed by two-terminal charge transport measurements. This allows us to isolate the sample from substrate-induced perturbations that usually obscure the effects of interactions in this system and to avoid effects of finite geometry. At low carrier density, we find a field-induced transition to an insulator that competes with the FQHE, allowing its observation only in the highest quality samples. We believe that these results will open the door to the physics of FQHE and other collective behaviour in graphene.

Integration of organic and inorganic electronic materials is one of the emerging approaches to achieve novel material functionalities. Here, we demonstrate a stable self-assembled monolayer of an alkylsilane grown at the surface of graphite and graphene. Detailed characterization of the system using scanning probe microscopy, X-ray photoelectron spectroscopy, and transport measurements reveals the monolayer structure and its effect on the electronic properties of graphene. The monolayer induces a strong surface doping with a high density of mobile holes (n > 10(13) cm(-2)). The ability to tune electronic properties of graphene via stable molecular self-assembly, including selective doping of steps, edges, and other defects, may have important implications in future graphene electronics.

Recently, fractional quantization of two-terminal conductance was reported in suspended graphene. The quantization, which was clearly visible in fields as low as 2 T and persistent up to 20 K in 12 T, was attributed to the formation of an incompressible fractional quantum Hall state. Here, we argue that the failure of earlier experiments to detect the integer and fractional quantum Hall effect with a Hall-bar lead geometry is a consequence of the invasive character of voltage probes in mesoscopic samples, which are easily shorted out owing to the formation of hot spots near the edges of the sample. This conclusion is supported by a detailed comparison with a solvable transport model. We also consider, and rule out, an alternative interpretation of the quantization in terms of the formation of a p-n-p junction, which could result from contact doping or density inhomogeneity. Finally, we discuss the estimate of the quasi-particle gap of the quantum Hall state. The gap value, obtained from the transport data using a conformal mapping technique, is considerably larger than in GaAs-based two-dimensional electron systems, reflecting the stronger Coulomb interactions in graphene.

Abstract:In this work, a new two-dimensional optics design method is proposed that enables the coupling of three ray sets with two lens surfaces. The method is especially important for optical systems designed for wide field of view and with clearly separated optical surfaces. Fermat's principle is used to deduce a set of functional differential equations fully describing the entire optical system. The presented general analytic solution makes it possible to calculate the lens profiles. Ray tracing results for calculated 15 th order Taylor polynomials describing the lens profiles demonstrate excellent imaging performance and the versatility of this new analytic design method. 101, 57-83 (1988). 8. J.C.W. Rogers, "Existence, uniqueness and construction of the solution of a system of ordinary functional differential equations with applications to the design of a perfectly focusing symmetric lens," IMA J. Appl. Math. 41,

Freeform optics constitutes a new technology that is currently driving substantial changes in illumination design. It liberates designers and engineers from restrictions of optical surface geometry, enabling them to achieve compact, lightweight, and efficient illumination systems with excellent optical performance. Freeform optics is currently used widely for both fundamental research and practical applications. This Review focuses on the design of freeform illumination optics, which is a key factor in advancing the development of illumination engineering. The design methods of freeform illumination optics can be divided into two groups: zero‐étendue algorithms based on ideal source assumption and design algorithms for extended light sources. The zero‐étendue algorithms include ray mapping method, Monge–Ampère equation method, and supporting quadric method. The algorithms for extended sources include illumination optimization, feedback design, and simultaneous multiple surfaces method. The characteristics and limitations of these design methods are illustrated and a summary of these methods with future outlooks is also given.

The economic use of high-efficiency solar cells in photovoltaics requires high concentration of sunlight and therefore precise dual-axis tracking of the sun. Due to their size and bulkiness, these trackers are less adequate for small- to mid-scale installations like flat rooftops. Our approach to combine concentrating and tracking of sunlight utilizes two laterally moving lens arrays. The presented analytic optics design method allows direct calculation of the free-form lens surfaces while incorporating the lateral movement. The obtained concentration performance exceeds a factor of 500. This demonstrates that one can benefit from high-efficiency solar cells and more compact and flexible single-axis trackers at the same time.

Abstract:The two-dimensional analytic optics design method presented in a previous paper [Opt. Express 20, 5576-5585 (2012)] is extended in this work to the three-dimensional case, enabling the coupling of three ray sets with two free-form lens surfaces. Fermat's principle is used to deduce additional sets of functional differential equations which make it possible to calculate the lens surfaces. Ray tracing simulations demonstrate the excellent imaging performance of the resulting free-form lenses described by more than 100 coefficients.

In this work the concept of tracking-integrated concentrating photovoltaics is studied and its capabilities are quantitatively analyzed. The design strategy desists from ideal concentration performance to reduce the external mechanical solar tracking effort in favor of a compact installation, possibly resulting in lower overall cost. The proposed optical design is based on an extended Simultaneous Multiple Surface (SMS) algorithm and uses two laterally moving plano-convex lenses to achieve high concentration over a wide angular range of ±24°. It achieves 500× concentration, outperforming its conventional concentrating photovoltaic counterparts on a polar aligned single axis tracker.