The quantum Hall effect provides a universal standard for electrical resistance that is theoretically based on only the Planck constant h and the electron charge e. Currently, this standard is implemented in GaAs/AlGaAs, but graphene's electronic properties have given hope for a more practical device. Here, we demonstrate that the experimental conditions necessary for the operation of devices made of high-quality graphene grown by chemical vapour deposition on silicon carbide can be extended and significantly relaxed compared with those for state-of-the-art GaAs/AlGaAs devices. In particular, the Hall resistance can be accurately quantized to within 1 × 10(-9) over a 10 T wide range of magnetic flux density, down to 3.5 T, at a temperature of up to 10 K or with a current of up to 0.5 mA. This experimental simplification highlights the great potential of graphene in the development of user-friendly and versatile quantum standards that are compatible with broader industrial uses beyond those in national metrology institutes. Furthermore, the measured agreement of the quantized Hall resistance in graphene and GaAs/AlGaAs, with an ultimate uncertainty of 8.2 × 10(-11), supports the universality of the quantum Hall effect. This also provides evidence of the relation of the quantized Hall resistance with h and e, which is crucial for the new Système International d'unités to be based on fixing such fundamental constants of nature.

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Monte Carlo algorithms are used to simulate the morphologies adopted by polymer chains in a polymer-blend film in the limits where the chains are mutually attractive (homophilic regime) and mutually repulsive (heterophilic regime) and then to simulate the drift transport of charges through the polymer chains. In the homophilic regime, chains aggregate into tangled domains resulting in a relatively high percolation threshold, a high density of configurational trap states, and slow, dispersive charge transport. In the heterophilic regime at the same polymer volume fraction, chains self-organize into a lacework pattern resulting in a low percolation threshold and efficient, trap-free charge transport. For homophilic morphologies interchain hopping is rate-limiting and mobility is insensitive to chain length, whereas for heterophilic morphologies intrachain transport is important and mobility increases with increasing chain length. The morphologies are used in simulations of photocurrent quantum efficiency for donor-acceptor blend photodiodes, which show that the effects of morphology on charge pair generation and recombination compete with the effect on transport, such that the optimum blend composition is sensitive to both morphology and recombination rate. We conclude that it is essential to consider the connectivity of and morphology adopted by polymer chains in the optimization of materials for organic solar cells.