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Pristine graphene and graphene-based heterostructures can exhibit exceptionally high electron mobility if their surface contains few electron-scattering impurities. Mobility directly influences electrical conductivity and its dependence on the carrier density. But linking these key transport parameters remains a challenging task for both theorists and experimentalists. Here, we report numerical and analytical models of carrier transport in graphene, which reveal a universal connection between graphene’s carrier mobility and the variation of its electrical conductivity with carrier density. Our model of graphene conductivity is based on a convolution of carrier density and its uncertainty, which is verified by numerical solution of the Boltzmann transport equation including the effects of charged impurity scattering and optical phonons on the carrier mobility. This model reproduces, explains, and unifies experimental mobility and conductivity data from a wide range of samples and provides a way to predict a priori all key transport parameters of graphene devices. Our results open a route for controlling the transport properties of graphene by doping and for engineering the properties of 2D materials and heterostructures. Graphene exhibits both extremely high electrical conductivity and electron mobility but an incomplete understanding of the underlying mechanisms so far limits potential applications in electrical devices. Here, the authors theoretically and experimentally investigate the role of charged impurities and optical phonons on the conductivity properties of graphene and establish a universal connection between the mobility and conductivity.

Magnetoencephalography (MEG) is a sophisticated tool which yields rich information on the spatial, spectral and temporal signatures of human brain function. Despite unique potential, MEG is limited by a low signal-to-noise ratio (SNR) which is caused by both the inherently small magnetic fields generated by the brain, and the scalp-to-sensor distance. The latter is limited in current systems due to a requirement for pickup coils to be cryogenically cooled. Recent work suggests that optically-pumped magnetometers (OPMs) might be a viable alternative to superconducting detectors for MEG measurement. They have the advantage that sensors can be brought to within ~4 mm of the scalp, thus offering increased sensitivity. Here, using simulations, we quantify the advantages of hypothetical OPM systems in terms of sensitivity, reconstruction accuracy and spatial resolution. Our results show that a multi-channel whole-head OPM system offers (on average) a fivefold improvement in sensitivity for an adult brain, as well as clear improvements in reconstruction accuracy and spatial resolution. However, we also show that such improvements depend critically on accurate forward models; indeed, the reconstruction accuracy of our simulated OPM system only outperformed that of a simulated superconducting system in cases where forward field error was less than 5%. Overall, our results imply that the realisation of a viable whole-head multi-channel OPM system could generate a step change in the utility of MEG as a means to assess brain electrophysiological activity in health and disease. However in practice, this will require both improved hardware and modelling algorithms.

We have investigated the geometry-induced magnetoresistance (MR) observed in a high mobility AlGaAs/GaAs electron billiard device. Our billiard is shaped by a surface gate arrangement incorporating a `bridging interconnect' fabrication technique which allows independent control of the cavity's central circular antidot and evolution from a regular square to a nominally chaotic environment in a single device. The low field MR signature of the device displays a marked fractal form with MR structure on a magnetic field scale much finer than that previously reported for generically similar electron-wave billiards.

We determine the one-dimensional periodic potential required to produce an energy band structure in which the effective mass m at the bottom of the first miniband is minimized, and the peak group velocity within the miniband is maximized, subject to the constraint of maintaining a fixed specified energy gap 1 between the first and second bands. This problem is of considerable interest for the design of semiconductor superlattices and optical lattices that exhibit high carrier mobility combined with low interband Zener tunneling. We show that the problem is solved by a class of periodic potentials, known as 1-gap potentials, which, remarkably, support only two distinct energy bands separated by a single energy gap. We use the unique properties of 1-gap potentials to derive semi-analytical formulae that can be used to predict, ab initio, the potential profile required to generate any physically possible value of m or 1. Our results provide a simple, but powerful, band structure engineering tool that should facilitate the design of superlattice structures and optical lattices with optimized transport properties.