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Insights into the fundamental properties of graphene's Dirac-Weyl fermions have emerged from studies of electron tunnelling transistors in which an atomically thin layer of hexagonal boron nitride (hBN) is sandwiched between two layers of high purity graphene. Here, we show that when a single defect is present within the hBN tunnel barrier, it can inject electrons into the graphene layers and its sharply defined energy level acts as a high resolution spectroscopic probe of electron-electron interactions in graphene. We report a magnetic field dependent suppression of the tunnel current flowing through a single defect below temperatures of ~2 K. This is attributed to the formation of a magnetically-induced Coulomb gap in the spectral density of electrons tunnelling into graphene due to electron-electron interactions. Electron-electron interactions are known to play an important role in the in-plane transport properties of graphene-based devices. Here, the authors investigate the role of electron-electron interactions on electrons tunnelling between the layers of a graphene/hBN/graphene tunnel transistor and demonstrate the emergence of a Coulomb gap at low temperatures and in quantising magnetic fields. [ABSTRACT FROM AUTHOR]

We use phenomenological modelling and detailed experimental studies of charge carrier transport to investigate the dependence of the electrical resistivity, ρ, on gate voltage, V g , for a series of monolayer graphene field effect transistors with mobilities, μ, ranging between 5000 and 250 000 cm2 V−1 s−1 at low-temperature. Our measurements over a wide range of temperatures from 4 to 400 K can be fitted by the universal relation μ = 4 / e δ n max for all devices, where ρ max is the resistivity maximum at the neutrality point and δn is an 'uncertainty' in the bipolar carrier density, given by the full width at half maximum of the resistivity peak expressed in terms of carrier density, n. This relation is consistent with thermal broadening of the carrier distribution and the presence of the disordered potential landscape consisting of so-called electron–hole puddles near the Dirac point. To demonstrate its utility, we combine this relation with temperature-dependent linearised Boltzmann transport calculations that include the effect of optical phonon scattering. This approach demonstrates the similarity in the temperature-dependent behaviour of carriers in different types of single layer graphene transistors with widely differing carrier mobilities. It can also account for the relative stability, over a wide temperature range, of the measured carrier mobility of each device. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]