Universal mobility characteristics of graphene originating from charge scattering by ionised impurities

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

A magnetically-induced Coulomb gap in graphene due to electron-electron interactions

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.</p