Patterning graphene with a helium ion microscope: Observation of metal-insulator transition induced by disorder

A helium ion microscope is used to produce nanoscale patterns on different regions of a graphene device. The patterns consist of uniformly spaced strips with varying spacing in each region. Measurements of the longitudinal magnetoconductivity in each region at different temperatures and carrier densities reveal a transition from metallic to insulating regimes as the density of defects increases. We use the weak localization theory and Mott's theory for disordered two-dimensional systems to analyze the conductivity as it crosses the threshold value of $4{e}^{2}/\phantom{\rule{0.0pt}{0ex}}h$.