  Graphene has been proposed as a promising material for future nanoelectronics
because of its unique electronic properties. Understanding the scaling behavior
of this new nanomaterial under common experimental conditions is of critical
importance for developing graphene-based nanoscale devices. We present a
comprehensive experimental and theoretical study on the influence of edge
disorder and bulk disorder on the minimum conductivity of graphene ribbons. For
the first time, we discovered a strong non-monotonic size scaling behavior
featuring a peak and saturation minimum conductivity. Through extensive
numerical simulations and analysis, we are able to attribute these features to
the amount of edge and bulk disorder in graphene devices. This study elucidates
the quantum transport mechanisms in realistic experimental graphene systems,
which can be used as a guideline for designing graphene-based nanoscale devices
with improved performance.
