Phase coherent transport in graphene nanoribbons and graphene nanoribbon arrays

We have experimentally investigated quantum interference corrections to the conductivity of graphene nanoribbons at temperatures down to 20 mK studying both weak localization (WL) and universal conductance fluctuations (UCFs). Since in individual nanoribbons at milli-Kelvin temperatures the UCFs strongly mask the weak localization feature we employ both gate averaging and ensemble averaging to suppress the UCFs. This allows us to extract the phase coherence length from both WL and UCF at all temperatures. Above 1 K the phase coherence length is suppressed due to Nyquist scattering, whereas at low temperatures we observe a saturation of the phase coherence length at a few hundred nanometers, which exceeds the ribbon width, but stays below values typically found in bulk graphene. To better describe the experiments at elevated temperatures, we extend the formula for one-dimensional (1D) weak localization in graphene, which was derived in the limit of strong intervalley scattering, to include all elastic scattering rates.