  The flow of charge carriers in materials can, under some circumstances, mimic
the flow of viscous fluids. In order to visualize the consequences of such
effects, new methodologies must be developed that can probe the quasiparticle
flow profile with nm-scale resolution as the geometric parameters of the system
are continuously evolved. In this work, scanning tunneling potentiometry (STP)
is used to image quasiparticle flow around engineered electrostatic barriers in
graphene/hBN heterostructures. Measurements are performed as electrostatic dams
- defined by lateral pn-junction barriers - are broken within the graphene
sheet, and carriers move through conduction channels with physical widths that
vary continuously from pinch-off to um-scale. Local, STP measurements of the
electrochemical potential allow for direct characterization of the evolving
flow profile, which we compare to finite-element simulations of a Stokesian
fluid with varying parameters. Our results reveal distinctly non-Ohmic flow
profiles, with charge dipoles forming across barriers due to carrier scattering
and accumulation on the upstream side, and depletion downstream. Conductance
measurements of individual channels, meanwhile, reveal that at low temperatures
the quasiparticle flow is ballistic, but as the temperature is raised there is
a Knudsen-to-Gurzhi regime crossover where the fluid becomes viscous and the
channel conductance exceeds the ballistic limit set by Sharvin conductance.
These results provide a clear illustration of how carrier flow in a Fermi fluid
evolves as a function of carrier density, channel width, and temperature. They
also demonstrate how STP can be used to extract key parameters of quasiparticle
transport, with a spatial resolution that exceeds that of other methods by
orders of magnitude.
