Mapping transport in space: A new window
into ballistic and hydrodynamic flow of
electrons
The measurement of transport in electronic systems is the most common way to characterize their
properties. This method, despite its numerous advantages, is inherently limited by the simple fact that it
measures only globally averaged quantities that are accessed by adding contacts to the device. In this
talk we discuss a new measurement technique, using a scanning single electron transistor, that enables
us to map both the current and voltage at each spatial point in a two-dimensional electronic system,
thereby acquiring a wealth of previously hidden information on the nature of electronic flow within it.
We first demonstrate the technique by visualizing the flow of electrons around a bend and mapping the
resistivity in a graphene sample. We then focus on the measurement of flow profiles in ultra-clean
graphene channels, where a transition from ballistic to hydrodynamic flow of electrons is expected to
take place at elevated temperatures. Hydrodynamic electronic flow is a new and little explored
transport regime, which brings the notion of viscosity into the forefront of research in interacting
electrons. We demonstrate, for the first time, parabolic flow profiles of electrons in a conducting
channel, which constitutes a viscosity dominated Poiseuille flow regime, in stark contrast with the
conventional Ohmic and ballistic pictures.