Nanoscale imaging of viscous and nonlocal transport in electron fluids using scanning tunneling potentiometry

Ballistic and hydrodynamic electron flow can develop in materials when carrier momentum is conserved over long distance and time scales. These transport regimes - which can be accessed in ultraclean materials such as graphene - are characterized by a breakdown of Ohm's law, leading to distinctive spatial distributions of the current density and electrochemical potential. In this talk, I will show scanning tunneling potentiometry (STP) measurements of the electrochemical potential induced by DC transport in monolayer graphene as a function of carrier density, temperature, and out-of-plane magnetic field. First, STP images are recorded as current flows through electrostatic constrictions with gate-tunable widths that are "drawn" with the STM tip. Measurements of the electrochemical potential drop through these constrictions reveal nonlocal (wavevector-dependent) corrections to the conductivity. While heating the system from 4.5 K to 77 K, enhanced electron-electron scattering leads to a crossover from ballistic to hydrodynamic flow, identified by superballistic conductance through the constrictions and a suppression of Landauer residual resistivity dipoles. Next, upon increasing the magnetic field from 0.2 to 1.4 T at 4.5 K, STP imaging of magnetotransport around a circular electrostatic barrier reveals a diffusive-to-ballistic crossover resulting from Landau level quantization. The diffusive regime at low magnetic fields is characterized by spiral-like textures in the electrochemical potential that are consistent with "winding" current flows around the barrier. At higher fields approaching the ballistic regime, the equipotential contours unwind and two concentric ring-shaped features emerge, along which the Hall field is locally enhanced. Detailed theoretical modeling using the Boltzmann kinetic equation and tight-binding simulations show that these ring features are a finite size effect caused by spatial extent of cyclotron edge modes near the barrier.