The superballistic paradox for electron hydrodynamics in graphene: relevance of tomographic dynamics

Transport in 2D materials, such as graphene or gallium arsenide heterostructures, exhibits exotic hydrodynamic signatures. For instance, superballistic conduction, also known as the Gurzhi effect, reduces dissipation in devices. However, contrary to conventional fluids and the original predictions, the decrease in resistance in constrictions or antidot superlattices is observed even at close-to-zero temperatures. We study the Boltzmann equation for electron flow. Considering classical electron collisions yields an initial increase, as studied by Knudsen in conventional fluids. Tomographic dynamics are a particularity of electrons at low temperatures, which, in this limiting case, predict only head-on collisions. We study them and show that the resistance decreases even at close-to-zero temperatures, in agreement with experiments. Even without assuming a functional dependence of the relaxation rates on temperature, a decrease in resistance evidences tomographic dynamics. In addition to tomographic dynamics, unique features of electrons include the Molenkamp effect and lattice anisotropy in materials such as PdCoO2. Therefore, graphene constitutes a unique platform for hydrodynamic phenomena that goes beyond a conventional fluid.