Magnetotransport of tomographic electrons in confined geometries

A recent new paradigm in electron transport is hydrodynamic flow of charges in high-mobility devices, where frequent electron collisions lead to the buildup of a collective electron flow profile. The conventional description of this hydrodynamic regime is based on the fluid equations for a classical gas extended to include impurity scattering, known as the Stokes-Ohm equations. Here, we show that this description is fundamentally limited and will receive significant corrections in realistic devices. This is due to the distinct collisional relaxation in quantum-mechanical systems compared to classical systems, with even modes of the distribution function relaxing over significantly shorter length scales than odd modes (dubbed the "tomographic" effect). We establish an analytical description for three main effects of tomographic flows compared with traditional near-hydrodynamic theories: (i) Non-equilibrium effects from the boundaries penetrate significantly deeper into the flow domain; (ii) There is a significant additional velocity slip and (iii) strong rarefaction corrections (i.e., finite wavelength effects). We also show that these anomalous transport effects are rapidly suppressed with magnetic fields, which leads to a non-monotonic channel magneto-resistance. This latter effect can be used to, in principle, measure both the even- and odd-mode mean free paths.