Low-symmetry non-local transport in microstructured squares of delafossite metals

Intense work studying the ballistic regime of electron transport in two dimensional systems based on semiconductors and graphene had been thought to have established most of the key experimental facts of the field. In recent years, however, new forms of ballistic transport have become accessible in the quasi-two-dimensional delafossite metals, whose Fermi wavelength is a factor of 100 shorter than those typically studied in the previous work, and whose Fermi surfaces are nearly hexagonal in shape, and therefore strongly faceted. This has some profound consequences for results obtained from the classic ballistic transport experiment of studying bend and Hall resistances in mesoscopic squares fabricated from delafossite single crystals. We observe pronounced anisotropies in bend resistances and even a Hall voltage that is strongly asymmetric in magnetic field. Although some of our observations are non-intuitive at first sight, we show that they can be understood within a non-local Landauer-B\"uttiker analysis tailored to the symmetries of the square/hexagonal geometries of our combined device/Fermi surface system. Signatures of non-local transport can be resolved for squares of linear dimension of nearly 100 $\mu$m, approximately a factor of 15 larger than the bulk mean free path of the crystal from which the device was fabricated.