Using the two-dimensional, steady-state Vlasov theory derived in a previous paper, we further investigate properties of thin current sheets that result from exact particle motion. The self-consistent quasi-neutral structure of thin current sheets generally requires the presence of an electric potential, which is constant along field lines. We establish that potential differences of up to the ion thermal potential kTi/e may be present when the current sheet thickness becomes comparable to or smaller than a typical ion Larmor radius. We further explore the possible association of thin current sheets with the perpendicular electric fields that are part of the U-shaped potential structures above auroral arcs. For sufficiently small scales, the converging perpendicular electric field corresponds to two oppositely directed thin Hall current sheets. We construct such double current sheet models and confirm that they result in potentials with the postulated shape and, for sufficiently small scales, in substantial potential differences (in fractions of the ion thermal potential kTi/e). The formation of such double current sheets, found recently in simulations of an earthward collapsing entropy-depleted magnetic flux tube (bubble), may provide a further link between bursty bulk flows, bubbles, and auroral features.