  Electron-scale surface waves are shown to be unstable in the transverse plane
of a shear flow in an initially unmagnetized plasma, unlike in the
(magneto)hydrodynamics case. It is found that these unstable modes have a
higher growth rate than the closely related electron-scale Kelvin-Helmholtz
instability in relativistic shears. Multidimensional particle-in-cell
simulations verify the analytic results and further reveal the emergence of
mushroom-like electron density structures in the nonlinear phase of the
instability, similar to those observed in the Rayleigh Taylor instability
despite the great disparity in scales and different underlying physics.
Macroscopic ($\gg c/\omega_{pe}$) fields are shown to be generated by these
microscopic shear instabilities, which are relevant for particle acceleration,
radiation emission and to seed MHD processes at long time-scales.
