  The principal axes of the recently discovered anisotropic phases of 2D
electron systems at high Landau level occupancy are consistently oriented
relative to the crystal axes of the host semiconductor. The nature of the
native rotational symmetry breaking field responsible for this preferential
orientation remains unknown. Here we report on experiments designed to
investigate the origin and magnitude of this symmetry breaking field. Our
results suggest that neither micron-scale surface roughness features nor the
precise symmetry of the quantum well potential confining the 2D system are
important factors. By combining tilted field transport measurements with
detailed self-consistent calculations we estimate that the native anisotropy
energy, whatever its origin, is typically ~ 1 mK per electron.
