  Electron gases at the surfaces of (001), (110), and (111) oriented SrTiO3
(STO) have been created using Ar+-irradiation with fully metallic behavior and
low-temperature-mobility as large as 5500 cm2V-1s-1, 1300 cm2V-1s-1 and 8600
cm2V-1s-1 for (001)-, (110)-, and (111)-surfaces, respectively. The in-plane
anisotropic magnetoresistance (AMR) have been studied for the samples with the
current along different crystal axis directions to subtract the Lorentz Force
effect. The AMR shows features which coincide with the fixed orientations to
the crystalline axes, with 4-fold, 2-fold and nearly-6-fold symmetries for
(001)-, (110) and (111)-surfaces, respectively, independent of the current
directions. These features are possibly caused by the polarization of spin
orbit texture of the 2D Fermi surfaces. In addition, a 6-fold to 2-fold
symmetry breaking for (111)-surfaces is observed. Our results demonstrate the
effect of symmetry of two-dimensional electronic structure on the transport
behaviors for the electron gases at STO surfaces.
