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.
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