Electronic and structural reconstructions of the polar (111) SrTiO3 surface

Polar surfaces are known to be unstable due to the divergence of the surface electrostatic energy. Here we report on the experimental determination, by grazing incidence x-ray diffraction, of the surface structure of polar Ti-terminated (111) ${\mathrm{SrTiO}}_{3}$ single crystals. We find that the polar instability of the $1\ifmmode\times\else\texttimes\fi{}1$ surface is solved by a pure electronic reconstruction mechanism, which induces out-of-plane ionic displacements typical of the polar response of ${\mathrm{SrTiO}}_{3}$ layers to an electron confining potential. On the other hand, the surface instability can be also eliminated by a structural reconstruction driven by a change in the surface stoichiometry, which induces a variety of $3\ifmmode\times\else\texttimes\fi{}3$ (111) ${\mathrm{SrTiO}}_{3}$ surfaces consisting in an incomplete Ti (surface)--${\mathrm{O}}_{2}$ (subsurface) layer covering the $1\ifmmode\times\else\texttimes\fi{}1$ Ti-terminated (111) ${\mathrm{SrTiO}}_{3}$ truncated crystal. In both cases, the ${\mathrm{TiO}}_{6}$ octahedra are characterized by trigonal distortions affecting the structural and the electronic symmetry of several unit cells from the surface. These findings show that the stabilization of the polar (111) ${\mathrm{SrTiO}}_{3}$ surface can lead to the formation of quasi-two-dimensional electron systems characterized by radically different ground states which depend on the surface reconstructions.