Stability of a Flexible Polar Ionic Crystal Surface: Metastable Alumina and One-Dimensional Surface Metallicity

A first-principles study of $\ensuremath{\kappa}\ensuremath{-}{\mathrm{Al}}_{2}{\mathrm{O}}_{3}(001)$ and $(00\overline{1})$ reveals new features of ion-surface stability and electronic structure. The need to generalize Tasker's rules for surface stability of low-symmetry crystals is shown. Structurally, the presence of bulk tetrahedral Al ( ${\mathrm{Al}}^{T}$) causes giant surface relaxations, with O termination at (001). Surface-layer ${\mathrm{Al}}^{T}$ are strongly unfavored. This is understood with Pauling's rules and thus generally applicable to metastable aluminas. The bulk charge asymmetry and Al-sublattice anisotropy caused by the ${\mathrm{Al}}^{T}$ create a 1D metallic surface state at $(00\overline{1})$.