GaNm-plane: Atomic structure, surface bands, and optical response

Density-functional-theory calculations are combined with many-body perturbation theory in order to elucidate the geometry, electronic, and optical properties of the $wz\ensuremath{-}\mathrm{GaN}(1\overline{1}00$) surface, i.e., the so-called $m$-plane. The optical absorption and reflection anisotropy related to electronic transitions between surface states are identified by comparison with measured data covering transition energies from 2.4 up to 5.4 eV. Our results show a surface relaxation mechanism consistent with the electron counting rule that causes a moderate buckling of the GaN surface dimers and gives rise to two distinct surface states: The doubly occupied N dangling bonds form a surface band that is resonant with the GaN valence-band edge at the center of the Brillouin zone, whereas the empty Ga dangling bonds occur within the GaN band gap closely following the dispersion of the conduction-band edge. These two states contribute strongly to the formation of surface excitons that redshift the optical absorption with respect to the bulk optical response. The surface optical absorption i.e., the excitonic onset below the bulk band gap followed by a broad absorption band at higher energies related to the dispersion of the surface band structure, is calculated in agreement with the experimental data.