Excitons and Optical Spectrum of the $\mathrm{Si}\left(111\right)-(2\times 1)$ Surface

We investigate excitons at the $\mathrm{Si}\left(111\right)-(2\times 1)$ surface and their optical spectrum from first principles. This is done by solving the Bethe-Salpeter equation for the two-particle Green's function, including the electron-hole interaction. The optical spectrum of the surface is dominated by a surface exciton formed from the $\pi$-bonded surface states. The excitonic binding energy is more than 1 order of magnitude larger than in bulk Si. The two-particle wave function of the exciton state is strongly localized at the surface and exhibits distinct anisotropy due to the surface reconstruction.