Optical spin- and current-injection study on Si(111)-In surfaces

We present a theoretical study of the optical generation of one-photon spin and current injection onto In-adsorbed Si(111) surfaces with $4\times 2$ and $8\times 2$ reconstructions. The spin injection, under incidence of circularly polarized light into nonmagnetic semiconductors, creates spin-polarized electrons in the conduction bands. The current injection is a nonlinear second-order effect that is allowed in materials without inversion symmetry. In bulk centrosymmetric crystals, the optical injection of current can only be observed at the surface wherein the inversion of symmetry might be broken. We report calculations for the degree of spin polarization and current-injection spectra which are calculated in a full electronic band structure scheme at the level of GW scissor-energy correction. Our results show an anisotropic behavior of the spin- and current-injection optical response. We obtain maximum percentages of the degree of spin polarization of 30% and 35% for the $4\times 2$ and $8\times 2$ surface reconstructions, respectively. It is also possible to optically generate injection current coming mainly from the first two top layers on both In-adsorbed surface reconstructions.

Figure 1

Top views of the In-adsorbed Si(111) surface reconstructions: (a) $4\times 1$, (b) $4\times 2$, and (c) $8\times 2$. The dark (blue) and light (yellow) circles represent the In and Si atoms, respectively. The $x$ and $y$ directions are along the [$11\overline{2}$] and [110] crystallographic directions, correspondingly. The possible rectangular and diagonal unit cells are defined by continuous and dotted lines.

Figure 2

(a) Brillouin zone and (b) LDA band structure of the Si(111)-In $4\times 2$ surface. Spin-orbit interaction was considered in the calculation.

Figure 3

LDA band structure of the Si(111)-In $8\times 2$ surface. Spin-orbit interaction was considered in the calculation.

Figure 4

Spectra of the surface degree of spin polarization along direction $i$, ${\mathcal{D}}_i^{\mathrm{s}}$, for the reconstructions (a) $4\times 2$ and (b) $8\times 2$ of the Si(111)-In surface under incidence of circularly polarized light.

Figure 5

Spectra of the injection current tensor components, (a) ${\eta }_{xyx}$ and (b) ${\eta }_{yyx}$, for the $4\times 2$ reconstruction of the Si(111)-In surface. The plot shows different surface layer contributions to the respective surface or total spectra, ${\eta }_{iyx}^{\mathrm{s}}$.

Figure 6

Spectra of the injection current tensor components, (a) ${\eta }_{xyx}$ and (b) ${\eta }_{yyx}$, for the $8\times 2$ reconstruction of the Si(111)-In surface. The plot shows different surface layer contributions to the respective surface or total spectra, ${\eta }_{iyx}^{\mathrm{s}}$.