Triangular Mott-Hubbard Insulator Phases of $\mathrm{Sn}/\mathrm{Si}(111)$ and $\mathrm{Sn}/\mathrm{Ge}(111)$ Surfaces

The ground state of $\mathrm{Sn}/\mathrm{Si}(111)$ and $\mathrm{Sn}/\mathrm{Ge}(111)$ surface $\alpha$ phases is reexamined theoretically, based on ab initio calculations where correlations are approximately included through the orbital dependence of the Coulomb interaction (in the local $\mathrm{\text{density}}+\mathrm{\text{Hubbard}}U$ approximation). The effect of correlations is to destabilize the vertical buckling in $\mathrm{Sn}/\mathrm{Ge}(111)$ and to make the surface magnetic, with a metal-insulator transition for both systems. This signals the onset of a stable narrow gap Mott-Hubbard insulating state, in agreement with very recent experiments. Antiferromagnetic exchange is proposed to be responsible for the observed $\Gamma$-point photoemission intensity, as well as for the partial metallization observed above 60 K in $\mathrm{Sn}/\mathrm{Si}(111)$. Extrinsic metallization of $\mathrm{Sn}/\mathrm{Si}(111)$ by, e.g., alkali doping, could lead to a novel 2D triangular superconducting state of this and similar surfaces.

Figure 1

$\mathrm{Sn}/\mathrm{Si}(111)$ (dashed lines) and $\mathrm{Sn}/\mathrm{Ge}(111)$ (solid lines) $\sqrt{3}$ calculations for increasing correlation parameter $U$: (a) minimum band gap; (b) spin moment per adatom; (c) Sn vertical height measured over the outer semiconductor plane; (d) magnetic exchange splitting. Lines are guides for the eye.

Figure 2

$\mathrm{Sn}/\mathrm{Ge}(111)$: Total energy per adatom as a function of $3\times 3$ up-down distortion $\Delta$. LDA (solid line) and $\mathrm{LSDA}+U$, $U=4\mathrm{eV}$ (dashed line). The zero of energy is at $\Delta =0.0\AA$ in both cases. Inset: Schematics of the $\sqrt{3}\times \sqrt{3}R30°$ unit cell (dashed line) and the $3\times 3$ unit cell (solid line). Black spheres represent Sn adatoms, gray spheres Si (Ge) atoms of the first and second layer.

Figure 3

(a) $\mathrm{Sn}/\mathrm{Si}(111)$: $\mathrm{LDA}+U$ spin-up bands (solid line) and spin-down bands (dashed line) for the ferrimagnetic $3\times 3$ phase. (b) Total density of electronic states (solid line) showing the gap at the Fermi level (zero).

Figure 4

Schematic phase diagram of $\mathrm{Sn}/\mathrm{Si}(111)$ in the temperature-interaction plane. The arrow describes the entropy-induced metallization due to AF order in the MI.