Indium $\sqrt{7}\times \sqrt{3}$ on Si(111): A Nearly Free Electron Metal in Two Dimensions

We present measurements of the Fermi surface and underlying band structure of a single layer of indium on Si(111) with $\sqrt{7}\times \sqrt{3}$ periodicity. Electrons from both indium valence electrons and silicon dangling bonds contribute to a nearly free, two-dimensional metal on a pseudo-4-fold lattice, which is almost completely decoupled at the Fermi level from the underlying hexagonal silicon lattice. The mean free path inferred from our data is quite long, suggesting the system might be a suitable model for studying the ground state of two-dimensional metals.

Figure 1

Structural characterization of $\sqrt{7}\times \sqrt{3}$ indium on Si(111). (a) LEED pattern at 144 eV. The inset indicates the strongest spots relative to the $\sqrt{7}\times \sqrt{3}$ Brillouin zone. (b) Plan view of the $\sqrt{7}\times \sqrt{3}$ unit cell of indium atoms determined by Kraft et al. [8, 9]. (c) The reciprocal lattice points $\mathbf{G}$, the basis vectors [$(hk)H$, $(hk)R$, and $(hk)$] and Brillouin zones for unreconstructed $1\times 1$, rectangular pseudo-4-fold, and $\sqrt{7}\times \sqrt{3}$ symmetries, respectively.

Figure 2

Fermi contours and underlying bands of $\sqrt{7}\times \sqrt{3}$ indium on Si(111). (a) The intensity at $E_{\mathrm{F}}$ for $h\nu =89.5\mathrm{e}\mathrm{V}$, together with Brillouin zones from Fig. 1. Raw data are shown in the upper right quadrant. The rest of the data are obtained by mirror symmetry operations. (b) The experimental data of (a) averaged over each $\sqrt{7}\times \sqrt{3}$ Brillouin zone according to translational/reflection symmetry, together with a plane-wave calculation for $\sqrt{7}\times \sqrt{3}$ symmetry as described in the text. (c) The measured electronic bands similarly backfolded in the reduced BZ for the line $k_y=0$. The overplotted bands are solid (simulated) and dashed (guides to the eye). The top of the bulk silicon valence band maximum is indicated by an arrow.

Figure 3

(a) Momentum distribution curve at $E_{\mathrm{F}}$ for point $c$ of Fig. 2. (b) Average terrace geometry (dimensions in nanometers). The crossing corresponds to the momentum vector ${\mathbf{k}}_c$.