Mechanism of the Band Gap Opening across the Order-Disorder Transition of $\mathrm{Si}(111)(4\times 1)\mathrm{\text{−}}\mathrm{In}$

The ground state properties of indium atom chains on the $\mathrm{Si}(111)8\times 2\mathrm{\text{−}}\mathrm{In}$ surface and the nature of their insulator-metal (IM) transition near 120 K are under intense dispute. We compare experimental scanning tunneling microscopy (STM) images of the low temperature (LT) $8\times 2$ phase with STM image calculations from Density Functional Theory (DFT). Our LT studies clearly indicate the existence of a frozen shear distortion between neighboring atom chains, resulting in the formation of indium hexagons. Tunneling spectra furthermore indicate that the IM transition coincides with the collapse of a $\sim 0.3\mathrm{eV}$ surface-state band gap at the $\Gamma$ point of the $4\times 2$ Brillouin zone. This implies that the IM transition is driven by a shear phonon, not by Fermi surface nesting.

Figure 1

Top view of the $\mathrm{Si}(111)4\times 1\mathrm{\text{−}}\mathrm{In}$ (a) and $\mathrm{Si}(111)8\times 2\mathrm{\text{−}}\mathrm{In}$ (b) surface (hexagon model; Ref. 13). Panels (c) and (d) show the calculated $4\times 1$ and $4\times 2$ surface-state bands along the In chains. Brillouin zones are indicated.

Figure 2

Experimental (a), (c) and theoretical (b), (d) STM images with filled states on the left and empty states on the right. The tunneling bias in panels (a) and (b) is 0.5 V. The bias in panels (c) and (d) is 1.5 V.

Figure 3

(a) Tunneling spectra of the $4\times 2$ surface at different temperatures. The solid (green) line through the bottom spectrum is a six parameter fit using Eq. (3). All other fits, represented by the solid (red) lines, employed three adjustable parameters. (b) Tunneling spectra on a semilog scale, showing a thermovoltage and thermionic $I\mathrm{\text{−}}V$ characteristics. (c) $dI/dV$ spectra at various temperatures. Note the conductance offset at 120 K, signifying an abrupt IM transition. (d) Fitting of the 120 K spectra for the various STS set-points. The solid (red) lines represent the fits, assuming half-Gaussian distributions for ${\Delta }_1$ and ${\Delta }_2$. (All the fittings are superimposed over the experimental data curves.)

Figure 4

Theoretical gap distributions at (a) 50 K and (b) 200 K; (c) Simulated $dI/dV$ spectra of the $4\times 2$ surface, showing nearly identical tunneling gaps at 50 and at 90 K and a clear conductance offset 160 and at 200 K. Inset: calculated $dI/dV$ spectrum of a static $4\times 1$ structure. (d) Gap distributions at the $\Gamma$ and $X^{\prime }$ points at 50 and at 200 K, respectively.