Observation of a Mott Insulating Ground State for $\mathrm{Sn}/\mathrm{Ge}(111)$ at Low Temperature

We report an investigation on the properties of 0.33 ML of Sn on Ge(111) at temperatures down to 5 K. Low-energy electron diffraction and scanning tunneling microscopy show that the ($3\times 3$) phase formed at $\sim 200\mathrm{K}$, reverts to a new $(\sqrt{3}\times \sqrt{3})R30°$ phase below 30 K. The vertical distortion characteristic of the ($3\times 3$) phase is lost across the phase transition, which is fully reversible. Angle-resolved photoemission experiments show that, concomitantly with the structural phase transition, a metal-insulator phase transition takes place. The $(\sqrt{3}\times \sqrt{3})R30°$ ground state is interpreted as the formation of a Mott insulator for a narrow half-filled band in a two-dimensional triangular lattice.

Figure 1

LEED patterns from (a) the ($3\times 3$) and (b) the $\mathrm{LT}-\sqrt{3}$ phase. The primary energy is 94 eV. Circles highlight ($1\times 1$) (green, large), ($3\times 3$) (blue, small), and $\sqrt{3}$ (red, dashed) spots.

Figure 2

Top: $18\times 11{\mathrm{nm}}^2$ STM image ($V=-1.4\mathrm{V}$, $I=1.0\mathrm{nA}$, $T=5\mathrm{K}$) of the $\mathrm{LT}-\sqrt{3}$ phase. Bottom: $7\times 5{\mathrm{nm}}^2$ STM image of the ($3\times 3$) ($V=-1.0\mathrm{V}$, $I=1.0\mathrm{nA}$, $T=112\mathrm{K}$) phase and $\mathrm{LT}-\sqrt{3}$ ($V=-1.4\mathrm{V}$, $I=1.0\mathrm{nA}$, $T=5\mathrm{K}$), respectively. Below, we show directly extracted height profiles corresponding to the direction highlighted in the STM image, and a histogram of the atomic heights found in each case.

Figure 3

Binding energy shift of Ge $3d$ (circles), Sn $4d$ (squares), and valence band leading edge (filled triangles) vs temperature. Values at 120 K are taken as a reference. Inset: enlarged view of the behavior for $T<30\mathrm{K}$. Lines are a guide to the eye.

Figure 4

Top: symmetrized angle-resolved photoemission spectra shown in gray scale (bright color means more intensity), as a function of emission angle along the $[11\overline{2}]$ direction for both the ($3\times 3$) (left) and the $\mathrm{LT}-\sqrt{3}$ (right) phases. Symmetry points correspond to the ($3\times 3$) Brillouin zone. Bottom: two selected symmetrized spectra corresponding to the crossing point of the surface state (horizontal yellow line in top panel) at 140 (left) and 12 K (right). Energy scales are referred to $E_F$.