Origin of the metal-insulator transition of indium atom wires on Si(111)

As a prototypical one-dimensional electron system, self-assembled indium (In) nanowires on the Si(111) surface have been believed to drive a metal-insulator transition by a charge-density-wave (CDW) formation due to Fermi surface nesting. Here, our first-principles calculations demonstrate that the structural phase transition from the high-temperature $4\times 1$ phase to the low-temperature $8\times 2$ phase occurs through an exothermic reaction with the consecutive bond-breaking and bond-making processes, giving rise to an energy barrier between the two phases as well as a gap opening. This atomistic picture for the phase transition not only identifies its first-order nature but also solves a long-standing puzzle of the origin of the metal-insulator transition in terms of the $\times 2$ periodic lattice reconstruction of In hexagons via bond breakage and new bond formation, not by the Peierls-instability-driven CDW formation.

Figure 1

(a) Top view of the optimized $4\times 1$ (left panel) and $4\times 2$ (right panel) structures. The dark and gray circles represent In and Si atoms, respectively. For distinction, Si atoms below In chains are drawn with small circles. Each unit cell is indicated by the dashed line. The STM images of the $4\times 1$ and $4\times 2$ structures is displayed in panel (b), together with the overlap of the coupled double Peierls-dimerized chain model (from Ref. [23]): Schematic of two dimerized phases, A (with a positive displacement $\mathrm{\Delta }$) and B (with a negative $\mathrm{\Delta }$), of a single Peierls chain is also given on the right side.

Figure 2

(a) Schematics of four degenerate CDW ground phases (denoted as AA, BA, BB, and AB) in a coupled double Peierls-dimerized chain model (from Ref. [23]). (b) Atomistic picture for the formation of the four degenerate hexagon structures. The dashed lines in panel (b) indicate the $4\times 2$ unit cell. For comparison with the Peierls dimerization in panel (a), the filled ellipses (or half-ellipses) are drawn in the outer In atoms of the $4\times 2$ structure in panel (b).

Figure 3

(a) Calculated energy profile along the transition path from the $4\times 1$ to the $4\times 2$ structure. (b) Atomic geometries and surface band structures of the $4\times 1$ structure, the $T$ state, the $I$ state, and the $4\times 2$ structure. The surface Brillouin zones of the $4\times 1$ and $4\times 2$ structures are also drawn. The In-In interatomic distances (in Å) are given. The energy zero in panel (b) represents the Fermi level.

Figure 4

Schematic diagrams of the soliton formation. In the top panel, the initial bond-breaking and bond-making positions are marked (X), and the arrows represent the propagations of In hexagons. In the inset, the soliton configuration $\mathrm{AA}\to \mathrm{BA}$ between the AA and BA CDW phases is from Ref. [23]. The corresponding soliton structure is sketched based on the hexagon model, together with the possible bond-breaking and bond-making processes for the soliton movement. The kink atom indicated by the small arrow in the inset is drawn with bright color.