The In adsorbed Si(111) 4x1 reconstructed surface is known to undergoes a phase transition at about 130 K to (8x2) structure with decreasing temperature. The In adatoms formed quasi one-dimensional chains and this transition is the metal-insulator transition as the Peierls transition or the Charge Density Wave (CDW) transition [1-4].
The properties accompanied with the transition are explained with a simple Ising model [5]. In order to discuss more detail of this phase transition, we construct the continuous displacement model that consists of the nearest neighbour pair interaction along the atomic chain and the four-body interaction perpendicular to the atomic chain as corresponding to the previous Ising model. We consider two order parameters indicating the displacement of In adatoms in 4x1 unit cell. For the surface electronic states, we use the tight binding model based on the density functional calculations. [6].
We performed Monte Carlo simulations, estimated the atomic displacement and calculated the surface electronic properties around the transition temperatures. We discussed the distribution of displacements with the Patterson map of the X-ray diffraction and the temperature dependence of the conductivity. We also discussed the temperature dependence of the surface band structure with the density of states projected into the reciprocal space (RDOS), which can be compared with the photoemission measurements.
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[5] Y. Yagi and A. Yoshimori, J. Phys. Soc. Jpn 74 (2005) 831.
[6] C. González, et al., Phys. Rev. Lett. 96 (2006) 136101.
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