Peierls instability as the insulating origin of the Na/Si(111)-(3 × 1) surface with a Na coverage of 2/3 monolayers

Abstract

Density functional theory (DFT) calculations are used to investigate the insulating origin of the Na/Si(111)-(3 × 1) surface with a Na coverage of 2/3 monolayers. In the coverage definition, one monolayer refers to one Na atom per surface Si atom, so this surface contains an odd number of electrons (i.e., three Si dangling-bond electrons plus two Na electrons) per 3 × 1 unit cell. Interestingly, this odd-electron surface has been ascribed to a Mott–Hubbard insulator to account for the measured insulating band structure with a gap of about 0.8 eV. Here, we instead propose a Peierls instability as the origin of the experimental band gap. The concept of Peierls instability is fundamental in one-dimensional metal systems but has not been taken into account in previous studies of this surface. Our DFT calculations demonstrate that the linear chain structure of Si dangling bonds in this surface is energetically unstable with respect to a × 2 buckling modulation, and the buckling-induced band gap of 0.79 eV explains well the measured insulating nature.