The mechanism for the 3×3 distortion of Sn/Ge(111)

Abstract

We show that two distinct 3 × 3 ground states, one nonmagnetic, metallic, and distorted, the other magnetic, semimetallic (or insulating) and undistorted, compete in α-phase adsorbates on semiconductor (111) surfaces. In Sn/Ge(111), LSDA/GGA calculations indicate, in agreement with experiment, that the distorted metallic ground state prevails. The reason for stability of this state is analysed, and is traced to a sort of bond density wave, specifically a modulation of the antibonding state filling between the adatom and a Ge-Ge bond directly underneath.

Disproportionation Phenomena on Free and StrainedSn/Ge(111)andSBallabio1, Profeta2, Gironcoli3 et al. 2002Phys. Rev. Lett.Self Cite374220View full textAdd to dashboardCite

“…Figure 1 summarizes the zero-temperature phase diagram versus strain, the order parameter and energy gain being given for the 3×3 distorted state relative to the corresponding fully relaxed √ 3× √ 3 state at the same strain, for both Sn/Ge and Sn/Si. At zero strain, in agreement with experiment and with previous calculations 15,16,21 , Sn/Ge is 1U distorted, with ∆z ∼ 0.34Å, whereas Sn/Si is 0U (undistorted). Positive strain (in-plane expansion) causes Sn/Ge to lose its distortion, through a 1U-0U transition.…”

Order-disorder character of the(3×3)to(3×3Petaccia1, Floreano2, Goldoni3 et al. 2001Phys. Rev. B29280View full textAdd to dashboardCite

“…their bond angle and length remain almost unchanged. This rippled structure is in good agreement with both the SXRD experiments 9 and recent density-functional theory (DFT) calculations 22,23 for the LT (3 × 3)-phase. In this paper, we report on the evolution of the Sn 4d core levels and on their PED patterns at different temperatures.…”

Competing charge ordering and Mott phases in a correlated Sn/Ge(111) two-dimensional triangular lattice

“…This error bar, associated with the precision in the LDA calculations, limits our ability to accurately determine the energy difference between different phases. However, the LDA calculations for the one up-two down metallic (3 × 3) structure 38,39 yields surface bands in good agreement with the photoemission experiments (see below). In particular, one band fully occupied, associated with the up atom, is located around 0.2 eV from the two partially filled bands crossing the Fermi associated with the two down atoms.…”