Periodic lattice distortion accompanying the charge-density-wave transition for Sn/Ge(111)

Abstract

The periodic lattice distortion ͑PLD͒ accompanying the charge-density-wave ͑CDW͒ transition ͑at Ϫ60°C͒ in the ␣ phase of Sn on Ge͑111͒ has been determined by combining the distinct sensitivities of low-energy electron diffraction ͑LEED͒ and surface x-ray diffraction ͑SXRD͒. New LEED I-V data combined with a SXRD analysis yield a significant lattice distortion. The PLD accompanying the CDW transition is a 0.37-Å vertical rippling of the Sn atoms accompanied by a perpendicular ͑0.17 Å͒ and parallel ͑0.12 Å͒ distortion of the first-layer Ge atoms, consistent with a band Jahn-Teller-like distortion. ͓S0163-1829͑99͒01128-5͔A charge-density-wave ͑CDW͒ transition has been observed for thin films ͑␣ phase with 1 3 monolayer density͒ of Pb and Sn on the ͑111͒ surface of Ge, using a variable temperature scanning tunneling microscope ͑STM͒. 1,2 STM images reveal a (3ϫ3) symmetry in the low-temperature CDW phase with the filled and empty state images being complimentary. 1,2 Electron-diffraction studies of both of these systems show that there is a commensurate lattice distortion that accompanies the CDW transition, from a roomtemperature (ͱ3ϫͱ3)R30°structure ͑labeled ͱ3͒ to a (3 ϫ3) low-temperature structure. 1,2 For the Pb film, firstprinciples density-functional calculations confirmed that the CDW (3ϫ3) phase was in fact the ground state of the system, and that the Fermi contour of the high-temperature ͱ3 phase, confirmed by angle-resolved photoemission measurements, 3 had a shape that would suggest Fermi surface nesting. 1 It was proposed, based on these calculations, that the transition was driven by Fermi surface nesting, 1 but stabilized by electron correlation effects, since experiments showed that this CDW transition was accompanied by a metal-to-nonmetal transition, 1,4 unexplainable with band theory.At first glance, the behavior of the Sn film is very similar to that of the Pb film. The CDW transition is at Ϫ60°C compared to Ϫ20°C for Pb, the STM images are nearly identical, and the commensurate lattice distortion, as seen with low-energy electron diffraction ͑LEED͒, is qualitatively similar. Upon close inspection, the details are significantly different. First-principles density-functional calculations show that the CDW configuration is not the ground state for Sn/Ge. 2 Both theory 2,5 and experiment 6 indicate that Fermi surface nesting is not an appropriate model for this transition, and there is no metal-to-nonmetal transition for Sn/Ge. 2,6 Scandolo et al. 5 proposed, based on theoretical calculations, that the ͱ3 phase is paramagnetic and is unstable towards a commensurate spin-density wave with periodicity (3ϫ3) and magnetization 1 3 . Le Lay et al. 7 proposed, based on core-level data, that dynamic fluctuations between the sp 3 /sp 2 hybridization states at room temperature would condense into a (3ϫ3) low-temperature phase. A key to determining the origin of the CDW transition in the Sn/Ge͑111͒ system is the structure of the periodic lattice distortion accompanying the electronic transition.A recent surfac...

Two-Dimensional Phase Transition Mediated by Extrinsic Defects

“…We have chosen the recently discovered charge ordering transition in the a phase of Sn on Ge(111) [11][12][13][14][15][16][17] to study the interplay between a phase transition and defects. One-third of a monolayer of Sn forms a metastable ͑ p 3 3 p 3 ͒ overlayer on this surface at room temperature (RT).…”

Disproportionation Phenomena on Free and StrainedSn/Ge(111)andSBallabio1, Profeta2, Gironcoli3 et al. 2002Phys. Rev. Lett.374220View full textAdd to dashboardCite

“…The main reason of interest lies in the electronic driving force behind the transition, namely the presence of a half filled surface state, suggestive 3 of a two-dimensional surface charge-density wave (SCDW) mechanism 6 . Recent X-ray data show that the transition is accompanied by static freezing and long-range ordering of a 3 × 3 periodic structural distortion, consisting mainly of a "buckling" of Sn adatoms by ∼ 0.35Å along the surface normal 7,8 . In the distortion, adatoms are generally believed to follow a "1 up, 2 down" (1U) pattern, but there is evidence that under some as yet unclear circumstances a non-negligible portion of the surface distorts with the opposite phase, namely a "2 up, 1 down" (2U) pattern 9,10 .…”

Phase Transitions in Two Dimensions: The Case of Sn Adsorbed on Ge(111) Surfaces

“…Note added: Zhang et al have re-analyzed their previously published SXRD data for the Ge(111)/Sn phases [8] in conjunction with IV-LEED data [12] and find an outward displacement of 0.37Å for one Sn atom. However, the displacements in the substrate differ from the values reported in this letter.…”