Fermi surfaces and energy gaps in Sn/Ge(111)

One third of a monolayer of Sn adsorbed on Ge(111) undergoes a broad phase transition upon cooling from a (root3 x root3)R30degrees normal phase at room temperature to a (3 x 3) phase at low temperatures. Since band-structure calculations for the ideal (root3 x root3)R30degrees phase show no Fermi-surface nesting, the underlying mechanism for this transition has been a subject of much debate. Evidently, defects formed by Ge substitution for Sn in the adlayer, at a concentration of just a few percent, play a key role in this complex phase transition. Surface areas near these defects are pinned to form (3 x 3) patches above the transition temperature. Angle-resolved photoemission is employed to examine the temperature-dependent band structure, and the results show an extended gap forming in k-space as a result of band splitting at low temperatures. On account of the fact that the room temperature phase is actually a mixture of (root3 x root3)R30degrees areas and defect-pinned (3 x 3) areas, the band structure for the pure (root3 x root3)R30degrees phase is extracted by a difference-spectrum method. The results are in excellent agreement with band calculations. The mechanism for the (3 x 3) transition is discussed in terms of a response function and a tight-binding cluster calculation. A narrow bandwidth and a small group velocity near the Fermi surface render the system highly sensitive to surface perturbations, and formation of the (3 x 3) phase is shown to involve a Peierls-like lattice distortion mediated by defect doping. Included in the discussion, where appropriate, are dynamic effects and many-body effects that have been previously proposed as possible mechanisms for the phase transition.