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9.4 Conclusions
The Pb/Si(557) system is an example of a system that is strongly coupled in 2D.
Contrary to the standard impression gained from literature, this must be also true
for systems that exhibit a 1D band structure close to the Fermi level like In/Si(111)
[ 10 , 11 ], as obvious from their well-ordered arrays of metallic chains. The difference
between the Pb system and those examples is that not only electronic levels far
below the Fermi level are responsible for 2D ordering but also the electrons close to
the Fermi level take part in the 2D interaction. As we have shown, this fact does not
prevent occurrence of 1D conductance, but gives rise to a number of phenomena not
seen in systems with a purely 1D Fermi surface.
The most prominent one is the occurrence of Pb-induced self-stabilized re-
ordering of the step structure at the surface. It is this self-organized generation of
new average terrace widths that does not exist without the Pb coverage and leads
to a Pb concentration of 1.31 ML to complete 1D band filling and to 1D con-
ductance. In the direction normal to the steps the switching-off of conductance is
equivalent to CDW formation. The associated Fermi nesting can be destroyed by
temperature. Although there is still a structural phase transition, the step structure
does not undergo a “normal” Peierls transition, because of the different nature of
step-step and step-surface interactions. Only a small distortion of the regular (223)
facet orientation is seen.
CDW formation because of periodic step decoration and the split-off electronic
states associated with chains at step edges is another phenomenon that was not seen
previously. Here the structural phase transition is completely missing. This means
that the 1D ordering of Pb chains at the step edges is a purely electronic effect with
weak coupling to the lattice and to the step structure. Therefore, no structural phase
transition can be driven by the interplay between these interactions.
These results show that our understanding of these phenomena is still far from
being complete and still require more effort both from the experimental side and
from the theoretical side in order to elucidate the wealth of phenomena generated
by this intriguing interplay of interactions in various dimensions.
Acknowledgments It is a pleasure to acknowledge the very fruitful and continuing collaboration
with my coworkers, in particular with C. Tegenkamp, M. Czubanowski, M. Gauch, and D. Lüker-
mann. This work was supported by the Deutsche Forschungsgemeinschaft.
References
1. G. Grüner, The dynamics of charge-density waves. Rev. Modern Phys. 60 , 1129 (1988)
2. J.M. Luttinger, An exactly soluble model of a Many-Fermion System. J. Math. Phys. (N.Y.)
4 , 1154 (1963)
3. M.G. Zacher, E. Arrigoni, W. Hanke, J.R. Schrieffer, Systematic numerical study of spin-
charge separation in one dimension. Phys. Rev. B 57 , 6370 (1998)
4. G.Grüner, Density Waves in Solids (Addison-Wesley, New York, 1994)
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