Strictly speaking, one-dimensional structure is unattainable in the physical world, since unlike lines in mathematics, real objects never quite have zero "height" and "width". However, long objects with very small cross-section can behave approximately like one-dimensional ones. Typically, the requirement is that the cross-section is smaller than the wavelength of electrons in the structure, which means 1-10 nm for metals and semiconductors at room temperature. Quantum mechanics then effectively constrains the "perpendicular" motion of electrons in such a wire and along the wire they behave as if it was one-dimensional. Incidentally, the smallest physical wire that one can imagine is made of a string of atoms, i.e. only 1 atom wide. The trick is that for an atomic wire to be one-dimensional, each one of these atoms must be exactly like any other one, which turns out to be difficult to achieve, since such configuration is usually not the lowest energy one (see Peierls distortion).

Truly one-dimensional or quasi one-dimensional structures can serve as a testing ground for our understanding of the way fundamental physics laws scale with dimensionality of the system. For a long time these questions remained primarily in the domain of elegant theoretical problems, since some of the properties for 1D cases can actually be calculated. With the developments in the materials fabrication and characterization experimentalists also became intrigued by the possibility of actually creating low-dimensional systems. In fact 2D electron gases are used in modern devices already. Experimental observations of 1D behavior proves to be more evasive. However the prospect of seeing such predicted exotic phenomena as Luttinger liquid and charge-spin separation encourages people to keep trying.

Surfaces and specifically stepped surfaces can be used in a couple of ways to create 1D or at least quasi-1D structures. One approach (above image, left) amounts to making nanowires by step decoration or a related process. For clear experimental signatures of 1D behavior these wires preferably should be metallic and "much longer than wider". You can see some results on trying to make such wires on UW-Madison group's MRSEC site. Here I will focus more on the second approach (above image, right) which involves anisotropic surface reconstructions, or essentially self-assembled atomic chains.

Quite a few of surfaces exhibiting such strongly anisotropic reconstructions have been investigated for signs of 1D behavior. There is however a couple of "show-stoppers" that apply in most cases. First is that even on well-prepared surfaces often the 1D structures can be oriented along several equivalent directions thus effectively scrambling measurement results. Stepped surfaces in fact can help in this case, by breaking the symmetry of the surface in a well-defined way. Second problem is that most 1D-candidate structures are inherently unstable with respect to so-called Peierls distortion which usually destroys the required uniformity along the atomic chains. There is really no way around this effect, so one has to look for systems that happen to be stable against it.

The following are two examples of such 1D-candidate reconstructions that we have investigated:

Ca-induced "3x1" on Si(111)
Au-induced "5x1" on Si(111)

Links to Related Topics:
Stepped Silicon Surfaces
Step-induced Single Domain Reconstructions
Peierls distortion
Nanowires by Step Decoration

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